diff --git a/_data/core.yml b/_data/core.yml
index 79b1c671..e5696010 100644
--- a/_data/core.yml
+++ b/_data/core.yml
@@ -1,302 +1,336 @@
 ## Defaults:
 ### - property infix => arity 2
 ### - property prefix => arity 1
-### - property suffix => arity 1(((((
+### - property suffix => arity 1
 ### - property set, number => arity 0
 
 
 defaultfixity:
-   - fixity: function
-     concepts:
-       - concept: curl
-         characters: [∇]
-       - concept: divergence
-         characters: [∇]
-       - concept: gradient
-         characters: [∇]
-       - concept: laplacian
-         characters: [∆]
-
-   - fixity: prefix
-     concepts:
-       - concept: angle
-         characters: [∠]
-       - concept: angle-measure
-         characters: [∡]
-       - concept: change
-         characters: ["Δ"]
-       - concept: for-all
-         characters: [∀]
-       - concept: measured-angle
-         characters: [∡]
-       - concept: minus
-         characters: ["-", "−"]
-       - concept: not
-         characters: [¬]
-       - concept: number-of
-         characters: ["#"]
-       - concept: partial-derivative
-         characters: [∂]
-       - concept: right-angle
-         characters: [∟]
-       - concept: square-root-of
-         characters: [√]
-       - concept: there-does-not-exist
-         characters: [∄]
-       - concept: there-exists
-         characters: [∃]
-
-   - fixity: infix
-     concepts:
-       - concept: and
-         characters: [⁤∧]
-       - concept: applied-to
-         characters: [⁡U+2061]
-       - concept: approximately
-         characters: [≈]
-       - concept: congruent
-         characters: [≅]
-       - concept: cartesian-product
-         characters: [×]
-       - concept: composed-with
-         characters: [∘]
-       - concept: cross-product
-         characters: [×]
-       - concept: defined-as
-         characters: ["≝", "=", "≔"]
-       - concept: dimensional-product
-         characters: [×]
-         link: dimensional-product*infix
-       - concept: divided-by
-         characters: [/, ÷, ":"]
-       - concept: divides
-         characters: ["|", "∣"]
-       - concept: does-not-belong-to
-         characters: [∉]
-       - concept: does-not-divide
-         characters: [∤]
-       - concept: dot-product
-         characters: ["·"]
-       - concept: downwards-diagonal-ellipsis
-         characters: ["⋱"]
-       - concept: direct-product
-         characters: [×]
-       - concept: element-of
-         characters: [∈, ∊]
-       - concept: ellipsis
-         characters: ["…", "⋯"]
-       - concept: equals
-         characters: ["="]
-       - concept: equivalent-to
-         characters: [≡]
-       - concept: evaluates-to
-         characters: ["→"]
-       - concept: given
-         characters: ["|"]
-       - concept: greater-than
-         characters: [">"]
-       - concept: greater-than-or-equal-to
-         characters: [≥, ≧]
-       - concept: identically-equals
-         characters: [≡]
-       - concept: if-and-only-if
-         characters: ["⟺"]
-       - concept: implies
-         characters: [⇒]
-       - concept: inner-product
-         characters: [⋅]
-       - concept: intersection
-         characters: [∩]
-       - concept: less-than
-         characters: ["<"]
-       - concept: less-than-or-equal-to
-         characters: [≤, ≦]
-       - concept: list-separator
-         characters: [",", ";"]
-       - concept: maps-to
-         characters: ["→"]
-       - concept: member-of
-         characters: [∈, ∊]
-       - concept: minus
-         characters: ["-", "−"]
-       - concept: minus-or-plus
-         characters: [∓]
-       - concept: not-subset
-         characters: [⊄]
-       - concept: not-superset
-         characters: [⊅]
-       - concept: not-equal-to
-         characters: [≠]
-       - concept: not-member-of
-         characters: [∉]
-       - concept: not-parallel-to
-         characters: [∦]
-       - concept: obtained-from
-         characters: [←]
-       - concept: or
-         characters: [∨]
-       - concept: outer-product
-         characters: [⊗]
-       - concept: parallel-to
-         characters: [∥]
-       - concept: perpendicular
-         characters: ["⟂"]
-       - concept: plus
-         characters: [+, U+2064]
-       - concept: plus-or-minus
-         characters: [±]
-       - concept: precedes
-         characters: [≺]
-       - concept: proportional
-         characters: [∝, ∷, ∼, ~]
-       - concept: range-separator
-         characters: ["-", "‐", "‑", "–", "—"]
-       - concept: ratio
-         characters: [":", "∶"]
-       - concept: set-difference
-         characters: ["∼", "~", "-", "−", "\\"]
-       - concept: similar
-         characters: [≅]
-       - concept: subset
-         characters: [⊂]
-       - concept: subset-or-equal
-         characters: [⊆]
-       - concept: succeeds
-         characters: [≻]
-       - concept: such-that
-         characters: [":", "|"]
-       - concept: superset
-         characters: [⊃]
-       - concept: superset-or-equal
-         characters: [⊇]
-       - concept: tilde
-         characters: [~]
-       - concept: times
-         characters: ["*", "·", "×", "∗"]
-       - concept: union
-         characters: [∪]
-       - concept: upwards-diagonal-ellipsis
-         characters: ["⋰"]
-       - concept: vertical-ellipsis
-         characters: ["⋮"]
-       - concept: xor
-         characters: [⊕]
-
-   - fixity: postfix
-     concepts:
-       - concept: factorial
-         characters: ["!"]
-       - concept: percent
-         characters: ["%"]
-
-   - fixity: nofix
-     concepts:
-       - concept: diameter
-         characters: ["d"]
-       - concept: distance
-         characters: ["d", "D"]
-       - concept: probability
-         characters: ["P"]
-       - concept: radius
-         characters: ["r"]
-       - concept: volume
-         characters: ["V"]
+  - fixity: function
+    concepts:
+      - concept: curl
+        characters: [∇]
+      - concept: divergence
+        characters: [∇]
+      - concept: gradient
+        characters: [∇]
+      - concept: laplacian
+        characters: [∆]
+
+  - fixity: prefix
+    concepts:
+      - concept: angle
+        characters: [∠]
+      - concept: angle-measure
+        characters: [∡]
+      - concept: change
+        characters: ["Δ"]
+      - concept: for-all
+        characters: [∀]
+      - concept: measured-angle
+        characters: [∡]
+      - concept: minus
+        characters: ["-", "−"]
+      - concept: not
+        characters: [¬]
+      - concept: number-of
+        characters: ["#"]
+      - concept: partial-derivative
+        characters: [∂]
+      - concept: right-angle
+        characters: [∟]
+      - concept: square-root-of
+        characters: [√]
+      - concept: there-does-not-exist
+        characters: [∄]
+      - concept: there-exists
+        characters: [∃]
+
+  - fixity: infix
+    concepts:
+      - concept: and
+        characters: [⁤∧]
+      - concept: applied-to
+        characters: [⁡U+2061]
+      - concept: approximately
+        characters: [≈]
+      - concept: congruent
+        characters: [≅]
+      - concept: cartesian-product
+        characters: [×]
+      - concept: composed-with
+        characters: [∘]
+      - concept: cross-product
+        characters: [×]
+      - concept: defined-as
+        characters: ["≝", "=", "≔"]
+      - concept: dimensional-product
+        characters: [×]
+        link: dimensional-product*infix
+      - concept: divided-by
+        characters: [/, ÷, ":"]
+      - concept: divides
+        characters: ["|", "∣"]
+      - concept: does-not-belong-to
+        characters: [∉]
+      - concept: does-not-divide
+        characters: [∤]
+      - concept: dot-product
+        characters: ["·"]
+      - concept: downwards-diagonal-ellipsis
+        characters: ["⋱"]
+      - concept: direct-product
+        characters: [×]
+      - concept: element-of
+        characters: [∈, ∊]
+      - concept: ellipsis
+        characters: ["…", "⋯"]
+      - concept: equals
+        characters: ["="]
+      - concept: equivalent-to
+        characters: [≡]
+      - concept: evaluates-to
+        characters: ["→"]
+      - concept: given
+        characters: ["|"]
+      - concept: greater-than
+        characters: [">"]
+      - concept: greater-than-or-equal-to
+        characters: [≥, ≧]
+      - concept: identically-equals
+        characters: [≡]
+      - concept: if-and-only-if
+        characters: ["⟺"]
+      - concept: implies
+        characters: [⇒]
+      - concept: inner-product
+        characters: [⋅]
+      - concept: intersection
+        characters: [∩]
+      - concept: less-than
+        characters: ["<"]
+      - concept: less-than-or-equal-to
+        characters: [≤, ≦]
+      - concept: list-separator
+        characters: [",", ";"]
+      - concept: maps-to
+        characters: ["→"]
+      - concept: member-of
+        characters: [∈, ∊]
+      - concept: minus
+        characters: ["-", "−"]
+      - concept: minus-or-plus
+        characters: [∓]
+      - concept: not-subset
+        characters: [⊄]
+      - concept: not-superset
+        characters: [⊅]
+      - concept: not-equal-to
+        characters: [≠]
+      - concept: not-member-of
+        characters: [∉]
+      - concept: not-parallel-to
+        characters: [∦]
+      - concept: obtained-from
+        characters: [←]
+      - concept: or
+        characters: [∨]
+      - concept: outer-product
+        characters: [⊗]
+      - concept: parallel-to
+        characters: [∥]
+      - concept: perpendicular
+        characters: ["⟂"]
+      - concept: plus
+        characters: [+, U+2064]
+      - concept: plus-or-minus
+        characters: [±]
+      - concept: precedes
+        characters: [≺]
+      - concept: proportional
+        characters: [∝, ∷, ∼, ~]
+      - concept: range-separator
+        characters: ["-", "‐", "‑", "–", "—"]
+      - concept: ratio
+        characters: [":", "∶"]
+      - concept: set-difference
+        characters: ["∼", "~", "-", "−", "\\"]
+      - concept: similar
+        characters: [≅]
+      - concept: subset
+        characters: [⊂]
+      - concept: subset-or-equal
+        characters: [⊆]
+      - concept: succeeds
+        characters: [≻]
+      - concept: such-that
+        characters: [":", "|"]
+      - concept: superset
+        characters: [⊃]
+      - concept: superset-or-equal
+        characters: [⊇]
+      - concept: tilde
+        characters: [~]
+      - concept: times
+        characters: ["*", "·", "×", "∗"]
+      - concept: union
+        characters: [∪]
+      - concept: upwards-diagonal-ellipsis
+        characters: ["⋰"]
+      - concept: vertical-ellipsis
+        characters: ["⋮"]
+      - concept: xor
+        characters: [⊕]
+
+  - fixity: postfix
+    concepts:
+      - concept: factorial
+        characters: ["!"]
+      - concept: percent
+        characters: ["%"]
+
+  - fixity: nofix
+    concepts:
+      - concept: diameter
+        characters: ["d"]
+      - concept: distance
+        characters: ["d", "D"]
+      - concept: probability
+        characters: ["P"]
+      - concept: radius
+        characters: ["r"]
+      - concept: volume
+        characters: ["V"]
 
-   - fixity: silent
-     concepts:
-       - concept: invisible-separator
-         characters: [⁣U+2063]
-       - concept: invisible-times
-         characters: [⁢U+2062]
+  - fixity: silent
+    concepts:
+      - concept: invisible-separator
+        characters: [⁣U+2063]
+      - concept: invisible-times
+        characters: [⁢U+2062]
 
 
 concepts:
-
-  ## From chapter 4 of MathML3
-
-  ## - concept: TODO numbers representations
-
+  
   ## ================ 4.4.1 functions and inverses ====================
-  - title: functions and inverses
-    intents:
-    - concept: closed-interval
-      arity: 2
-      property: function
-      en: closed interval between $1 and $2
-      fr: intervalle fermé entre $1 et $2
-
-    - concept: closed-open-interval
-      arity: 2
-      property: function
-      en: interval between $1 (included) and $2
-      fr: intervalle ouvert à droite entre $1 et $2
-
-    - concept: open-closed-interval
-      arity: 2
-      property: function
-      en:  interval between $1 and $2, included
+  
+  - concept: closed-open-interval
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: interval between $a1 (included) and $a2
+      fr: intervalle ouvert à droite entre $a1 et $a2
+  
+  - concept: open-closed-interval
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en:  interval between $a1 and $a2, included
       fr: intervalle ouvert à gauche...
-
-    - concept: open-interval
-      arity: 2
-      property: function
-      en: open interval between $1 and $2
+  
+  - concept: open-interval
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: open interval between $a1 and $a2
       fr: intervalle ouvert
-
-    - concept: inverse
-      arity: 1
-      property: function*
-      en: inverse of $1
-      comments:
+  
+  - concept: closed-interval
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: closed interval between $a1 and $a2
+      fr: intervalle fermé entre $a1 et $a2
+
+  - concept: inverse
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function*
+    speech:
+      en: inverse of $a1
+    comments:
       - "`inverse` can be used for function inverses, matrix inverses, etc."
-
-    - concept: inverse
-      arity: 1
-      property: postfix
-      en: $1 inverse
-
-    - concept: domain
-      arity: 1
-      property: function
-      en: domain of $1
-      fr: domaine de définition de $1
-
-    - concept: codomain
-      arity: 1
-      property: function
-      en: codomain of $1
-      fr: ensemble d'arrivée de $1
-
-    - concept: image
-      arity: 1
-      property: function*
-      en: image of $1
-      fr: image de $1
-
-    - concept: fraction
-      arity: 2
-      property: function
-      en: fraction $1 over $2 end fraction
-
-    - concept: mixed-fraction
-      arity: 2
-      property: function
-      en: $1 and $2
-      comments:
-      - "$1 is a positive integer and $2 is a fraction with positive numerical components.
+  
+  - concept: inverse
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: postfix
+    speech:
+      en: $a1 inverse
+  
+  - concept: domain
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: domain of $a1
+      fr: domaine de définition de $a1
+  
+  - concept: codomain
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: codomain of $a1
+      fr: ensemble d'arrivée de $a1
+  
+  - concept: image
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function*
+    speech:
+      en: image of $a1
+      fr: image de $a1
+  
+  - concept: fraction
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: fraction $a1 over $a2 end fraction
+  
+  - concept: mixed-fraction
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: $a1 and $a2
+    comments:
+      - "$a1 is a positive integer and $a2 is a fraction with positive numerical components.
         The second argument can be an `mfrac` (normal or beveled) or can be a linear fraction using `/`"
-
-    - concept: quotient
-      arity: 2
-      property: function
-      en: integer part of $1 divided by $2
-      fr: quotient de $1 par $2
-
-    - concept: evaluated-at
-      arity: 2
-      property: infix
-      en: $1 evaluated-at $2
-      comments:
+  
+  - concept: quotient
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: integer part of $a1 divided by $a2
+      fr: quotient de $a1 par $a2
+  
+  - concept: evaluated-at
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    speech:
+      en: $a1 evaluated-at $a2
+    comments:
       - "Two common notations are
         <math><mrow><msub><mrow><mrow><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>|</mo></mrow></mrow><mn>3</mn></msub></mrow></math>
         and
@@ -310,173 +344,253 @@ concepts:
           </msub>
         </math>
         "
-    - concept: remainder
-      arity: 2
-      property: function
-      en: the remainder of $1 divided by $2
-      fr: reste de la divsion de $1 par $2
-
-    - concept: max
-      arity: ">=1"
-      property: function
-      en: "max of $1, ..."
-
-    - concept: min
-      arity: ">=1"
-      property: function
-      en: "min of $1, ..."
-
-    - concept: power
-      arity: 2
-      property: infix
-      conditions:
-        - condition: "$2=2"
-          en: "$1 squared"
-          fr: "$1 carré"
-        - condition: "$2=3"
-          en: "$1 cubed"
-          fr: "$1 cube"
-        - condition: ""
-          en: "$1 to the $2<i>th</i> power"
-          fr: "$1 à la $2"
-
-
-    - concept: root
-      arity: 2
-      property: function
-      conditions:
-        - condition: "$2=2"
-          en: "square root of $1"
-        - condition: "$2=3"
-          en: "cube root of $1"
-        - condition: "$2=4"
-          en: "fourth root of $1"
-        - condition: ""
-          en: "$2<i>th</i> root of $1"
-
-    - concept: greatest-common-divisor
-      arity: ">=2"
-      property: function
-      en: greatest common divisor of $1, $2, ...
-      fr: plus grand commun diviseur de $1, $2, ...
-
-    - concept: least-common-multiple
-      arity: ">=2"
-      property: function
-      en: lest common multiple of  $1, $2, ...
-      fr: plus grand commun diviseur de $1, $2, ...
-
-    - concept: absolute-value
-      arity: 1
-      property: function
-      en: absolute value of $1
-      fr: valeur absolue de $1
-      de: Betrag von $1
-
-    - concept: complex-conjugate
-      arity: 1
-      property: function
-      en: complex conjugate of $1
-      fr: $1 conjugé
-
-    - concept: complex-arg
-      arity: 1
-      property: function
-      en: arg of $1
-
-    - concept: real-part
-      arity: 1
-      property: function
+  - concept: remainder
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: the remainder of $a1 divided by $a2
+      fr: reste de la divsion de $a1 par $a2
+  
+  - concept: max
+    subject-area: functions and inverses
+    arity: ">=1"
+    arguments: [$a1, ...]
+    property: function
+    speech:
+      en: "max of $a1, ..."
+  
+  - concept: min
+    subject-area: functions and inverses
+    arity: ">=1"
+    arguments: [$a1, ...]
+    property: function
+    speech:
+      en: "min of $a1, ..."
+  
+  - concept: power
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    conditions:
+      - condition: "$a2=2"
+        speech:
+          en: "$a1 squared"
+          fr: "$a1 carré"
+      - condition: "$a2=3"
+        speech:
+          en: "$a1 cubed"
+          fr: "$a1 cube"
+      - condition: ""
+        speech:
+          en: "$a1 to the $a2<i>th</i> power"
+          fr: "$a1 à la $a2"
+  
+  
+  - concept: root
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    conditions:
+      - condition: "$a2=2"
+        speech:
+          en: "square root of $a1"
+      - condition: "$a2=3"
+        speech:
+          en: "cube root of $a1"
+      - condition: "$a2=4"
+        speech:
+          en: "fourth root of $a1"
+      - condition: ""
+        speech:
+          en: "$a2<i>th</i> root of $a1"
+  
+  - concept: greatest-common-divisor
+    subject-area: functions and inverses
+    arity: ">=2"
+    arguments: [$a1, $a2, ...]
+    property: function
+    speech:
+      en: greatest common divisor of $a1, $a2, ...
+      fr: plus grand commun diviseur de $a1, $a2, ...
+  
+  - concept: least-common-multiple
+    subject-area: functions and inverses
+    arity: ">=2"
+    arguments: [$a1, $a2, ...]
+    property: function
+    speech:
+      en: lest common multiple of  $a1, $a2, ...
+      fr: plus grand commun diviseur de $a1, $a2, ...
+  
+  - concept: least-common-denominator
+    subject-area: functions and inverses
+    arity: ">=2"
+    arguments: [$a1, $a2, ...]
+    property: function
+    speech:
+      en: "least common denominator of $a1, $a2, ..."
+
+  - concept: absolute-value
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: absolute value of $a1
+      fr: valeur absolue de $a1
+      de: Betrag von $a1
+  
+  - concept: complex-conjugate
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: complex conjugate of $a1
+      fr: $a1 conjugé
+  
+  - concept: complex-arg
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: arg of $a1
+  
+  - concept: real-part
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - real part of $1
-      - imaginary part of $1
-      
-    - concept: imaginary-part
-      arity: 1
-      property: function
-      en: imaginary part of $1
-
-    - concept: polar-coordinate
-      arity: 2
-      property: function
-      en: "polar coordinate $1 comma $2"
-      comment:
-      - "The first argument is the radius, the second argument is the polar angle, the third arguments is the azimuthal angle."
-      - "Example: <math><mo>(</mo><mi>r</mi><mo>,</mo><mo>&#xA0;</mo><mi>&#x3B8;</mi><mo>)</mo></math>"
-
-    - concept: spherical-coordinate
-      arity: 3
-      property: function
-      en: "spherical coordinate $1 comma $2, comma $3"
-      comment:
-      - "The first argument is the radius, the second argument is the angle."
-      - "Example: <math><mo>(</mo><mi>r</mi><mo>,</mo><mi>&#x3A6;</mi><mo>,</mo><mi>&#x3B8;</mi><mo>)</mo></math>"
-
-    - concept: cartesian-coordinate
-      arity: ">=2"
-      property: function
-      en: "cartesian coordinate $1 comma $2 ..."
-      comment:
-      - "Example: <math><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math>"
-
-    - concept: coordinate
-      arity: ">=2"
-      property: function
-      en: "coordinate $1 comma $2 ..."
-      comment:
-      - "This a generic coordinate that doesn't specify the coordinate system. It takes 2 or more arguments."
-      - "Example: <math><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math>"
-
-    - concept: floor
-      arity: 1
-      property: function
-      en: floor of $1
-
-    - concept: ceiling
-      arity: 1
-      property: function
-      en: ceiling of $1
-
-    - concept: round
-      arity: 1
-      property: function
-      en: rounded-value of $1
-      comments:
+        - real part of $a1
+        - imaginary part of $a1
+    
+  - concept: imaginary-part
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: imaginary part of $a1
+  
+  - concept: polar-coordinate
+    subject-area: functions and inverses
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: "polar coordinate $a1 comma $a2"
+    comment:
+    - "The first argument is the radius, the second argument is the polar angle, the third arguments is the azimuthal angle."
+    - "Example: <math><mo>(</mo><mi>r</mi><mo>,</mo><mo>&#xA0;</mo><mi>&#x3B8;</mi><mo>)</mo></math>"
+  
+  - concept: spherical-coordinate
+    subject-area: functions and inverses
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    property: function
+    speech:
+      en: "spherical coordinate $a1 comma $a2, comma $a3"
+    comment:
+    - "The first argument is the radius, the second argument is the angle."
+    - "Example: <math><mo>(</mo><mi>r</mi><mo>,</mo><mi>&#x3A6;</mi><mo>,</mo><mi>&#x3B8;</mi><mo>)</mo></math>"
+  
+  - concept: cartesian-coordinate
+    subject-area: functions and inverses
+    arity: ">=2"
+    arguments: [$a1, $a2, ...]
+    property: function
+    speech:
+      en: "cartesian coordinate $a1 comma $a2 ..."
+    comment:
+    - "Example: <math><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math>"
+  
+  - concept: coordinate
+    subject-area: functions and inverses
+    arity: ">=2"
+    arguments: [$a1, $a2, ...]
+    property: function
+    speech:
+      en: "coordinate $a1 comma $a2 ..."
+    comment:
+    - "This a generic coordinate that doesn't specify the coordinate system. It takes 2 or more arguments."
+    - "Example: <math><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math>"
+  
+  - concept: floor
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: floor of $a1
+  
+  - concept: ceiling
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: ceiling of $a1
+  
+  - concept: round
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: rounded-value of $a1
+    comments:
       - "This sometimes uses the notation
         <math><mo>&#x230A;</mo><mi>x</mi><mo>&#x2309;</mo></math>
         or
         <math><mo>[</mo><mi>x</mi><mo>]</mo></math>"
-
-    - concept: fractional-part
-      arity: 1
-      property: function
-      en: fractional part of $1
-
+  
+  - concept: fractional-part
+    subject-area: functions and inverses
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: fractional part of $a1
+  
   ## ====================== 4.4.4 Calculus ============================
-  - title: calculus
-    intents:
-    - concept: definite-integral
-      arity: 1
-      property: ???
-      en: "integral over $1"
-      comments:
+  - concept: definite-integral
+    subject-area: calculus
+    arity: 1
+    arguments: [$a1]
+    property: ???
+    speech:
+      en: "integral over $a1"
+    comments:
       - "integral sign is not an argument"
-
-    - concept: definite-integral
-      arity: 2
-      property: ???
-      en: "integral from $1 to $2"
-      comments:
+  
+  - concept: definite-integral
+    subject-area: calculus
+    arity: 2
+    arguments: [$a1, $a2]
+    property: ???
+    speech:
+      en: "integral from $a1 to $a2"
+    comments:
       - "integral sign is not an argument"
-    
-
-    - concept: derivative
-      arity: 3
-      property: ???
+  
+  
+  - concept: derivative
+    subject-area: calculus
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    property: ???
+    speech:
       en:
-      - "(verbose) the $3 derivative of $1 with respect to $2"
-      - "(terse) d <$3 if $3 != 1> $1 by d $2 <$3 if $3 != 1>"
-      comments:
+        - "(verbose) the $a3 derivative of $a1 with respect to $a2"
+        - "(terse) d <$a3 if $a3 != 1> $a1 by d $a2 <$a3 if $a3 != 1>"
+    comments:
       - "the terse reading only makes sense for Leibniz notation such as 
           <math><mfrac><mrow><msup><mi>d</mi><mn>2</mn></msup><mi>y</mi></mrow><mrow><mi>d</mi><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></math>
           or
@@ -498,14 +612,17 @@ concepts:
             </mrow>
           </mfrac>
           ```
-
-
-    - concept: partial-derivative
-      arity: ">=3"
-      property: ???
+  
+  
+  - concept: partial-derivative
+    subject-area: calculus
+    arity: ">=3"
+    arguments: [$a1, $a2, $a3, ...]
+    property: ???
+    speech:
       en:
-      - "partial <sum $3+2i> $1 partial $2 <$3 if $3 != 1> [partial $4 <$5 if $5 != 1> ...]"
-      comments:
+        - "partial <sum $a3+2i> $a1 partial $a2 <$a3 if $a3 != 1> [partial $a4 <$a5 if $a5 != 1> ...]"
+    comments:
       - |
         ```
         <mfrac intent='partial-derivative($f, x, 2, y, 1)'>
@@ -519,12 +636,15 @@ concepts:
           </mrow>
         </mfrac>
         ```
-
-    - concept: limit
-      arity: 1
-      property: prefix
-      en: "limit as $1"
-      comments:
+  
+  - concept: limit
+    subject-area: calculus
+    arity: 1
+    arguments: [$a1]
+    property: prefix
+    speech:
+      en: "limit as $a1"
+    comments:
       - "limit is not an argument, but intent should be on `msub` or `munder`"
       - "There are several arrows used for limits. "
       - "Example: <math>
@@ -548,39 +668,49 @@ concepts:
       - "Another notation that might be spoken similarly is
         <math><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi></mrow><mrow><mi>x</mi><mo>→</mo><msup><mn>0</mn><mo>-</mo></msup></mrow></munder></math>
         "
-    
-    - concept: tends-to
-      arity: 2
-      property: infix
-      en: "$1 tends to $2"
-      comments:
+  
+  - concept: tends-to
+    subject-area: calculus
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    speech:
+      en: "$a1 tends to $a2"
+    comments:
       - "see \"limit\" example"
-    
-    - concept: tends-to-from-above
-      arity: 2
-      property: infix
-      en: "$1 tends to from above $2"
-      comments:
+  
+  - concept: tends-to-from-above
+    subject-area: calculus
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    speech:
+      en: "$a1 tends to from above $a2"
+    comments:
       - "see \"limit\" example"
-    
-    - concept: tends-to-from-below
-      arity: 2
-      property: infix
-      en: "$1 tends to from below $2"
-      comments:
+  
+  - concept: tends-to-from-below
+    subject-area: calculus
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    speech:
+      en: "$a1 tends to from below $a2"
+    comments:
       - "see \"limit\" example"
-
+  
   ## ====================== 4.4.5 Sets ============================
-  - title: Sets
-    intents:
-    - concept: set
-      arity: 1
-      property: function
-      en: "set of $1"
-      comments:
+  - concept: set
+    subject-area: sets
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "set of $a1"
+    comments:
       - |
                the argument to `set` is typically an `mrow`. For example:
-
+    
                ```
                <math>
                 <mrow intent='set($members)'>
@@ -598,398 +728,532 @@ concepts:
                 </mrow>
                </math>
                ```
-
-    - concept: set-difference
-      arity: 2
-      property: function
-      en: "set difference of $1 and $2"
-      comments:
+  
+  - concept: set-difference
+    subject-area: sets
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: "set difference of $a1 and $a2"
+    comments:
       - "This can be spoken in many ways. See other entry for infix speech."
       - "There are several notations that are used and their order of appearance differs:
         <math><mi>A</mi><mo>-</mo><mi>B</mi></math>, <math><mi>A</mi><mo>\\</mo><mi>B</mi></math>"
-
-    - concept: set-difference
-      arity: 2
-      property: infix
-      en: "\"$1 minus $2\" or \"$2 subtracted from $1\""
-      comments:
+  
+  - concept: set-difference
+    subject-area: sets
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    speech:
+      en: "\"$a1 minus $a2\" or \"$a2 subtracted from $a1\""
+    comments:
       - "This can be spoken in many ways. See other entry for functional speech."
       - "See functional form for some notational usages."
-
-    - concept: complement
-      arity: 1
-      property: function
-      en: "complement of $1"
-      comments:
+  
+  - concept: complement
+    subject-area: sets
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "complement of $a1"
+    comments:
       - "This can be spoken in many ways. See other entry for functional speech."
       - "Two notations used for complement are: 
         <math><msup><mi>A</mi><mi>C</mi></msup></math>, <math><msup><mi>A</mi><mo>'</mo></msup></math>"
-
-    - concept: empty-set
-      arity: 0
+  
+  - concept: empty-set
+    subject-area: sets
+    arity: 0
+    arguments: []
+    speech:
       en: "empty set"
-      comments:
+    comments:
       - "Three notations used for empty set are: { }, ∅, and ∅"
-
-
-    - concept: cardinality
-      arity: 1
-      property: function
-      comments:
+  
+  
+  - concept: cardinality
+    subject-area: sets
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "often used with matchfix single vertical bars"
-
-    - concept: list
-      arity: ">=0"
-      en: "list of $1, ..."
-
-    - concept: tuple
-      arity: ">=0"
-      en: "tuple of $1, ..."
-
-    ## ====================== 4.4.6 sequence and series ============================
-  - title: sequence and series
-    intents:
-    - concept: sum
-      arity: 1
-      property: function
-      en: "sum of $1"
-      comments:
+  
+  - concept: list
+    subject-area: sets
+    arity: ">=0"
+    arguments: [$a1, ...]
+    speech:
+      en: "list of $a1, ..."
+  
+  - concept: tuple
+    subject-area: sets
+    arity: ">=0"
+    arguments: [$a1, ...]
+    speech:
+      en: "tuple of $a1, ..."
+  
+  ## ====================== 4.4.6 sequence and series ============================
+  - concept: sum
+    subject-area: sequences and series
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "sum of $a1"
+    comments:
       - usually on `<mrow>`
-
-    - concept: sum
-      arity: 2
-      property: function
-      en: "sum over $1 of $2"
-      comments:
+  
+  - concept: sum
+    subject-area: sequences and series
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: "sum over $a1 of $a2"
+    comments:
       - usually on `<munder>` or `<msub>`
-
-    - concept: sum
-      arity: 3
-      property: function
-      en: "sum from $1 to $2 of $3"
-      comments:
+  
+  - concept: sum
+    subject-area: sequences and series
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    property: function
+    speech:
+      en: "sum from $a1 to $a2 of $a3"
+    comments:
       - usually on `<munderover>` or `<msubsup>`
-
-    - concept: product
-      arity: 1
-      property: function
-      en: "product of $1"
-      comments:
+  
+  - concept: product
+    subject-area: sequences and series
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "product of $a1"
+    comments:
       - usually on `<mrow>`
-        
-    - concept: product
-      arity: 2
-      property: function
-      en: "product over $1 of $2"
-      comments:
+      
+  - concept: product
+    subject-area: sequences and series
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: "product over $a1 of $a2"
+    comments:
       - usually on `<munder>` or `<msub>`
-
-    - concept: product
-      arity: 3
-      property: function
-      en: "product from $1 to $2 of $3"
-      comments:
+  
+  - concept: product
+    subject-area: sequences and series
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    property: function
+    speech:
+      en: "product from $a1 to $a2 of $a3"
+    comments:
       - usually on `<munderover>` or `<msubsup>`
-
-
-    ## ====================== 4.4.7 elementary classical functions ======================
-  - title: elementary classical functions
-    intents:
-    - concept: sine
-      arity: 1
-      property: function
-      en: "sine $1"
-      fr: "sinus $1"
-      comments:
+  
+  
+  ## ====================== 4.4.7 elementary classical functions ======================
+  - concept: sine
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "sine $a1"
+      fr: "sinus $a1"
+    comments:
       - used as 'sin', 'sen'
-
-    - concept: cosine
-      arity: 1
-      property: function
+  
+  - concept: cosine
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - "(verbose) cosine $1"
-      - "(terse) cos $1"
-
-    - concept: tangent
-      arity: 1
-      property: function
+        - "(verbose) cosine $a1"
+        - "(terse) cos $a1"
+  
+  - concept: tangent
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - "(verbose) tangent $1"
-      - "(terse) tan $1"
-      comments:
+        - "(verbose) tangent $a1"
+        - "(terse) tan $a1"
+    comments:
       - used as 'tan', 'tg'
-
-    - concept: secant
-      arity: 1
-      property: function
+  
+  - concept: secant
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - "(verbose) secant $1"
-      - "(terse) seech $1"
-      comments:
+        - "(verbose) secant $a1"
+        - "(terse) seech $a1"
+    comments:
       - used as 'sec'
-
-    - concept: cosecant
-      arity: 1
-      property: function
+  
+  - concept: cosecant
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - "(verbose) cosecant $1"
-      - "(terse) co-seech $1"
-      comments:
+        - "(verbose) cosecant $a1"
+        - "(terse) co-seech $a1"
+    comments:
       - used as 'csc'
-
-    - concept: cotangent
-      arity: 1
-      property: function
+  
+  - concept: cotangent
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - "(verbose) cotangent $1"
-      - "(terse) co-tan $1"
-      comments:
+        - "(verbose) cotangent $a1"
+        - "(terse) co-tan $a1"
+    comments:
       - used as 'cot'
-
-
-    ## inverse trig functions
-    - concept: arcsine
-      arity: 1
-      property: function
+  
+  
+  ## inverse trig functions
+  - concept: arcsine
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - "(verbose) arcsine $1"
-      comments:
+        - "(verbose) arcsine $a1"
+    comments:
       - "used as 'arcsin', 'arc sin'"
       - "this is distinct from sin inverse (<math><msup><mi>sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>)"
-
-    - concept: arccosine
-      arity: 1
-      property: function
+  
+  - concept: arccosine
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - "(verbose) arccosine $1"
-      comments:
+        - "(verbose) arccosine $a1"
+    comments:
       - "used as 'arccos', 'arc cos'"
-
-    - concept: arctangent
-      arity: 1
-      property: function
+  
+  - concept: arctangent
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - "(verbose) arctangent $1"
-      comments:
+        - "(verbose) arctangent $a1"
+    comments:
       - "used as 'arctan', 'arc tan'"
-
-    - concept: arcsecant
-      arity: 1
-      property: function
+  
+  - concept: arcsecant
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - "(verbose) arcsecant $1"
-      comments:
+        - "(verbose) arcsecant $a1"
+    comments:
       - "used as 'arcsec', 'arc sec'"
-
-    - concept: arccosecant
-      arity: 1
-      property: function
+  
+  - concept: arccosecant
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - "(verbose) arc-cosecant $1"
-      comments:
+        - "(verbose) arc-cosecant $a1"
+    comments:
       - "used as 'arccos', 'arc cos'"
-
-    - concept: arccotangent
-      arity: 1
-      property: function
+  
+  - concept: arccotangent
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-      - "(verbose) arc-cotangent $1"
-      comments:
+        - "(verbose) arc-cotangent $a1"
+    comments:
       - "used as 'arccos', 'arc cos'"
-
-    ## hyperbolic trig functions
-    - concept: hyperbolic-sine
-      arity: 1
-      property: function
-      comments:
+  
+  ## hyperbolic trig functions
+  - concept: hyperbolic-sine
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "<a href='https://www.youtube.com/watch?v=jA-pkiwLVjA'>youtube</a>"
       - "used as 'sinh'"
+    speech:
       en:
-        - "short form 'shine $1'"
+        - "short form 'shine $a1'"
       fr:
-        - "sinus hyperbolique $1"
-
-
-    - concept: hyperbolic-cosine
-      arity: 1
-      property: function
-      comments:
+        - "sinus hyperbolique $a1"
+  
+  
+  - concept: hyperbolic-cosine
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "<a href='https://www.youtube.com/watch?v=jA-pkiwLVjA'>youtube</a>"
       - "used as 'cosh'"
+    speech:
       en:
-        - "short form 'cosh $1'"
+      - "short form 'cosh $a1'"
       fr:
-       - "cosh $1"
-       - "kosh $1"
-
-    - concept: hyperbolic-tangent
-      arity: 1
-      property: function
-      comments:
+       - "cosh $a1"
+       - "kosh $a1"
+  
+  - concept: hyperbolic-tangent
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "<a href='https://www.youtube.com/watch?v=jA-pkiwLVjA'>youtube</a>"
       - "used as 'tanh'"
+    speech:
       en:
-        - "short form American 'tanch $1'"
-        - "short form British 'than $1'"
-
-    - concept: hyperbolic-secant
-      arity: 1
-      property: function
-      comments:
+        - "short form American 'tanch $a1'"
+        - "short form British 'than $a1'"
+  
+  - concept: hyperbolic-secant
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "<a href='https://www.youtube.com/watch?v=jA-pkiwLVjA'>youtube</a>"
       - "used as 'sech'"
+    speech:
       en:
-        - "short form American 'sech $1'"
-        - "short form British 'shek $1'"
-
-    - concept: hyperbolic-cosecant
-      arity: 1
-      property: function
-      comments:
+        - "short form American 'sech $a1'"
+        - "short form British 'shek $a1'"
+  
+  - concept: hyperbolic-cosecant
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "<a href='https://www.youtube.com/watch?v=jA-pkiwLVjA'>youtube</a>"
       - "used as 'cosech'"
+    speech:
       en:
-        - "short form American 'cosech $1'"
-        - "short form British 'coshek $1'"
-
-
-    - concept: hyperbolic-cotangent
-      arity: 1
-      property: function
-      comments:
+        - "short form American 'cosech $a1'"
+        - "short form British 'coshek $a1'"
+  
+  
+  - concept: hyperbolic-cotangent
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "<a href='https://www.youtube.com/watch?v=jA-pkiwLVjA'>youtube</a>"
       - "used as 'coth'"
+    speech:
       en:
-        - "short form American 'coth $1'"
-        - "short form British 'coath $1'"
-
-
-
-    ## inverse hyperbolic trig functions
-    - concept: arc-hyperbolic-sine
-      arity: 1
-      property: function
-      comments:
+        - "short form American 'coth $a1'"
+        - "short form British 'coath $a1'"
+  
+  
+  
+  ## inverse hyperbolic trig functions
+  - concept: arc-hyperbolic-sine
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "used as 'asinh'"
+    speech:
       en:
-        - "short form 'arc shine $1'"
+        - "short form 'arc shine $a1'"
       fr:
-        - "sinus hyperbolique $1"
-
-
-    - concept: arc-hyperbolic-cosine
-      arity: 1
-      property: function
-      comments:
+        - "sinus hyperbolique $a1"
+  
+  
+  - concept: arc-hyperbolic-cosine
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "used as 'acosh'"
+    speech:
       en:
-        - "short form 'arc cosh $1'"
+        - "short form 'arc cosh $a1'"
       fr:
-       - "cosh $1"
-       - "kosh $1"
-
-    - concept: arc-hyperbolic-tangent
-      arity: 1
-      property: function
-      comments:
+        - "cosh $a1"
+        - "kosh $a1"
+  
+  - concept: arc-hyperbolic-tangent
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "used as 'atanh'"
+    speech:
       en:
-        - "short form American 'arc tanch $1'"
-        - "short form British 'arc than $1'"
-
-    - concept: arc-hyperbolic-secant
-      arity: 1
-      property: function
-      comments:
+        - "short form American 'arc tanch $a1'"
+        - "short form British 'arc than $a1'"
+  
+  - concept: arc-hyperbolic-secant
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "used as 'asech'"
+    speech:
       en:
-        - "short form American 'arc sech $1'"
-        - "short form British 'arc shek $1'"
-
-    - concept: arc-hyperbolic-cosecant
-      arity: 1
-      property: function
-      comments:
+        - "short form American 'arc sech $a1'"
+        - "short form British 'arc shek $a1'"
+  
+  - concept: arc-hyperbolic-cosecant
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "used as 'acsch'"
+    speech:
       en:
-        - "short form American 'arc cosech $1'"
-        - "short form British 'arc coshek $1'"
-
-
-    - concept: arc-hyperbolic-cotangent
-      arity: 1
-      property: function
-      comments:
+        - "short form American 'arc cosech $a1'"
+        - "short form British 'arc coshek $a1'"
+  
+  
+  - concept: arc-hyperbolic-cotangent
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "used as 'acoth'"
+    speech:
       en:
-        - "short form American 'arc coth $1'"
-        - "short form British 'arc coath $1'"
-
-
-    ## exponential related functions
-    - concept: exponential
-      arity: 1
-      property: function
+        - "short form American 'arc coth $a1'"
+        - "short form British 'arc coath $a1'"
+  
+  
+  ## exponential related functions
+  - concept: exponential
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-        - "exponential of $1"
-
-    - concept: natural-logarithm
-      arity: 1
-      property: function
+      - "exponential of $a1"
+  
+  - concept: natural-logarithm
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
       en:
-        - "natural log of $1"
-        - "log of $1"
-
-    - concept: logarithm
-      arity: 1
-      property: function
-      en: "log of $1"
-
-    - concept: logarithm
-      arity: 2
-      property: function
-      en: "log base $2 of $1"
-
-
-
-
-    ## ====================== 4.4.8 Statistics ======================
-  - title: Statistics and Probability
-    intents:
-    - concept: mean
-      arity: 1
-      property: function
-      en: "mean of $1"
-      comments:
+      - "natural log of $a1"
+      - "log of $a1"
+  
+  - concept: logarithm
+    subject-area: elementary classical functions
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "log of $a1"
+  
+  - concept: logarithm
+    subject-area: elementary classical functions
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: "log base $a2 of $a1"
+  
+  
+  
+  
+  ## ====================== 4.4.8 Statistics ======================
+  - concept: mean
+    subject-area: Statistics and Probability
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "mean of $a1"
+    comments:
       - "This might be display as <math><mover><mi>x</mi><mo>&#xAF;</mo></mover></math>"
-
-    - concept: standard-deviation
-      arity: 1
-      property: function
-      en: "standard deviation of $1"
-
-    - concept: variance
-      arity: 1
-      property: function
-      en: "variance of $1"
-
-    - concept: median
-      arity: 1
-      property: function
-      en: "median of $1"
-
-    - concept: mode
-      arity: 1
-      property: function
-      en: "mode of $1"
-
-
-
-    - concept: conditional-probability
-      arity: 2
-      property: function
-      en: "probability of $1 given $2"
-      comments:
+  
+  - concept: standard-deviation
+    subject-area: Statistics and Probability
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "standard deviation of $a1"
+  
+  - concept: variance
+    subject-area: Statistics and Probability
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "variance of $a1"
+  
+  - concept: median
+    subject-area: Statistics and Probability
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "median of $a1"
+  
+  - concept: mode
+    subject-area: Statistics and Probability
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "mode of $a1"
+  
+  
+  
+  - concept: conditional-probability
+    subject-area: Statistics and Probability
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: "probability of $a1 given $a2"
+    comments:
       - |
                 The intent should be on the `mrow` that includes the "P"
       
@@ -1007,468 +1271,589 @@ concepts:
                   </mrow>
                  </math>
                  ```
-
-    ## ====================== 4.4.9 Linear Algebra ======================
-  - title: Linear Algebra
-    intents:
-    - concept: vector
-      arity: 1
-      property: function
-
-    - concept: matrix
-      arity: 1
-      property: function
-      comments:
+  
+  ## ====================== 4.4.9 Linear Algebra ======================
+  - concept: vector
+    subject-area: Linear Algebra
+    arity: 1
+    arguments: [$a1]
+    property: function
+  
+  - concept: matrix
+    subject-area: Linear Algebra
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly
-
-    - concept: determinant
-      arity: 1
-      property: function
-      comments:
+  
+  - concept: determinant
+    subject-area: Linear Algebra
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly
-
-    - concept: adjugate
-      arity: 1
-      property: function
-      comments:
+  
+  - concept: adjugate
+    subject-area: Linear Algebra
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "sometimes used when computing an inverse matrix"
-
-    - concept: magnitude
-      arity: 1
-      property: function
-      comments:
+  
+  - concept: magnitude
+    subject-area: Linear Algebra
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "often used with matchfix single or double vertical bars"
-
-    - concept: norm
-      arity: 1
-      property: function
-      comments:
+  
+  - concept: norm
+    subject-area: Linear Algebra
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "often used with matchfix double vertical bars"
-
-    - concept: span
-      arity: 1
-      property: function
-      comments:
+  
+  - concept: span
+    subject-area: Linear Algebra
+    arity: 1
+    arguments: [$a1]
+    property: function
+    comments:
       - "often used with matchfix angle brackets"
-
-    - concept: unit-vector
-      arity: 1
-      property: prefix
-      comments:
+  
+  - concept: unit-vector
+    subject-area: Linear Algebra
+    arity: 1
+    arguments: [$a1]
+    property: prefix
+    comments:
       - "Example: <math><mover><mi>x</mi><mo>^</mo></mover></math>"
+    speech:
       en: "unit vector x"
-
-    - concept: identity-matrix
-      arity: 0
-      comments:
+  
+  - concept: identity-matrix
+    subject-area: Linear Algebra
+    arity: 0
+    arguments: []
+    comments:
       - "This is typically represented as 'I' or bold-faced '𝐈'"
+    speech:
       en: "identity matrix"
-
-    - concept: transpose
-      arity: 1
-      property: postfix
-      en: "$1 transpose"
-      fr: "$1 transposée"
-
-    - concept: transpose
-      arity: 1
-      property: function
-      default: false
-      en: "transpose of $1"
-      fr: "transposée de $1"
-
-    - concept: dimensional-product
-      arity: ">=2"
-      property: infix
-      default: false
-      en: "$1 by $2 ..."
-      comments:
+  
+  - concept: transpose
+    subject-area: Linear Algebra
+    arity: 1
+    arguments: [$a1]
+    property: postfix
+    speech:
+      en: "$a1 transpose"
+      fr: "$a1 transposée"
+  
+  - concept: transpose
+    subject-area: Linear Algebra
+    arity: 1
+    arguments: [$a1]
+    property: function
+    default: false
+    speech:
+      en: "transpose of $a1"
+      fr: "transposée de $a1"
+  
+  - concept: dimensional-product
+    subject-area: Linear Algebra
+    arity: ">=2"
+    arguments: [$a1, $a2, ...]
+    property: infix
+    default: false
+    speech:
+      en: "$a1 by $a2 ..."
+    comments:
       - "This is typically used with the `×` operator and can be placed on that character as a 0-arity concept name.
-                A common use would be describe the size of a matrix. For example <math><mi>m</mi><mo>×</mo><mi>n</mi></math>."
-
-
-    ## ====================== 4.4.10 Constants and Sets ======================
-  - title: Constants and Sets
-    intents:
-      - concept: set-of-integers
-        arity: 0
-        en:
+        A common use would be describe the size of a matrix. For example <math><mi>m</mi><mo>×</mo><mi>n</mi></math>."
+  
+  
+  ## ====================== 4.4.10 Constants and Sets ======================
+  - concept: set-of-integers
+    subject-area: Constants and Sets
+    arity: 0
+    arguments: []
+    speech:
+      en:
         - "(verbose) set of all integers"
         - "(terse) Z"
-        fr: "Z"
-
-      - concept: set-of-reals
-        arity: 0
-        en:
+      fr: "Z"
+  
+  - concept: set-of-reals
+    subject-area: Constants and Sets
+    arity: 0
+    arguments: []
+    speech:
+      en:
         - "(verbose) set of all real numbers"
         - "(terse) R"
-
-      - concept: set-of-rationals
-        arity: 0
-        en:
+  
+  - concept: set-of-rationals
+    subject-area: Constants and Sets
+    arity: 0
+    arguments: []
+    speech:
+      en:
         - "(verbose) set of all rational numbers"
         - "(terse) R"
-
-      - concept: set-of-natural-numbers
-        arity: 0
-        en:
+  
+  - concept: set-of-natural-numbers
+    subject-area: Constants and Sets
+    arity: 0
+    arguments: []
+    speech:
+      en:
         - "(verbose) set of all natural numbers"
         - "(terse) N"
-
-      - concept: set-of-complex-numbers
-        arity: 0
-        en:
+  
+  - concept: set-of-complex-numbers
+    subject-area: Constants and Sets
+    arity: 0
+    arguments: []
+    speech:
+      en:
         - "(verbose) set of all complex numbers"
         - "(terse) C"
-
-      - concept: set-of-primes
-        arity: 0
-        en:
+  
+  - concept: set-of-primes
+    subject-area: Constants and Sets
+    arity: 0
+    arguments: []
+    speech:
+      en:
         - "(verbose) set of all prime numbers"
         - "(terse) P"
-
-      - concept: exponential-e
-        arity: 0
-        en: "e"
-        fr: "e"
-
-      - concept: imaginary-i
-        arity: 0
-        en: "i"
-        fr: "i"
-
-      - concept: differential-d
-        arity: 0
-        en: "d"
-        fr: "d"
-  
-      - concept: golden-ratio
-        arity: 0
-        en: "golden ratio"
-        fr: "d"
-        comments:
-        - "Often denoted as φ"
-
-
-
+  
+  - concept: exponential-e
+    subject-area: Constants and Sets
+    arity: 0
+    arguments: []
+    speech:
+      en: "e"
+      fr: "e"
+  
+  - concept: imaginary-i
+    subject-area: Constants and Sets
+    arity: 0
+    arguments: []
+    speech:
+      en: "i"
+      fr: "i"
+  
+  - concept: differential-d
+    subject-area: Constants and Sets
+    arity: 0
+    arguments: []
+    speech:
+      en: "d"
+      fr: "d"
+  
+  - concept: golden-ratio
+    subject-area: Constants and Sets
+    arity: 0
+    arguments: []
+    speech:
+      en: "golden ratio"
+      fr: "d"
+    comments:
+      - "Often denoted as φ"
+  
+  
+  
   ## other areas =======================================================
-
-  - title: Geometry
-    intents:
-      - concept: line-segment
-        arity: 2
-        property: prefix
-        en:
-        - "line segment $1 $2"
-        comments:
-        - "Example: (`mover`): <math><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>_</mo></mover></math>"
-
-      - concept: directed-line-segment
-        arity: 2
-        property: prefix
-        en:
-        - "directed line segment $1 $2"
-        comments:
-        - "Example: (`mover`): <math><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover></math>"
-
-      - concept: line
-        arity: 2
-        property: prefix
-        en:
-        - "line $1 $2"
-        comments:
-        - "Example: (`mover`): <math><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>↔</mo></mover></math>"
-
-      - concept: ray
-        arity: 2
-        property: prefix
-        en:
-        - "ray $1 $2"
-        comments:
-        - "Example: (`mover`): <math><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover></math>"
-
-      - concept: arc
-        arity: 2
-        property: prefix
-        en:
-        - "arc $1 $2"
-        comments:
-        - "Example: (`mover`): <math><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>⌒</mo></mover></math>"
-
-      - concept: length
-        arity: 1
-        property: function
-        en:
-        - "length of $1"
-        comments:
-        - "It may be necessary to 'nest' the intent as shown here for the example:
-          <math><mrow intent='length(line-segment($start, $end))'>
-                 <mi arg='start' mathvariant='normal'>A</mi>
-                 <mi arg='end' mathvariant='normal'>B</mi>
-              </mrow></math>"
-        - "The markup for this is:"
-        - |
-          ```
-          <mrow intent='length(line-segment($start, $end))'>
-                 <mi arg='start' mathvariant='normal'>A</mi>
-                 <mi arg='end' mathvariant='normal'>B</mi>
-          </mrow>
-          ```
-
-      - concept: area
-        arity: 1
-        property: function
-        en:
-        - "area of $1"
-        comments:
-        - "There are many notations. Here's one: 
-            <math><mrow intent='area($a,$b,$c,$d)'><mo>[</mo><mi arg='a' mathvariant='normal'>A</mi><mi arg='b' mathvariant='normal'>B</mi><mi arg='c' mathvariant='normal'>C</mi><mi arg='d'  mathvariant='normal'>D</mi><mo>]</mo></mrow></math>"
-        - "The markup for this is:"
-        - |
-          ```
-          <mrow intent='area($shape)'>
-              <mo>[</mo>
-              <mrow arg='shape'>
-                  <mi mathvariant='normal'>A</mi>
-                  <mi mathvariant='normal'>B</mi>
-                  <mi mathvariant='normal'>C</mi>
-                  <mi mathvariant='normal'>D</mi>
-                  <mo>]</mo>
-              </mrow>
-          </mrow>
-          ```
-        - "It may be necessary to 'nest' the intent as shown in the `length` intent"
-      - concept: point
-        arity: ">=1"
-        property: ???
-        en:
-        - "point $1 [comma $2 ...]"
-        comment:
-        - "Example: <math><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math>"
-
-      - concept: volume
-        arity: 1
-        property: function
-        en:
-        - "volume of $1"
-        comments:
-        - "See comments for `length` and `volume` for examples of how this might be marked up"
-
-  - title: Fill in the blank
-    intents:
-      - concept: blank
-        arity: 0
-        en:
+  
+  - concept: line-segment
+    subject-area: Geometry
+    arity: 2
+    arguments: [$a1, $a2]
+    property: prefix
+    speech:
+      en:
+        - "line segment $a1 $a2"
+    comments:
+      - "Example: (`mover`): <math><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>_</mo></mover></math>"
+  
+  - concept: directed-line-segment
+    subject-area: Geometry
+    arity: 2
+    arguments: [$a1, $a2]
+    property: prefix
+    speech:
+      en:
+        - "directed line segment $a1 $a2"
+    comments:
+      - "Example: (`mover`): <math><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover></math>"
+  
+  - concept: line
+    subject-area: Geometry
+    arity: 2
+    arguments: [$a1, $a2]
+    property: prefix
+    speech:
+      en:
+        - "line $a1 $a2"
+    comments:
+      - "Example: (`mover`): <math><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>↔</mo></mover></math>"
+  
+  - concept: ray
+    subject-area: Geometry
+    arity: 2
+    arguments: [$a1, $a2]
+    property: prefix
+    speech:
+      en:
+        - "ray $a1 $a2"
+    comments:
+      - "Example: (`mover`): <math><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover></math>"
+  
+  - concept: arc
+    subject-area: Geometry
+    arity: 2
+    arguments: [$a1, $a2]
+    property: prefix
+    speech:
+      en:
+        - "arc $a1 $a2"
+    comments:
+      - "Example: (`mover`): <math><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>⌒</mo></mover></math>"
+  
+  - concept: length
+    subject-area: Geometry
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en:
+        - "length of $a1"
+    comments:
+      - "It may be necessary to 'nest' the intent as shown here for the example:
+        <math><mrow intent='length(line-segment($start, $end))'>
+               <mi arg='start' mathvariant='normal'>A</mi>
+               <mi arg='end' mathvariant='normal'>B</mi>
+            </mrow></math>"
+      - "The markup for this is:"
+      - |
+        ```
+        <mrow intent='length(line-segment($start, $end))'>
+               <mi arg='start' mathvariant='normal'>A</mi>
+               <mi arg='end' mathvariant='normal'>B</mi>
+        </mrow>
+        ```
+  
+  - concept: area
+    subject-area: Geometry
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en:
+        - "area of $a1"
+    comments:
+      - "There are many notations. Here's one: 
+         <math><mrow intent='area($a,$b,$c,$d)'><mo>[</mo><mi arg='a' mathvariant='normal'>A</mi><mi arg='b' mathvariant='normal'>B</mi><mi arg='c' mathvariant='normal'>C</mi><mi arg='d'  mathvariant='normal'>D</mi><mo>]</mo></mrow></math>"
+      - "The markup for this is:"
+      - |
+        ```
+        <mrow intent='area($shape)'>
+            <mo>[</mo>
+            <mrow arg='shape'>
+                <mi mathvariant='normal'>A</mi>
+                <mi mathvariant='normal'>B</mi>
+                <mi mathvariant='normal'>C</mi>
+                <mi mathvariant='normal'>D</mi>
+                <mo>]</mo>
+            </mrow>
+        </mrow>
+        ```
+      - "It may be necessary to 'nest' the intent as shown in the `length` intent"
+
+  - concept: point
+    subject-area: Geometry
+    arity: ">=1"
+    arguments: [$a1, ...]
+    property: ???
+    speech:
+      en:
+        - "point $a1 [comma $a2 ...]"
+    comment:
+    - "Example: <math><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math>"
+  
+  - concept: volume
+    subject-area: Geometry
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en:
+        - "volume of $a1"
+    comments:
+      - "See comments for `length` and `volume` for examples of how this might be marked up"
+  
+  - concept: blank
+    subject-area: Fill in the blank
+    arity: 0
+    arguments: []
+    speech:
+      en:
         - "blank"
-        comments:
-        - "blanks can be represented in many ways in MathML. Some examples:"
-        - "`<mi intent='blank'>__</mi>`"
-        - "`<mi intent='blank'>?</mi>`"
-        - "`<mo intent='blank'>□</mo>`"
-        - "`<mspace intent='blank' width='3em'/>`"
-        - "`<menclose intent='blank' notation='box'>`<br/> `<mspace width='3em'/>`<br/> `</menclose>`"
-
-  - title: Separators
-    intents:
-      - concept: time-separator
-        arity: 2
-        property: infix
-        en: $1 $2
-        comments:
-        - "separates hours and minutes and is typically silent"
-        - "Example: 2:31"
-
-
-  - title: General Concepts
-    intents:
-      - concept: fenced-group
-        arity: 1
-        property: function
-        en: "fenced-group of $1"
-        comments:
-        - "this includes parens, brackets, and braces"
-
-      - concept: ordered-pair
-        arity: 2
-        property: function
-        en: "the pair $1 and $2"
-      
-      - concept: indexed-by
-        arity: 2
-        property: infix
-        en: "$1 indexed by $2"
-        comments:
-        - "this is typically a subscript and might also be spoken as '$1 sub $2'"
-
-      - concept: highlight
-        arity: 1
-        property: postfix
-        en: "$1 highlighted"
-        comments:
-        - "this typically would be used inside of a larger expression and not on its own"
-        - "this might be used with `<menclose notation='box'>` or similar. It might also be used with color changes, although may be done with CSS"
-
-      - concept: least-common-denominator
-        arity: ">=2"
-        property: function
-        en: "least common denominator of $1, $2, ..."
-
-      - concept: rate
-        arity: 2
-        property: infix
-        en: "$1 per $2"
-        comments:
-        - "Typically used with units"
-        - "Used with `mfrac` or `/`"
-
-      - concept: translation
-        arity: 2
-        property: function
-        en: "translation by $1 comma $2"
-        comments:
-        - "Example: <math><msub><mi>T</mi><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></msub></math>"
-        
-      - concept: constraint
-        arity: 2
-        property: infix
-        en: "fraction 2 over x minus 1 with constraint x not equal to 1"
-        comments:
-        - "Example: <math><mfrac><mn>2</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>,</mo><mo>&#xA0;</mo><mi>x</mi><mo>&#x2260;</mo><mn>1</mn></math>"
-        
-      - concept: binomial-coefficient
-        arity: 2
-        property: infix
-        en: "$1 choose $2"
-        comments:
-        - "There are many notations used for the binomial coefficient. Here are some of them: 
-          <math><mrow intent='binomial-coefficent($power, $term)'>
-            <mo>(</mo>
-            <mfrac linethickness='0'>
-                <mi arg='power'>n</mi>
-                <mi arg='term'>k</mi>
-            </mfrac>
-            <mo>)</mo>
-          </mrow></math>, 
-          <math>
-            <msubsup intent='binomial-coefficent($power, $term>)'>
-              <mi>C</mi>
-              <mi arg='term'>k</mi>
-              <mi arg='power'>n</mi>
-            </msubsup>
-          </math>, 
-          <math>
-            <mmultiscripts intent='binomial-coefficent($power, $term)'>
-              <mi>C</mi>
-              <mi arg='term'>k</mi> <none/>
-              <mprescripts/>
-              <mi arg='power'>n</mi> <none/>
-            </mmultiscripts>
-          </math>"
-
-      - concept: pochhammer
-        arity: 2
-        property: function
-        en: "$2 permutation of $1"
-        comments:
-        - "There are many notations for this: some of them are 
-            <math>
-              <msubsup><mi>P</mi><mi>k</mi><mi>n</mi></msubsup>
-              <mo>,</mo><mo>&#xA0;</mo>
-              <mmultiscripts><mi>P</mi><mi>k</mi><none/><mprescripts/><mi>n</mi><none/></mmultiscripts>
-              <mo>,</mo><mo>&#xA0;</mo>
-              <mmultiscripts><mi>P</mi><mi>k</mi><none/><mprescripts/><none/><mi>n</mi></mmultiscripts>
-              <mo>,</mo><mo>&#xA0;</mo>
-              <msub><mi>P</mi><mrow><mi>n</mi><mo>,</mo><mi>k</mi></mrow></msub>
-              <mo>,</mo><mo>&#xA0;</mo>
-              <mi>P</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)
-              </mo><mo>,</mo><mo>&#xA0;</mo>
-              <msup><mi>n</mi><menclose notation='bottom'><mi>k</mi></menclose></msup>
-          </math>"
-        - "The first of these would be marked up as:"
-        - |
-          ```
-          <msubsup intent='pochhammer($n, $k)'>
-              <mi>P</mi>
-              <mi arg='k'>k</mi>
-              <mi arg='n'>n</mi>
-          </msubsup>
-          ```
-
-      - concept: permutation-cycle
-        arity: ">=2"
-        property: function
-        en: "permutation cycle of $1 $2 ..."
-        comments:
-        - "A common notation for a permutation cycle is <math><mo>(</mo>
-                <mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable>
-                <mo>)</mo></math>"
-        - "This would be marked up as:"
-        - |
-          ```
-          <mrow intent='permutation-cycle($arg1, $arg2, $arg3)'
+    comments:
+      - "blanks can be represented in many ways in MathML. Some examples:"
+      - "`<mi intent='blank'>__</mi>`"
+      - "`<mi intent='blank'>?</mi>`"
+      - "`<mo intent='blank'>□</mo>`"
+      - "`<mspace intent='blank' width='3em'/>`"
+      - "`<menclose intent='blank' notation='box'>`<br/> `<mspace width='3em'/>`<br/> `</menclose>`"
+  
+  - concept: time-separator
+    subject-area: Separators
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    speech:
+      en: $a1 $a2
+    comments:
+      - "separates hours and minutes and is typically silent"
+      - "Example: 2:31"
+  
+  
+  - concept: fenced-group
+    subject-area: General Concepts
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "fenced-group of $a1"
+    comments:
+      - "this includes parens, brackets, and braces"
+  
+  - concept: ordered-pair
+    subject-area: General Concepts
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: "the pair $a1 and $a2"
+  
+  - concept: indexed-by
+    subject-area: General Concepts
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    speech:
+      en: "$a1 indexed by $a2"
+    comments:
+      - "this is typically a subscript and might also be spoken as '$a1 sub $a2'"
+  
+  - concept: highlight
+    subject-area: General Concepts
+    arity: 1
+    arguments: [$a1]
+    property: postfix
+    speech:
+      en: "$a1 highlighted"
+    comments:
+      - "this typically would be used inside of a larger expression and not on its own"
+      - "this might be used with `<menclose notation='box'>` or similar. It might also be used with color changes, although may be done with CSS"
+  
+  
+  - concept: rate
+    subject-area: General Concepts
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    speech:
+      en: "$a1 per $a2"
+    comments:
+      - "Typically used with units"
+      - "Used with `mfrac` or `/`"
+  
+  - concept: translation
+    subject-area: General Concepts
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: "translation by $a1 comma $a2"
+    comments:
+      - "Example: <math><msub><mi>T</mi><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></msub></math>"
+    
+  - concept: constraint
+    subject-area: General Concepts
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    speech:
+      en: "fraction 2 over x minus 1 with constraint x not equal to 1"
+    comments:
+      - "Example: <math><mfrac><mn>2</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>,</mo><mo>&#xA0;</mo><mi>x</mi><mo>&#x2260;</mo><mn>1</mn></math>"
+    
+  - concept: binomial-coefficient
+    subject-area: General Concepts
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    speech:
+      en: "$a1 choose $a2"
+    comments:
+      - "There are many notations used for the binomial coefficient. Here are some of them: 
+        <math><mrow intent='binomial-coefficent($power, $term)'>
           <mo>(</mo>
-            <mtable><mtr>
-               <mtd><mn arg='arg1'>1</mn></mtd>
-               <mtd><mn arg='arg2'>3</mn></mtd>
-               <mtd><mn arg='arg3'>2</mn></mtd>
-            </mtr></mtable>
+          <mfrac linethickness='0'>
+              <mi arg='power'>n</mi>
+              <mi arg='term'>k</mi>
+          </mfrac>
           <mo>)</mo>
-          ```
-
-      - concept: embellished-name
-        arity: 2
-        property: infix
-        en: "$1 with annotation $2"
-        comments:
-        - "used with `mover` or `munder`"
- 
+        </mrow></math>, 
+        <math>
+          <msubsup intent='binomial-coefficent($power, $term>)'>
+            <mi>C</mi>
+            <mi arg='term'>k</mi>
+            <mi arg='power'>n</mi>
+          </msubsup>
+        </math>, 
+        <math>
+          <mmultiscripts intent='binomial-coefficent($power, $term)'>
+            <mi>C</mi>
+            <mi arg='term'>k</mi> <none/>
+            <mprescripts/>
+            <mi arg='power'>n</mi> <none/>
+          </mmultiscripts>
+        </math>"
+  
+  - concept: pochhammer
+    subject-area: General Concepts
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: "$a2 permutation of $a1"
+    comments:
+      - "There are many notations for this: some of them are 
+          <math>
+            <msubsup><mi>P</mi><mi>k</mi><mi>n</mi></msubsup>
+            <mo>,</mo><mo>&#xA0;</mo>
+            <mmultiscripts><mi>P</mi><mi>k</mi><none/><mprescripts/><mi>n</mi><none/></mmultiscripts>
+            <mo>,</mo><mo>&#xA0;</mo>
+            <mmultiscripts><mi>P</mi><mi>k</mi><none/><mprescripts/><none/><mi>n</mi></mmultiscripts>
+            <mo>,</mo><mo>&#xA0;</mo>
+            <msub><mi>P</mi><mrow><mi>n</mi><mo>,</mo><mi>k</mi></mrow></msub>
+            <mo>,</mo><mo>&#xA0;</mo>
+            <mi>P</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)
+            </mo><mo>,</mo><mo>&#xA0;</mo>
+            <msup><mi>n</mi><menclose notation='bottom'><mi>k</mi></menclose></msup>
+        </math>"
+      - "The first of these would be marked up as:"
+      - |
+        ```
+        <msubsup intent='pochhammer($n, $k)'>
+            <mi>P</mi>
+            <mi arg='k'>k</mi>
+            <mi arg='n'>n</mi>
+        </msubsup>
+        ```
+  
+  - concept: permutation-cycle
+    subject-area: General Concepts
+    arity: ">=2"
+    arguments: [$a1, $a2, ...]
+    property: function
+    speech:
+      en: "permutation cycle of $a1 $a2 ..."
+    comments:
+      - "A common notation for a permutation cycle is <math><mo>(</mo>
+              <mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable>
+              <mo>)</mo></math>"
+      - "This would be marked up as:"
+      - |
+        ```
+        <mrow intent='permutation-cycle($arg1, $arg2, $arg3)'
+        <mo>(</mo>
+          <mtable><mtr>
+             <mtd><mn arg='arg1'>1</mn></mtd>
+             <mtd><mn arg='arg2'>3</mn></mtd>
+             <mtd><mn arg='arg3'>2</mn></mtd>
+          </mtr></mtable>
+        <mo>)</mo>
+        ```
+  
+  - concept: embellished-name
+    subject-area: General Concepts
+    arity: 2
+    arguments: [$a1, $a2]
+    property: infix
+    speech:
+      en: "$a1 with annotation $a2"
+    comments:
+      - "used with `mover` or `munder`"
    
-  - title: Grouping
-    intents:
-      - concept: fenced-group
-        arity: 1
-        property: function
-        en: "fenced-group of $1"
-        comments:
-        - "this includes parens, brackets, and braces"
-
-      - concept: annotation
-        arity: 2
-        property: function
-        en: "$1 which is $2"
-        comments:
-        - "used with `mover` or `munder`"
-        - "Example: <math><munder><munder><mrow><msub><mi mathvariant='normal'>H</mi><mn>2</mn></msub><mi mathvariant='normal'>O</mi></mrow><mo>&#x23DF;</mo></munder><mtext>water</mtext></munder></math>"
-
-      - concept: braced-group
-        arity: 1
-        property: function
-        en: "grouped $1 end-grouped"
-        comments:
-        - "used with `mover` or `munder`"
-        - "Example: <math><munder><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mrow><mo>&#x23DF;</mo></munder></math>"
+     
+  - concept: fenced-group
+    subject-area: Grouping
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "fenced-group of $a1"
+    comments:
+      - "this includes parens, brackets, and braces"
+  
+  - concept: annotation
+    subject-area: Grouping
+    arity: 2
+    arguments: [$a1, $a2]
+    property: function
+    speech:
+      en: "$a1 which is $a2"
+    comments:
+      - "used with `mover` or `munder`"
+      - "Example: <math><munder><munder><mrow><msub><mi mathvariant='normal'>H</mi><mn>2</mn></msub><mi mathvariant='normal'>O</mi></mrow><mo>&#x23DF;</mo></munder><mtext>water</mtext></munder></math>"
+  
+  - concept: braced-group
+    subject-area: Grouping
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "grouped $a1 end-grouped"
+    comments:
+      - "used with `mover` or `munder`"
+      - "Example: <math><munder><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mrow><mo>&#x23DF;</mo></munder></math>"
+  
+  - concept: repeating-decimal
+    subject-area: Grouping
+    arity: 1
+    arguments: [$a1]
+    property: function
+    speech:
+      en: "repeating decimal $a1"
+    comments:
+      - "typically used in when there is a bar over the repeating part of a decimal or dots over the first and last digits."
+      - "Example: <math><mfrac><mn>1</mn><mn>22</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>0</mn><mover><mn>45</mn><mo>_</mo></mover></math>"
+      - "This right hand side of this might be might be marked up as:"
+      - |
+        ```
+        <mn>0.0</mn>
+        <mover intent='repeating-decimal($repeat)'>
+            <mn arg='repeat'>45</mn>
+            <mo>_</mo>
+        </mover>
+        ```
+      - "or using the elementary math elements in MathML full as"
+      - |
+        ```
+        <mstack intent='_(0.0, repeating-decimal(45)'>
+          <msline length="2"/>
+          <mn>0.045</mn>
+        </mstack>
+        ```
 
-      - concept: repeating-decimal
-        arity: 1
-        property: function
-        en: "repeating decimal $1"
-        comments:
-        - "typically used in when there is a bar over the repeating part of a decimal or dots over the first and last digits."
-        - "Example: <math><mfrac><mn>1</mn><mn>22</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>0</mn><mover><mn>45</mn><mo>_</mo></mover></math>"
-        - "This right hand side of this might be might be marked up as:"
-        - |
-          ```
-          <mn>0.0</mn>
-          <mover intent='repeating-decimal($repeat)'>
-              <mn arg='repeat'>45</mn>
-              <mo>_</mo>
-          </mover>
-          ```
-        - "or using the elementary math elements in MathML full as"
-        - |
-          ```
-          <mstack intent='_(0.0, repeating-decimal(45)'>
-            <msline length="2"/>
-            <mn>0.045</mn>
-          </mstack>
-          ```
diff --git a/_data/open.yml b/_data/open.yml
index 59e7e620..b9eced09 100644
--- a/_data/open.yml
+++ b/_data/open.yml
@@ -1,12744 +1,14759 @@
 
 concepts:
 
-  - title: Open Concepts
-    intents:
-  
-    - concept: abelian-category
-      arity: 0
+
+  - concept: abelian-category
+    arity: 0
+    arguments: []
+    speech:
       en: abelian category
-      property: symbol
-      area: "category theory"
-      mathml:
-       - "<math><mi intent='abelian-category'>Ab</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AbelianCategory.html"
-       - "https://en.wikipedia.org/wiki/Abelian_category"
-       - "https://ncatlab.org/nlab/show/abelian+category"
-       - "https://www.encyclopediaofmath.org/index.php/Abelian_category"
-    
-    - concept: abelian-integral
-      arity: 1
-      en: abelian integral of $1
-      property: indexed
-      area: "complex analysis"
-      mathml:
-       - "<math><mrow intent='abelian-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AbelianIntegral.html"
-       - "https://en.wikipedia.org/wiki/Abelian_integral"
-       - "https://www.encyclopediaofmath.org/index.php/Abelian_integral"
-    
-    - concept: abundance
-      arity: 1
-      en: abundance of $1
-      property: prefix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='abundance($a1)'><mi>A</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Abundance.html"
-    
-    - concept: abundancy
-      arity: 1
-      en: abundancy index  of $1
-      property: mixfix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='abundancy($a1)'><mi>σ</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>)</mo></mrow><mo>/</mo><mi>n</mi></mrow></math>"
-      notation: "sigma (n) / n"
-      urls: 
-       - "https://mathworld.wolfram.com/Abundancy.html"
-       - "https://en.wikipedia.org/wiki/Friendly_number"
-    
-    - concept: ackermann-function
-      arity: 1
-      en: ackermann function of $1
-      property: function
-      area: "computability theory"
-      mathml:
-       - "<math><mrow intent='ackermann-function($a1)'><mi>A</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Ackermann_function"
-       - "https://www.encyclopediaofmath.org/index.php/Ackermann_function"
-       - "https://mathworld.wolfram.com/AckermannFunction.html"
-    
-    - concept: ad
-      arity: 1
-      en: a d $1
-      property: postfix. prefix
-      area: "calendar units"
-      mathml:
-       - "<math><mrow intent='ad($a1)'><mi>AD</mi><mo>&#x2009;</mo><mn arg='a1'>2024</mn></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Anno_Domini"
-    
-    - concept: additive-inverse
-      arity: 1
-      en: additive inverse of $1
-      property: prefix
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='additive-inverse($a1)'><mo>-</mo><mi arg='a1'>n</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Additive_inverse"
-      alias:
-       - opposite
-       - sign-change
-       - negation
-    
-    - concept: adiabatic-invariant-first
-      arity: 0
+    property: symbol
+    subject-area: "category theory"
+    mathml:
+     - "<math><mi intent='abelian-category'>Ab</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AbelianCategory.html"
+     - "https://en.wikipedia.org/wiki/Abelian_category"
+     - "https://ncatlab.org/nlab/show/abelian+category"
+     - "https://www.encyclopediaofmath.org/index.php/Abelian_category"
+  
+  - concept: abelian-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: abelian integral of $a1
+    property: indexed
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mrow intent='abelian-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AbelianIntegral.html"
+     - "https://en.wikipedia.org/wiki/Abelian_integral"
+     - "https://www.encyclopediaofmath.org/index.php/Abelian_integral"
+  
+  - concept: abundance
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: abundance of $a1
+    property: prefix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='abundance($a1)'><mi>A</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Abundance.html"
+  
+  - concept: abundancy
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: abundancy index  of $a1
+    property: mixfix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='abundancy($a1)'><mi>σ</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>)</mo></mrow><mo>/</mo><mi>n</mi></mrow></math>"
+    notation: "sigma (n) / n"
+    urls: 
+     - "https://mathworld.wolfram.com/Abundancy.html"
+     - "https://en.wikipedia.org/wiki/Friendly_number"
+  
+  - concept: ackermann-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: ackermann function of $a1
+    property: function
+    subject-area: "computability theory"
+    mathml:
+     - "<math><mrow intent='ackermann-function($a1)'><mi>A</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Ackermann_function"
+     - "https://www.encyclopediaofmath.org/index.php/Ackermann_function"
+     - "https://mathworld.wolfram.com/AckermannFunction.html"
+  
+  - concept: ad
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: a d $a1
+    property: postfix. prefix
+    subject-area: "calendar units"
+    mathml:
+     - "<math><mrow intent='ad($a1)'><mi>AD</mi><mo>&#x2009;</mo><mn arg='a1'>2024</mn></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Anno_Domini"
+  
+  - concept: additive-inverse
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: additive inverse of $a1
+    property: prefix
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='additive-inverse($a1)'><mo>-</mo><mi arg='a1'>n</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Additive_inverse"
+    alias:
+     - opposite
+     - sign-change
+     - negation
+  
+  - concept: adiabatic-invariant-first
+    arity: 0
+    arguments: []
+    speech:
       en: adiabatic invariant first
-      property: symbol
-      area: "plasma physics"
-      mathml:
-       - "<math><mi intent='adiabatic-invariant-first'>μ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AdiabaticInvariant.html"
-       - "https://en.wikipedia.org/wiki/Adiabatic_invariant"
-       - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant"
-    
-    - concept: adiabatic-invariant-second
-      arity: 0
+    property: symbol
+    subject-area: "plasma physics"
+    mathml:
+     - "<math><mi intent='adiabatic-invariant-first'>μ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AdiabaticInvariant.html"
+     - "https://en.wikipedia.org/wiki/Adiabatic_invariant"
+     - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant"
+  
+  - concept: adiabatic-invariant-second
+    arity: 0
+    arguments: []
+    speech:
       en: adiabatic invariant second
-      property: symbol
-      area: "plasma physics"
-      mathml:
-       - "<math><mi intent='adiabatic-invariant-second'>J</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AdiabaticInvariant.html"
-       - "https://en.wikipedia.org/wiki/Adiabatic_invariant"
-       - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant"
-    
-    - concept: adiabatic-invariant-third
-      arity: 0
+    property: symbol
+    subject-area: "plasma physics"
+    mathml:
+     - "<math><mi intent='adiabatic-invariant-second'>J</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AdiabaticInvariant.html"
+     - "https://en.wikipedia.org/wiki/Adiabatic_invariant"
+     - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant"
+  
+  - concept: adiabatic-invariant-third
+    arity: 0
+    arguments: []
+    speech:
       en: adiabatic invariant third
-      property: symbol
-      area: "plasma physics"
-      mathml:
-       - "<math><mi intent='adiabatic-invariant-third'>Φ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AdiabaticInvariant.html"
-       - "https://en.wikipedia.org/wiki/Adiabatic_invariant"
-       - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant"
-    
-    - concept: adjoint
-      arity: 1
-      en: adjoint of $1
-      property: 
-      area: 
-      mathml:
-       - "<math><mrow intent='adjoint($a1)'><msup><mi arg='a1'>G</mi><mo>′</mo></msup></mrow></math>"
-       - "<math><mrow intent='adjoint($a1)'><msup><mi arg='a1'>G</mi><mo>†</mo></msup></mrow></math>"
-       - "<math><mrow intent='adjoint($a1)'><msub><mi>Ad</mi><mi arg='a1'>g</mi></msub></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Adjoint.html"
-       - "https://en.wikipedia.org/wiki/Adjoint"
-       - "https://ncatlab.org/nlab/show/adjoint"
-    
-    - concept: adjoint-action
-      arity: 1
-      en: adjoint action of $1
-      property: "function/msub"
-      area: "lie algebra"
-      mathml:
-       - "<math><mrow intent='adjoint-action($a1)'><mi>ad</mi><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><msub intent='adjoint-action($a1)'><mi>ad</mi><mi arg='a1'>f</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Adjoint_representation_of_a_Lie_algebra"
-       - "https://en.wikipedia.org/wiki/Adjoint_representation"
-       - "https://ncatlab.org/nlab/show/adjoint+action"
-       - "https://www.encyclopediaofmath.org/index.php/Adjoint_action"
-      alias:
-       - adjoint-endomorphism
-    
-    - concept: adjoint-representation
-      arity: 1
-      en: adjoint representation of $1
-      property: function
-      area: "lie algebra"
-      mathml:
-       - "<math><mrow intent='adjoint-representation($a1)'><mi>Ad</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AdjointRepresentation.html"
-       - "https://en.wikipedia.org/wiki/Adjoint_representation"
-       - "https://ncatlab.org/nlab/show/adjoint+representation"
-    
-    - concept: adjugate
-      arity: 1
-      en: adjugate of $1
-      property: function
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='adjugate($a1)'><mi>adj</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Adjugate_matrix"
-    
-    - concept: affine-group
-      arity: 1
-      en: affine group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='affine-group($a1)'><mi>Aff</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AffineGroup.html"
-       - "https://en.wikipedia.org/wiki/Affine_group"
-       - "https://www.encyclopediaofmath.org/index.php/Affine_group"
-    
-    - concept: affine-hull
-      arity: 1
-      en: affine hull of $1
-      property: function
-      area: "affine geometry"
-      mathml:
-       - "<math><mrow intent='affine-hull($a1)'><mi>aff</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AffineHull.html"
-       - "https://en.wikipedia.org/wiki/Affine_hull"
-       - "https://www.encyclopediaofmath.org/index.php/Affine_hull"
-    
-    - concept: affine-line
-      arity: 0
+    property: symbol
+    subject-area: "plasma physics"
+    mathml:
+     - "<math><mi intent='adiabatic-invariant-third'>Φ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AdiabaticInvariant.html"
+     - "https://en.wikipedia.org/wiki/Adiabatic_invariant"
+     - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant"
+  
+  - concept: adjoint
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: adjoint of $a1
+    property: 
+    subject-area: 
+    mathml:
+     - "<math><mrow intent='adjoint($a1)'><msup><mi arg='a1'>G</mi><mo>′</mo></msup></mrow></math>"
+     - "<math><mrow intent='adjoint($a1)'><msup><mi arg='a1'>G</mi><mo>†</mo></msup></mrow></math>"
+     - "<math><mrow intent='adjoint($a1)'><msub><mi>Ad</mi><mi arg='a1'>g</mi></msub></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Adjoint.html"
+     - "https://en.wikipedia.org/wiki/Adjoint"
+     - "https://ncatlab.org/nlab/show/adjoint"
+  
+  - concept: adjoint-action
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: adjoint action of $a1
+    property: "function/msub"
+    subject-area: "lie algebra"
+    mathml:
+     - "<math><mrow intent='adjoint-action($a1)'><mi>ad</mi><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><msub intent='adjoint-action($a1)'><mi>ad</mi><mi arg='a1'>f</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Adjoint_representation_of_a_Lie_algebra"
+     - "https://en.wikipedia.org/wiki/Adjoint_representation"
+     - "https://ncatlab.org/nlab/show/adjoint+action"
+     - "https://www.encyclopediaofmath.org/index.php/Adjoint_action"
+    alias:
+     - adjoint-endomorphism
+  
+  - concept: adjoint-representation
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: adjoint representation of $a1
+    property: function
+    subject-area: "lie algebra"
+    mathml:
+     - "<math><mrow intent='adjoint-representation($a1)'><mi>Ad</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AdjointRepresentation.html"
+     - "https://en.wikipedia.org/wiki/Adjoint_representation"
+     - "https://ncatlab.org/nlab/show/adjoint+representation"
+  
+  - concept: adjugate
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: adjugate of $a1
+    property: function
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='adjugate($a1)'><mi>adj</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Adjugate_matrix"
+  
+  - concept: affine-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: affine group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='affine-group($a1)'><mi>Aff</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AffineGroup.html"
+     - "https://en.wikipedia.org/wiki/Affine_group"
+     - "https://www.encyclopediaofmath.org/index.php/Affine_group"
+  
+  - concept: affine-hull
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: affine hull of $a1
+    property: function
+    subject-area: "affine geometry"
+    mathml:
+     - "<math><mrow intent='affine-hull($a1)'><mi>aff</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AffineHull.html"
+     - "https://en.wikipedia.org/wiki/Affine_hull"
+     - "https://www.encyclopediaofmath.org/index.php/Affine_hull"
+  
+  - concept: affine-line
+    arity: 0
+    arguments: []
+    speech:
       en: affine line
-      property: symbol
-      area: "universal algebra?"
-      mathml:
-       - "<math><mi intent='affine-line'>𝔸</mi></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/affine+line"
-    
-    - concept: airy-function
-      arity: 1
-      en: airy function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='airy-function($a1)'><mi>Ai</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='airy-function($a1)'><mi>Bi</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AiryFunctions.html"
-       - "https://en.wikipedia.org/wiki/Airy_function"
-       - "https://dlmf.nist.gov/9.1"
-       - "https://dlmf.nist.gov/9.2#i"
-       - "https://dlmf.nist.gov/9.2#i"
-       - "https://ncatlab.org/nlab/show/Airy+function"
-       - "https://www.encyclopediaofmath.org/index.php/Airy_functions"
-    
-    - concept: albanese-variety
-      arity: 1
-      en: albanese variety of $1
-      property: function
-      area: "algebraic geometry"
-      mathml:
-       - "<math><mrow intent='albanese-variety($a1)'><mi>A</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='albanese-variety($a1)'><mi>Alb</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AlbaneseVariety.html"
-       - "https://en.wikipedia.org/wiki/Albanese_variety"
-       - "https://ncatlab.org/nlab/show/Albanese+variety"
-       - "https://www.encyclopediaofmath.org/index.php/Albanese_variety"
-    
-    - concept: aleph
-      arity: 0
+    property: symbol
+    subject-area: "universal algebra?"
+    mathml:
+     - "<math><mi intent='affine-line'>𝔸</mi></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/affine+line"
+  
+  - concept: airy-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: airy function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='airy-function($a1)'><mi>Ai</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='airy-function($a1)'><mi>Bi</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AiryFunctions.html"
+     - "https://en.wikipedia.org/wiki/Airy_function"
+     - "https://dlmf.nist.gov/9.1"
+     - "https://dlmf.nist.gov/9.2#i"
+     - "https://dlmf.nist.gov/9.2#i"
+     - "https://ncatlab.org/nlab/show/Airy+function"
+     - "https://www.encyclopediaofmath.org/index.php/Airy_functions"
+  
+  - concept: albanese-variety
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: albanese variety of $a1
+    property: function
+    subject-area: "algebraic geometry"
+    mathml:
+     - "<math><mrow intent='albanese-variety($a1)'><mi>A</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='albanese-variety($a1)'><mi>Alb</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AlbaneseVariety.html"
+     - "https://en.wikipedia.org/wiki/Albanese_variety"
+     - "https://ncatlab.org/nlab/show/Albanese+variety"
+     - "https://www.encyclopediaofmath.org/index.php/Albanese_variety"
+  
+  - concept: aleph
+    arity: 0
+    arguments: []
+    speech:
       en: aleph
-      property: symbol
-      area: "set theory"
-      mathml:
-       - "<math><mi intent='aleph'>ℵ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Aleph.html"
-       - "https://ncatlab.org/nlab/show/aleph"
-       - "https://www.encyclopediaofmath.org/index.php/Aleph"
-    
-    - concept: algebraics
-      arity: 0
+    property: symbol
+    subject-area: "set theory"
+    mathml:
+     - "<math><mi intent='aleph'>ℵ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Aleph.html"
+     - "https://ncatlab.org/nlab/show/aleph"
+     - "https://www.encyclopediaofmath.org/index.php/Aleph"
+  
+  - concept: algebraics
+    arity: 0
+    arguments: []
+    speech:
       en: algebraics
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='algebraics'>𝔸</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Algebraics.html"
-    
-    - concept: algebraic-closure
-      arity: 1
-      en: algebraic closure of $1
-      property: mover/msup
-      area: "algebra"
-      mathml:
-       - "<math><mover intent='algebraic-closure($a1)'><mi arg='a1'>A</mi><mo>¯</mo></mover></math>"
-       - "<math><msup intent='algebraic-closure($a1)'><mi arg='a1'>A</mi><mi>alg</mi></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AlgebraicClosure.html"
-       - "https://en.wikipedia.org/wiki/Algebraic_closure"
-       - "https://www.encyclopediaofmath.org/index.php/Algebraic_closure"
-    
-    - concept: almost-surely
-      arity: 1
-      en: almost surely of $1
-      property: 
-      area: "probability theory"
-      mathml:
-       - "<math><mrow intent='almost-surely($a1)'><mi arg='a1'>E</mi><mi>m.s.</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Almost_surely"
-    
-    - concept: alternating-factorial
-      arity: 1
-      en: alternating factorial of $1
-      property: function
-      area: "functions"
-      mathml:
-       - "<math><mrow intent='alternating-factorial($a1)'><mi>af</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Alternating_factorial"
-    
-    - concept: alternating-group
-      arity: 1
-      en: alternating group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='alternating-group($a1)'><mi>A</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='alternating-group($a1)'><mi>Alt</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AlternatingGroup.html"
-       - "https://en.wikipedia.org/wiki/Alternating_group"
-       - "https://www.encyclopediaofmath.org/index.php/Alternating_group"
-    
-    - concept: alternation
-      arity: 2
-      en: $1 alternation $2
-      property: infix
-      area: "logic"
-      mathml:
-       - "<math><mrow intent='alternation($a1,$a2)'><mi arg='a1'>X</mi><mo>|</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Alternation_(formal_language_theory)"
-       - "https://en.wikipedia.org/wiki/%E2%88%A8"
-       - "https://en.wikipedia.org/wiki/Logical_disjunction"
-       - "https://www.encyclopediaofmath.org/index.php/Alternation"
-      alias:
-       - disjunction
-       - or
-    
-    - concept: alternative-denial
-      arity: 2
-      en: $1 alternative denial $2
-      property: infix, prefix
-      area: "propositional calculus"
-      mathml:
-       - "<math><mrow intent='alternative-denial($a1,$a2)'><mi arg='a1'>p</mi><mo>|</mo><mi arg='a2'>q</mi></mrow></math>"
-       - "<math><mrow intent='alternative-denial($a1,$a2)'><mi arg='a1'>p</mi><mo>↑</mo><mi arg='a2'>q</mi></mrow></math>"
-       - "<math><mrow intent='alternative-denial($a1,$a2)'><mi>D</mi><mi arg='a1'>p</mi><mi arg='a2'>q</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AlternativeDenial.html"
-       - "https://en.wikipedia.org/wiki/Sheffer_stroke"
-      alias:
-       - sheffer-stroke
-       - nand
-    
-    - concept: amalgam
-      arity: 5
-      en: amalgam of $1 $2 $3 $4 $5
-      property: fenced, 5-tuple
-      area: "model theory"
-      mathml:
-       - "<math><mrow intent='amalgam($a1,$a2,$a2,$a3,$a4,$a5)'><mo>(</mo><mi arg='a1'>A</mi><mo>,</mo><mi arg='a2'>f</mi><mo>,</mo><mi arg='a3'>B</mi><mo>,</mo><mi arg='a4'>g</mi><mo>,</mo><mi arg='a5'>C</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Amalgamation_property"
-       - "https://ncatlab.org/nlab/show/amalgamation+property"
-    
-    - concept: amalgamated-product
-      arity: 3
-      en: Free product with amalgamation of $1 and $3 with respect to $2
-      property: indexed infix
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='amalgamated-product($a1,$a2,$a3)'><mi arg='a1'>A</mi><msub><mo>⁎</mo><mi arg='a3'>C</mi></msub><mi arg='a2'>B</mi></mrow></math>"
-      urls: 
-       - "https://math.stackexchange.com/questions/828828/amalgamated-product"
-       - "https://en.wikipedia.org/wiki/Free_product"
-       - "https://home.iiserb.ac.in/~kashyap/Group/thesis_abhay.pdf"
-      alias:
-       - amalgamated-free-product
-       - free-product-with-amalgamation
-    
-    - concept: analytic-manifold
-      arity: 0
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='algebraics'>𝔸</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Algebraics.html"
+  
+  - concept: algebraic-closure
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: algebraic closure of $a1
+    property: mover/msup
+    subject-area: "algebra"
+    mathml:
+     - "<math><mover intent='algebraic-closure($a1)'><mi arg='a1'>A</mi><mo>¯</mo></mover></math>"
+     - "<math><msup intent='algebraic-closure($a1)'><mi arg='a1'>A</mi><mi>alg</mi></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AlgebraicClosure.html"
+     - "https://en.wikipedia.org/wiki/Algebraic_closure"
+     - "https://www.encyclopediaofmath.org/index.php/Algebraic_closure"
+  
+  - concept: almost-surely
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: almost surely of $a1
+    property: 
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mrow intent='almost-surely($a1)'><mi arg='a1'>E</mi><mi>m.s.</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Almost_surely"
+  
+  - concept: alternating-factorial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: alternating factorial of $a1
+    property: function
+    subject-area: "functions"
+    mathml:
+     - "<math><mrow intent='alternating-factorial($a1)'><mi>af</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Alternating_factorial"
+  
+  - concept: alternating-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: alternating group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='alternating-group($a1)'><mi>A</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='alternating-group($a1)'><mi>Alt</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AlternatingGroup.html"
+     - "https://en.wikipedia.org/wiki/Alternating_group"
+     - "https://www.encyclopediaofmath.org/index.php/Alternating_group"
+  
+  - concept: alternation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 alternation $a2
+    property: infix
+    subject-area: "logic"
+    mathml:
+     - "<math><mrow intent='alternation($a1,$a2)'><mi arg='a1'>X</mi><mo>|</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Alternation_(formal_language_theory)"
+     - "https://en.wikipedia.org/wiki/%E2%88%A8"
+     - "https://en.wikipedia.org/wiki/Logical_disjunction"
+     - "https://www.encyclopediaofmath.org/index.php/Alternation"
+    alias:
+     - disjunction
+     - or
+  
+  - concept: alternative-denial
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 alternative denial $a2
+    property: infix, prefix
+    subject-area: "propositional calculus"
+    mathml:
+     - "<math><mrow intent='alternative-denial($a1,$a2)'><mi arg='a1'>p</mi><mo>|</mo><mi arg='a2'>q</mi></mrow></math>"
+     - "<math><mrow intent='alternative-denial($a1,$a2)'><mi arg='a1'>p</mi><mo>↑</mo><mi arg='a2'>q</mi></mrow></math>"
+     - "<math><mrow intent='alternative-denial($a1,$a2)'><mi>D</mi><mi arg='a1'>p</mi><mi arg='a2'>q</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AlternativeDenial.html"
+     - "https://en.wikipedia.org/wiki/Sheffer_stroke"
+    alias:
+     - sheffer-stroke
+     - nand
+  
+  - concept: amalgam
+    arity: 5
+    arguments: [$a1, $a2, $a3, $a4, $a5]
+    speech:
+      en: amalgam of $a1 $a2 $a3 $a4 $a5
+    property: fenced, 5-tuple
+    subject-area: "model theory"
+    mathml:
+     - "<math><mrow intent='amalgam($a1,$a2,$a2,$a3,$a4,$a5)'><mo>(</mo><mi arg='a1'>A</mi><mo>,</mo><mi arg='a2'>f</mi><mo>,</mo><mi arg='a3'>B</mi><mo>,</mo><mi arg='a4'>g</mi><mo>,</mo><mi arg='a5'>C</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Amalgamation_property"
+     - "https://ncatlab.org/nlab/show/amalgamation+property"
+  
+  - concept: amalgamated-product
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: Free product with amalgamation of $a1 and $a3 with respect to $a2
+    property: indexed infix
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='amalgamated-product($a1,$a2,$a3)'><mi arg='a1'>A</mi><msub><mo>⁎</mo><mi arg='a3'>C</mi></msub><mi arg='a2'>B</mi></mrow></math>"
+    urls: 
+     - "https://math.stackexchange.com/questions/828828/amalgamated-product"
+     - "https://en.wikipedia.org/wiki/Free_product"
+     - "https://home.iiserb.ac.in/~kashyap/Group/thesis_abhay.pdf"
+    alias:
+     - amalgamated-free-product
+     - free-product-with-amalgamation
+  
+  - concept: analytic-manifold
+    arity: 0
+    arguments: []
+    speech:
       en: analytic manifold
-      property: symbol
-      area: "topology"
-      mathml:
-       - "<math><msup intent='analytic-manifold'><mi>C</mi><mi>w</mi></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Analytic_manifold"
-       - "https://ncatlab.org/nlab/show/analytic+manifold"
-       - "https://www.encyclopediaofmath.org/index.php/Analytic_manifold"
-    
-    - concept: anger-function
-      arity: 1
-      en: anger function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='anger-function($a1)'><mi>J</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AngerFunction.html"
-       - "https://en.wikipedia.org/wiki/Anger_function"
-       - "https://dlmf.nist.gov/11.10#E1"
-       - "https://www.encyclopediaofmath.org/index.php/Anger_function"
-    
-    - concept: angle-of-parallelism
-      arity: 1
-      en: angle of parallelism of $1
-      property: function
-      area: "hyperbolic geometry"
-      mathml:
-       - "<math><mrow intent='angle-of-parallelism($a1)'><mi>Π</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AngleofParallelism.html"
-       - "https://en.wikipedia.org/wiki/Angle_of_parallelism"
-    
-    - concept: angular-momentum
-      arity: 0
+    property: symbol
+    subject-area: "topology"
+    mathml:
+     - "<math><msup intent='analytic-manifold'><mi>C</mi><mi>w</mi></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Analytic_manifold"
+     - "https://ncatlab.org/nlab/show/analytic+manifold"
+     - "https://www.encyclopediaofmath.org/index.php/Analytic_manifold"
+  
+  - concept: anger-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: anger function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='anger-function($a1)'><mi>J</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AngerFunction.html"
+     - "https://en.wikipedia.org/wiki/Anger_function"
+     - "https://dlmf.nist.gov/11.10#E1"
+     - "https://www.encyclopediaofmath.org/index.php/Anger_function"
+  
+  - concept: angle-of-parallelism
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: angle of parallelism of $a1
+    property: function
+    subject-area: "hyperbolic geometry"
+    mathml:
+     - "<math><mrow intent='angle-of-parallelism($a1)'><mi>Π</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AngleofParallelism.html"
+     - "https://en.wikipedia.org/wiki/Angle_of_parallelism"
+  
+  - concept: angular-momentum
+    arity: 0
+    arguments: []
+    speech:
       en: angular momentum
-      property: symbol
-      area: "classical mechanics"
-      mathml:
-       - "<math><mi intent='angular-momentum'>L</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Angular_momentum"
-       - "https://en.wikipedia.org/wiki/Introduction_to_angular_momentum"
-       - "https://ncatlab.org/nlab/show/angular+momentum"
-    
-    - concept: angular-velocity
-      arity: 0
+    property: symbol
+    subject-area: "classical mechanics"
+    mathml:
+     - "<math><mi intent='angular-momentum'>L</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Angular_momentum"
+     - "https://en.wikipedia.org/wiki/Introduction_to_angular_momentum"
+     - "https://ncatlab.org/nlab/show/angular+momentum"
+  
+  - concept: angular-velocity
+    arity: 0
+    arguments: []
+    speech:
       en: angular velocity
-      property: symbol
-      area: "classical mechanics"
-      mathml:
-       - "<math><mi intent='angular-velocity'>ω</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AngularVelocity.html"
-       - "https://en.wikipedia.org/wiki/Angular_velocity"
-       - "https://ncatlab.org/nlab/show/angular+velocity"
-    
-    - concept: anharmonic-ratio
-      arity: 4
-      en: "anharmonic ratio of $1 , $2 , $3 , $4"
-      property: fenced
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='anharmonic-ratio($a1,$a2,$a3,$a4)'><mo>(</mo><mi arg='a1'>A</mi><mo>,</mo><mi arg='a2'>B</mi><mo>;</mo><mi arg='a3'>C</mi><mo>,</mo><mi arg='a4'>D</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AnharmonicRatio.html"
-       - "https://en.wikipedia.org/wiki/Cross-ratio"
-       - "https://www.encyclopediaofmath.org/index.php/Anharmonic_ratio"
-    
-    - concept: annihilator
-      arity: 1
-      en: annihilator of $1
-      property: function
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='annihilator($a1)'><mi>Ann</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Annihilator.html"
-       - "https://en.wikipedia.org/wiki/Annihilator_(ring_theory)"
-       - "https://www.encyclopediaofmath.org/index.php/Annihilator"
-    
-    - concept: annulus
-      arity: 1
-      en: annulus of $1
-      property: function
-      area: "complex analysis"
-      mathml:
-       - "<math><mrow intent='annulus($a1)'><mi>ann</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Annulus_(mathematics)"
-       - "https://ncatlab.org/nlab/show/annulus"
-       - "https://mathworld.wolfram.com/Annulus.html"
-    
-    - concept: antiparticle
-      arity: 1
-      en: antiparticle of $1
-      property: mover
-      area: "particle physics"
-      mathml:
-       - "<math><mover intent='antiparticle($a1)'><mi arg='a1'>p</mi><mo>¯</mo></mover></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Antimatter"
-       - "https://en.wikipedia.org/wiki/Antiparticle"
-      alias:
-       - antimatter
-    
-    - concept: apartness-relation
-      arity: 2
-      en: $1 apartness relation $2
-      property: infix
-      area: "constructive mathematics"
-      mathml:
-       - "<math><mrow intent='apartness-relation($a1,$a2)'><mi arg='a1'>X</mi><mo>#</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Apartness_relation"
-       - "https://ncatlab.org/nlab/show/apartness+relation"
-    
-    - concept: apery-constant
-      arity: 0
+    property: symbol
+    subject-area: "classical mechanics"
+    mathml:
+     - "<math><mi intent='angular-velocity'>ω</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AngularVelocity.html"
+     - "https://en.wikipedia.org/wiki/Angular_velocity"
+     - "https://ncatlab.org/nlab/show/angular+velocity"
+  
+  - concept: anharmonic-ratio
+    arity: 4
+    arguments: [$a1, $a2, $a3, $a4]
+    speech:
+      en: "anharmonic ratio of $a1 , $a2 , $a3 , $a4"
+    property: fenced
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='anharmonic-ratio($a1,$a2,$a3,$a4)'><mo>(</mo><mi arg='a1'>A</mi><mo>,</mo><mi arg='a2'>B</mi><mo>;</mo><mi arg='a3'>C</mi><mo>,</mo><mi arg='a4'>D</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AnharmonicRatio.html"
+     - "https://en.wikipedia.org/wiki/Cross-ratio"
+     - "https://www.encyclopediaofmath.org/index.php/Anharmonic_ratio"
+  
+  - concept: annihilator
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: annihilator of $a1
+    property: function
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='annihilator($a1)'><mi>Ann</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Annihilator.html"
+     - "https://en.wikipedia.org/wiki/Annihilator_(ring_theory)"
+     - "https://www.encyclopediaofmath.org/index.php/Annihilator"
+  
+  - concept: annulus
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: annulus of $a1
+    property: function
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mrow intent='annulus($a1)'><mi>ann</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Annulus_(mathematics)"
+     - "https://ncatlab.org/nlab/show/annulus"
+     - "https://mathworld.wolfram.com/Annulus.html"
+  
+  - concept: antiparticle
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: antiparticle of $a1
+    property: mover
+    subject-area: "particle physics"
+    mathml:
+     - "<math><mover intent='antiparticle($a1)'><mi arg='a1'>p</mi><mo>¯</mo></mover></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Antimatter"
+     - "https://en.wikipedia.org/wiki/Antiparticle"
+    alias:
+     - antimatter
+  
+  - concept: apartness-relation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 apartness relation $a2
+    property: infix
+    subject-area: "constructive mathematics"
+    mathml:
+     - "<math><mrow intent='apartness-relation($a1,$a2)'><mi arg='a1'>X</mi><mo>#</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Apartness_relation"
+     - "https://ncatlab.org/nlab/show/apartness+relation"
+  
+  - concept: apery-constant
+    arity: 0
+    arguments: []
+    speech:
       en: apery constant
-      property: symbol
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='apery-constant'><mi>ζ</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AperysConstant.html"
-       - "https://en.wikipedia.org/wiki/Zeta(3)"
-       - "https://en.wikipedia.org/wiki/%CE%96(3)"
-       - "https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant"
-    
-    - concept: arcminute
-      arity: 1
-      en: arcminute of $1
-      property: unit
-      area: "SI-mentioned units"
-      mathml:
-       - "<math><mrow intent='arcminute($a1)'><mi>arcmin</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='arcminute($a1)'><mi>amin</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      notationa: "mo ′"
-      urls: 
-       - "https://mathworld.wolfram.com/Arcminute.html"
-       - "https://en.wikipedia.org/wiki/Minute_of_arc"
-       - "https://en.wikipedia.org/wiki/Arcsecond"
-       - "https://en.wikipedia.org/wiki/Second_(angle)"
-      alias:
-       - minute-arc
-       - minute-of-arc
-    
-    - concept: arcsecond
-      arity: 1
-      en: arcsecond of $1
-      property: unit
-      area: "SI-mentioned units"
-      mathml:
-       - "<math><mrow intent='arcsecond($a1)'><mi>arcsec</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='arcsecond($a1)'><mi>asec</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      notationa: "mo ′′"
-      urls: 
-       - "https://mathworld.wolfram.com/Arcminute.html"
-       - "https://en.wikipedia.org/wiki/Minute_of_arc"
-       - "https://en.wikipedia.org/wiki/Arcsecond"
-       - "https://en.wikipedia.org/wiki/Second_(angle)"
-    
-    - concept: area
-      arity: 0
+    property: symbol
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='apery-constant'><mi>ζ</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AperysConstant.html"
+     - "https://en.wikipedia.org/wiki/Zeta(3)"
+     - "https://en.wikipedia.org/wiki/%CE%96(3)"
+     - "https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant"
+  
+  - concept: arcminute
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: arcminute of $a1
+    property: unit
+    subject-area: "SI-mentioned units"
+    mathml:
+     - "<math><mrow intent='arcminute($a1)'><mi>arcmin</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='arcminute($a1)'><mi>amin</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    notationa: "mo ′"
+    urls: 
+     - "https://mathworld.wolfram.com/Arcminute.html"
+     - "https://en.wikipedia.org/wiki/Minute_of_arc"
+     - "https://en.wikipedia.org/wiki/Arcsecond"
+     - "https://en.wikipedia.org/wiki/Second_(angle)"
+    alias:
+     - minute-arc
+     - minute-of-arc
+  
+  - concept: arcsecond
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: arcsecond of $a1
+    property: unit
+    subject-area: "SI-mentioned units"
+    mathml:
+     - "<math><mrow intent='arcsecond($a1)'><mi>arcsec</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='arcsecond($a1)'><mi>asec</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    notationa: "mo ′′"
+    urls: 
+     - "https://mathworld.wolfram.com/Arcminute.html"
+     - "https://en.wikipedia.org/wiki/Minute_of_arc"
+     - "https://en.wikipedia.org/wiki/Arcsecond"
+     - "https://en.wikipedia.org/wiki/Second_(angle)"
+  
+  - concept: area
+    arity: 0
+    arguments: []
+    speech:
       en: area
-      property: symbol
-      area: "geometry"
-      mathml:
-       - "<math><mi intent='area'>A</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Area.html"
-       - "https://en.wikipedia.org/wiki/Area"
-       - "https://www.encyclopediaofmath.org/index.php/Area"
-    
-    - concept: arf-invariant
-      arity: 1
-      en: arf invariant of $1
-      property: function
-      area: "geometric topology"
-      mathml:
-       - "<math><mrow intent='arf-invariant($a1)'><mi>Arf</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ArfInvariant.html"
-       - "https://en.wikipedia.org/wiki/Arf_invariant"
-       - "https://en.wikipedia.org/wiki/Arf_invariant_of_a_knot"
-    
-    - concept: argument
-      arity: 1
-      en: argument of $1
-      property: function
-      area: "complex analysis"
-      mathml:
-       - "<math><mrow intent='argument($a1)'><mi>Arg</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Argument_(complex_analysis)"
-    
-    - concept: arithmetic-geometric-mean
-      arity: 1
-      en: arithmetic geometric mean of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='arithmetic-geometric-mean($a1)'><mi>agm</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='arithmetic-geometric-mean($a1)'><mi>AGM</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Arithmetic-GeometricMean.html"
-       - "https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_mean"
-       - "https://dlmf.nist.gov/19.8#i"
-       - "https://dlmf.nist.gov/19.8#SS1.p1"
-    
-    - concept: associated-legendre-polynomial
-      arity: 2
-      en: associated legendre polynomial of degree $1 and order $2
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow><msubsup intent='associated-legendre-polynomial($a1,m2)'><mi>P</mi><mi arg='a1'>ℓ</mi><mi arg='a2'>m</mi></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AssociatedLegendrePolynomial.html"
-       - "https://en.wikipedia.org/wiki/Associated_Legendre_polynomials"
-       - "https://dlmf.nist.gov/18.30#E6"
-    
-    - concept: associator
-      arity: 3
-      en: associator of $1, $2, $3
-      property: fenced
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='associator($a1,$a2,$a3)'><mo>[</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Associator.html"
-       - "https://en.wikipedia.org/wiki/Associator"
-       - "https://ncatlab.org/nlab/show/associator"
-       - "https://www.encyclopediaofmath.org/index.php/Associator"
-    
-    - concept: automorphism-group
-      arity: 1
-      en: automorphism group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='automorphism-group($a1)'><mi>Aut</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/AutomorphismGroup.html"
-       - "https://en.wikipedia.org/wiki/Automorphism"
-    
-    - concept: backward-difference
-      arity: 1
-      en: backward difference of $1
-      property: operator
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='backward-difference($a1)'><mi>∇</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BackwardDifference.html"
-       - "https://en.wikipedia.org/wiki/Finite_difference"
-       - "https://dlmf.nist.gov/18.1#EGx2"
-    
-    - concept: baire-space
-      arity: 0
+    property: symbol
+    subject-area: "geometry"
+    mathml:
+     - "<math><mi intent='area'>A</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Area.html"
+     - "https://en.wikipedia.org/wiki/Area"
+     - "https://www.encyclopediaofmath.org/index.php/Area"
+  
+  - concept: arf-invariant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: arf invariant of $a1
+    property: function
+    subject-area: "geometric topology"
+    mathml:
+     - "<math><mrow intent='arf-invariant($a1)'><mi>Arf</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ArfInvariant.html"
+     - "https://en.wikipedia.org/wiki/Arf_invariant"
+     - "https://en.wikipedia.org/wiki/Arf_invariant_of_a_knot"
+  
+  - concept: argument
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: argument of $a1
+    property: function
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mrow intent='argument($a1)'><mi>Arg</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Argument_(complex_analysis)"
+  
+  - concept: arithmetic-geometric-mean
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: arithmetic geometric mean of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='arithmetic-geometric-mean($a1)'><mi>agm</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='arithmetic-geometric-mean($a1)'><mi>AGM</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Arithmetic-GeometricMean.html"
+     - "https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_mean"
+     - "https://dlmf.nist.gov/19.8#i"
+     - "https://dlmf.nist.gov/19.8#SS1.p1"
+  
+  - concept: associated-legendre-polynomial
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: associated legendre polynomial of degree $a1 and order $a2
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow><msubsup intent='associated-legendre-polynomial($a1,m2)'><mi>P</mi><mi arg='a1'>ℓ</mi><mi arg='a2'>m</mi></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AssociatedLegendrePolynomial.html"
+     - "https://en.wikipedia.org/wiki/Associated_Legendre_polynomials"
+     - "https://dlmf.nist.gov/18.30#E6"
+  
+  - concept: associator
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: associator of $a1, $a2, $a3
+    property: fenced
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='associator($a1,$a2,$a3)'><mo>[</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Associator.html"
+     - "https://en.wikipedia.org/wiki/Associator"
+     - "https://ncatlab.org/nlab/show/associator"
+     - "https://www.encyclopediaofmath.org/index.php/Associator"
+  
+  - concept: automorphism-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: automorphism group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='automorphism-group($a1)'><mi>Aut</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/AutomorphismGroup.html"
+     - "https://en.wikipedia.org/wiki/Automorphism"
+  
+  - concept: backward-difference
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: backward difference of $a1
+    property: operator
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='backward-difference($a1)'><mi>∇</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BackwardDifference.html"
+     - "https://en.wikipedia.org/wiki/Finite_difference"
+     - "https://dlmf.nist.gov/18.1#EGx2"
+  
+  - concept: baire-space
+    arity: 0
+    arguments: []
+    speech:
       en: baire space
-      property: symbol
-      area: "set theory"
-      mathml:
-       - "<math><msup intent='baire-space'><mi>N</mi><mi>N</mi></msup></math>"
-       - "<math><msup intent='baire-space'><mi>ω</mi><mi>ω</mi></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BaireSpace.html"
-       - "https://en.wikipedia.org/wiki/Baire_space"
-       - "https://en.wikipedia.org/wiki/Baire_space_(set_theory)"
-       - "https://ncatlab.org/nlab/show/Baire+space"
-       - "https://www.encyclopediaofmath.org/index.php/Baire_space"
-    
-    - concept: barrel
-      arity: 1
-      en: $1 barrels
-      property: unit
-      area: "imperial units"
-      mathml:
-       - "<math><mrow intent='barrel($a1)'><mi arg='a1'>x</mi><mo>&#x2009;</mo><mi>bbl</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Barrel.html"
-       - "https://en.wikipedia.org/wiki/Barrelled_space"
-       - "https://en.wikipedia.org/wiki/Barrel_(unit)"
-    
-    - concept: bateman-function
-      arity: 2
+    property: symbol
+    subject-area: "set theory"
+    mathml:
+     - "<math><msup intent='baire-space'><mi>N</mi><mi>N</mi></msup></math>"
+     - "<math><msup intent='baire-space'><mi>ω</mi><mi>ω</mi></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BaireSpace.html"
+     - "https://en.wikipedia.org/wiki/Baire_space"
+     - "https://en.wikipedia.org/wiki/Baire_space_(set_theory)"
+     - "https://ncatlab.org/nlab/show/Baire+space"
+     - "https://www.encyclopediaofmath.org/index.php/Baire_space"
+  
+  - concept: barrel
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1 barrels
+    property: unit
+    subject-area: "imperial units"
+    mathml:
+     - "<math><mrow intent='barrel($a1)'><mi arg='a1'>x</mi><mo>&#x2009;</mo><mi>bbl</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Barrel.html"
+     - "https://en.wikipedia.org/wiki/Barrelled_space"
+     - "https://en.wikipedia.org/wiki/Barrel_(unit)"
+  
+  - concept: bateman-function
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: bateman function
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='bateman-function($a1,$a2)'><msub><mi>k</mi><mi arg='a1'>v</mi></msub><mrow><mo>(</mo><mi arg='a2'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BatemanFunction.html"
-       - "https://en.wikipedia.org/wiki/Bateman_function"
-       - "https://www.encyclopediaofmath.org/index.php/Bateman_function"
-    
-    - concept: baumslag-solitar-group
-      arity: 2
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='bateman-function($a1,$a2)'><msub><mi>k</mi><mi arg='a1'>v</mi></msub><mrow><mo>(</mo><mi arg='a2'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BatemanFunction.html"
+     - "https://en.wikipedia.org/wiki/Bateman_function"
+     - "https://www.encyclopediaofmath.org/index.php/Bateman_function"
+  
+  - concept: baumslag-solitar-group
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: baumslag solitar group
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='baumslag-solitar-group($a1,$a2)'><mi>BS</mi><mrow><mo>(</mo><mi arg='a1'>m</mi><mo>,</mo><mi arg='a2'>n</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Baumslag%E2%80%93Solitar_group"
-       - "https://www.encyclopediaofmath.org/index.php/Baumslag-Solitar_group"
-    
-    - concept: bc
-      arity: 1
-      en: $1 b c
-      property: postfix
-      area: "calendar units"
-      mathml:
-       - "<math><mrow intent='bc($a1)'><mn arg='a1'>2024</mn><mo>&#x2009;</mo><mi>BC</mi></mrow></math>"      
-      urls: 
-       - "https://en.wikipedia.org/wiki/Anno_Domini"
-    
-    - concept: beatty-sequence
-      arity: 1
-      en: $1<i>th</i> beatty sequence
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='beatty-sequence($a1)'><mi>𝓑</mi><mi arg='a1'>r</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BeattySequence.html"
-       - "https://en.wikipedia.org/wiki/Beatty_sequence"
-    
-    - concept: bell-number
-      arity: 1
-      en: $1<i>th</i> bell number
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='bell-number($a1)'><mi>B</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BellNumber.html"
-       - "https://en.wikipedia.org/wiki/Bell_number"
-       - "https://dlmf.nist.gov/26.7#i"
-       - "https://www.encyclopediaofmath.org/index.php/Bell_numbers"
-    
-    - concept: bell-polynomial
-      arity: ">=0"
-      en: $1<i>th</i> bell polynomial of $2, $3, ...
-      property: "indexed function"
-      area: "polynomials"
-      notation: "mrow msub B $1 ($2, ... $n"
-      urls: 
-       - "https://mathworld.wolfram.com/BellPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Bell_polynomials"
-       - "https://www.encyclopediaofmath.org/index.php/Bell_polynomial"
-    
-    - concept: berezin-integral
-      arity: 1
-      en: berezin integral of $1
-      property: indexed
-      area: "mathematical physics"
-      mathml:
-       - "<math><mrow intent='berezin-integral($a1)'><mo>∫</mo><mrow><mi arg='a1'>f</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Berezin_integral"
-       - "https://en.wikipedia.org/wiki/Grassmann_integral"
-       - "https://ncatlab.org/nlab/show/Berezin+integral"
-    
-    - concept: bergman-space
-      arity: 2
-      en: $1<i>th</i> bergman space of $2
-      property: "indexed function"
-      area: "complex analysis"
-      mathml:
-       - "<math><mrow intent='bergman-space($a1,$a2)'><msup><mi>A</mi><mi arg='a1'>n</mi></msup><mrow><mo>(</mo><mi arg='a2'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BergmanSpace.html"
-       - "https://en.wikipedia.org/wiki/Bergman_space"
-       - "https://www.encyclopediaofmath.org/index.php/Bergman_spaces"
-    
-    - concept: bernoulli-number
-      arity: 1
-      en: $1<i>th</i> bernoulli number
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='bernoulli-number($a1)'><mi>B</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BernoulliNumber.html"
-       - "https://en.wikipedia.org/wiki/Bernoulli_number"
-       - "https://dlmf.nist.gov/24.1#P1"
-       - "https://dlmf.nist.gov/24.2#i"
-       - "https://ncatlab.org/nlab/show/Bernoulli+number"
-       - "https://www.encyclopediaofmath.org/index.php/Bernoulli_numbers"
-    
-    - concept: bernoulli-polynomial
-      arity: 2
-      en: bernoulli polynomial $1 $2
-      property: "indexed function"
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='bernoulli-polynomial($a1,$a2)'><msub><mi>B</mi><mi arg='a1'>n</mi></msub><mrow><mo>(</mo><mi arg='a2'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BernoulliPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Bernoulli_polynomials"
-       - "https://dlmf.nist.gov/24.1#P1"
-       - "https://dlmf.nist.gov/24.2#i"
-       - "https://www.encyclopediaofmath.org/index.php/Bernoulli_polynomials"
-    
-    - concept: bessel-function
-      arity: 2
-      en: $1<i>th</i> bessel function of $2
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='bessel-function($a1,$a2)'><msub><mi>J</mi><mi arg='a1'>n</mi></msub><mrow><mo>(</mo><mi arg='a2'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BesselFunction.html"
-       - "https://en.wikipedia.org/wiki/Bessel_function"
-       - "https://dlmf.nist.gov/10.1"
-       - "https://www.encyclopediaofmath.org/index.php/Bessel_functions"
-    
-    - concept: bessel-function-of-second-kind
-      arity: 2
-      en: $1<i>th</i> bessel function of second kind of $2
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='bessel-function-of-second-kind($a1,$a2)'><msub><mi>Y</mi><mi arg='a1'>n</mi></msub><mrow><mo>(</mo><mi arg='a2'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BesselFunctionoftheSecondKind.html"
-       - "https://dlmf.nist.gov/10.2#E3"
-       - "https://www.encyclopediaofmath.org/index.php/Bessel_function_of_the_second_kind"
-    
-    - concept: bessel-polynomial
-      arity: 2
-      en: $1<i>th</i> bessel polynomial of $2
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='bessel-polynomial($a1,$a2)'><msub><mi>y</mi><mi arg='a1'>n</mi></msub><mrow><mo>(</mo><mi arg='a2'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BesselPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Bessel_polynomials"
-       - "https://dlmf.nist.gov/18.34#E1"
-       - "https://www.encyclopediaofmath.org/index.php/Bessel_polynomials"
-    
-    - concept: beta-distribution
-      arity: 1
-      en: beta distribution of $1
-      property: function
-      area: "probability theory"
-      mathml:
-       - "<math><mrow intent='beta-distribution($a1)'><mi>B</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='beta-distribution($a1)'><mi>Beta</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='beta-distribution($a1)'><mi>𝓑𝓮</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='beta-distribution($a1)'><mi>β</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BetaDistribution.html"
-       - "https://en.wikipedia.org/wiki/Beta_distribution"
-    
-    - concept: beta-function
-      arity: 1
-      en: beta function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='beta-function($a1)'><mi>B</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='beta-function($a1)'><mi>β</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BetaFunction.html"
-       - "https://en.wikipedia.org/wiki/%CE%92(x,_y)"
-       - "https://en.wikipedia.org/wiki/Beta_function_(physics)"
-       - "https://en.wikipedia.org/wiki/Beta_function"
-       - "https://dlmf.nist.gov/5.12"
-       - "https://dlmf.nist.gov/5.12#E1"
-       - "https://ncatlab.org/nlab/show/beta+function"
-      alias:
-       - euler-integral-of-the-first-kind
-    
-    - concept: betti-number
-      arity: 1
-      en: $1<i>th</i> betti number
-      property: "indexed symbol"
-      area: "graph theory"
-      mathml:
-       - "<math><msub intent='betti-number($a1)'><mi>b</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BettiNumber.html"
-       - "https://en.wikipedia.org/wiki/Betti_number"
-       - "https://ncatlab.org/nlab/show/Betti+number"
-       - "https://www.encyclopediaofmath.org/index.php/Betti_number"
-    
-    - concept: biconditional
-      arity: 2
-      en: $1 biconditional $2
-      property: infix
-      area: "logic"
-      mathml:
-       - "<math><mrow intent='biconditional($a1,$a2)'><mi arg='a1'>X</mi><mo>⇔</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='biconditional($a1,$a2)'><mi arg='a1'>X</mi><mo>≡</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='biconditional($a1,$a2)'><mi arg='a1'>X</mi><mo>iff</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Biconditional.html"
-       - "https://ncatlab.org/nlab/show/biconditional"
-      alias:
-       - iff
-       - if-and-only-if
-    
-    - concept: big-O
-      arity: 1
-      en: big O of $1
-      property: prefix
-      area: "complexity"
-      mathml:
-       - "<math><mrow intent='big-O($a1)'><mi>O</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Big_O_notation"
-       - "https://mathworld.wolfram.com/O.html"
-    
-    - concept: bigeometric-integral
-      arity: 1
-      en: bigeometric integral of $1
-      property: indexed
-      area: "calculus"
-      mathml:
-       - "<math><mrow intent='bigeometric-integral($a1)'><mo>∫</mo><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Product_integral"
-    
-    - concept: bijection
-      arity: 3
-      en: bijection, $1, of $2 to $3
-      property: mixfix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='bijection($a1,$a2,$a3)'><mi arg='a1'>f</mi><mo>:</mo><mi arg='a2'>X</mi><mo>⤖</mo><mi arg='a3'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Bijection#Definition"
-    
-    - concept: binary-golay-code
-      arity: 0
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='baumslag-solitar-group($a1,$a2)'><mi>BS</mi><mrow><mo>(</mo><mi arg='a1'>m</mi><mo>,</mo><mi arg='a2'>n</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Baumslag%E2%80%93Solitar_group"
+     - "https://www.encyclopediaofmath.org/index.php/Baumslag-Solitar_group"
+  
+  - concept: bc
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1 b c
+    property: postfix
+    subject-area: "calendar units"
+    mathml:
+     - "<math><mrow intent='bc($a1)'><mn arg='a1'>2024</mn><mo>&#x2009;</mo><mi>BC</mi></mrow></math>"      
+    urls: 
+     - "https://en.wikipedia.org/wiki/Anno_Domini"
+  
+  - concept: beatty-sequence
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> beatty sequence
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='beatty-sequence($a1)'><mi>𝓑</mi><mi arg='a1'>r</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BeattySequence.html"
+     - "https://en.wikipedia.org/wiki/Beatty_sequence"
+  
+  - concept: bell-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> bell number
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='bell-number($a1)'><mi>B</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BellNumber.html"
+     - "https://en.wikipedia.org/wiki/Bell_number"
+     - "https://dlmf.nist.gov/26.7#i"
+     - "https://www.encyclopediaofmath.org/index.php/Bell_numbers"
+  
+  - concept: bell-polynomial
+    arity: ">=0"
+    speech:
+      en: $a1<i>th</i> bell polynomial of $a2, $a3, ...
+    property: "indexed function"
+    subject-area: "polynomials"
+    notation: "mrow msub B $a1 ($a2, ... $n"
+    urls: 
+     - "https://mathworld.wolfram.com/BellPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Bell_polynomials"
+     - "https://www.encyclopediaofmath.org/index.php/Bell_polynomial"
+  
+  - concept: berezin-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: berezin integral of $a1
+    property: indexed
+    subject-area: "mathematical physics"
+    mathml:
+     - "<math><mrow intent='berezin-integral($a1)'><mo>∫</mo><mrow><mi arg='a1'>f</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Berezin_integral"
+     - "https://en.wikipedia.org/wiki/Grassmann_integral"
+     - "https://ncatlab.org/nlab/show/Berezin+integral"
+  
+  - concept: bergman-space
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1<i>th</i> bergman space of $a2
+    property: "indexed function"
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mrow intent='bergman-space($a1,$a2)'><msup><mi>A</mi><mi arg='a1'>n</mi></msup><mrow><mo>(</mo><mi arg='a2'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BergmanSpace.html"
+     - "https://en.wikipedia.org/wiki/Bergman_space"
+     - "https://www.encyclopediaofmath.org/index.php/Bergman_spaces"
+  
+  - concept: bernoulli-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> bernoulli number
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='bernoulli-number($a1)'><mi>B</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BernoulliNumber.html"
+     - "https://en.wikipedia.org/wiki/Bernoulli_number"
+     - "https://dlmf.nist.gov/24.1#P1"
+     - "https://dlmf.nist.gov/24.2#i"
+     - "https://ncatlab.org/nlab/show/Bernoulli+number"
+     - "https://www.encyclopediaofmath.org/index.php/Bernoulli_numbers"
+  
+  - concept: bernoulli-polynomial
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: bernoulli polynomial $a1 $a2
+    property: "indexed function"
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='bernoulli-polynomial($a1,$a2)'><msub><mi>B</mi><mi arg='a1'>n</mi></msub><mrow><mo>(</mo><mi arg='a2'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BernoulliPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Bernoulli_polynomials"
+     - "https://dlmf.nist.gov/24.1#P1"
+     - "https://dlmf.nist.gov/24.2#i"
+     - "https://www.encyclopediaofmath.org/index.php/Bernoulli_polynomials"
+  
+  - concept: bessel-function
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1<i>th</i> bessel function of $a2
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='bessel-function($a1,$a2)'><msub><mi>J</mi><mi arg='a1'>n</mi></msub><mrow><mo>(</mo><mi arg='a2'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BesselFunction.html"
+     - "https://en.wikipedia.org/wiki/Bessel_function"
+     - "https://dlmf.nist.gov/10.1"
+     - "https://www.encyclopediaofmath.org/index.php/Bessel_functions"
+  
+  - concept: bessel-function-of-second-kind
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1<i>th</i> bessel function of second kind of $a2
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='bessel-function-of-second-kind($a1,$a2)'><msub><mi>Y</mi><mi arg='a1'>n</mi></msub><mrow><mo>(</mo><mi arg='a2'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BesselFunctionoftheSecondKind.html"
+     - "https://dlmf.nist.gov/10.2#E3"
+     - "https://www.encyclopediaofmath.org/index.php/Bessel_function_of_the_second_kind"
+  
+  - concept: bessel-polynomial
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1<i>th</i> bessel polynomial of $a2
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='bessel-polynomial($a1,$a2)'><msub><mi>y</mi><mi arg='a1'>n</mi></msub><mrow><mo>(</mo><mi arg='a2'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BesselPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Bessel_polynomials"
+     - "https://dlmf.nist.gov/18.34#E1"
+     - "https://www.encyclopediaofmath.org/index.php/Bessel_polynomials"
+  
+  - concept: beta-distribution
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: beta distribution of $a1
+    property: function
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mrow intent='beta-distribution($a1)'><mi>B</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='beta-distribution($a1)'><mi>Beta</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='beta-distribution($a1)'><mi>𝓑𝓮</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='beta-distribution($a1)'><mi>β</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BetaDistribution.html"
+     - "https://en.wikipedia.org/wiki/Beta_distribution"
+  
+  - concept: beta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: beta function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='beta-function($a1)'><mi>B</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='beta-function($a1)'><mi>β</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BetaFunction.html"
+     - "https://en.wikipedia.org/wiki/%CE%92(x,_y)"
+     - "https://en.wikipedia.org/wiki/Beta_function_(physics)"
+     - "https://en.wikipedia.org/wiki/Beta_function"
+     - "https://dlmf.nist.gov/5.12"
+     - "https://dlmf.nist.gov/5.12#E1"
+     - "https://ncatlab.org/nlab/show/beta+function"
+    alias:
+     - euler-integral-of-the-first-kind
+  
+  - concept: betti-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> betti number
+    property: "indexed symbol"
+    subject-area: "graph theory"
+    mathml:
+     - "<math><msub intent='betti-number($a1)'><mi>b</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BettiNumber.html"
+     - "https://en.wikipedia.org/wiki/Betti_number"
+     - "https://ncatlab.org/nlab/show/Betti+number"
+     - "https://www.encyclopediaofmath.org/index.php/Betti_number"
+  
+  - concept: biconditional
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 biconditional $a2
+    property: infix
+    subject-area: "logic"
+    mathml:
+     - "<math><mrow intent='biconditional($a1,$a2)'><mi arg='a1'>X</mi><mo>⇔</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='biconditional($a1,$a2)'><mi arg='a1'>X</mi><mo>≡</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='biconditional($a1,$a2)'><mi arg='a1'>X</mi><mo>iff</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Biconditional.html"
+     - "https://ncatlab.org/nlab/show/biconditional"
+    alias:
+     - iff
+     - if-and-only-if
+  
+  - concept: big-O
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: big O of $a1
+    property: prefix
+    subject-area: "complexity"
+    mathml:
+     - "<math><mrow intent='big-O($a1)'><mi>O</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Big_O_notation"
+     - "https://mathworld.wolfram.com/O.html"
+  
+  - concept: bigeometric-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: bigeometric integral of $a1
+    property: indexed
+    subject-area: "calculus"
+    mathml:
+     - "<math><mrow intent='bigeometric-integral($a1)'><mo>∫</mo><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Product_integral"
+  
+  - concept: bijection
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: bijection, $a1, of $a2 to $a3
+    property: mixfix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='bijection($a1,$a2,$a3)'><mi arg='a1'>f</mi><mo>:</mo><mi arg='a2'>X</mi><mo>⤖</mo><mi arg='a3'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Bijection#Definition"
+  
+  - concept: binary-golay-code
+    arity: 0
+    arguments: []
+    speech:
       en: binary golay code
-      property: symbol
-      area: "coding theory"
-      mathml:
-       - "<math><msub intent='binary-golay-code'><mi>G</mi><mn>23</mn></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BinaryGolayCode.html"
-       - "https://ncatlab.org/nlab/show/binary+Golay+code"
-    
-    - concept: binomial-coefficient
-      arity: 2
-      en: binomial coefficient $1 choose $2
-      property: "indexed function"
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='binomial-coefficient($a1,$a2)'><mo>(</mo><mfrac linethickness='0pt'><mi arg='a1'>n</mi><mi arg='a2'>k</mi></mfrac><mo>)</mo></mrow></math>"
-       - "<math><mmultiscripts intent='binomial-coefficient($a1,$a2)'><mi>C</mi><mi arg='a2'>k</mi><mrow/><mprescripts/><mrow/><mi arg='a1'>n</mi></mmultiscripts></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BinomialCoefficient.html"
-       - "https://en.wikipedia.org/wiki/Binomial_coefficient"
-       - "https://dlmf.nist.gov/1.2#E1"
-       - "https://dlmf.nist.gov/26.3#SS1.p1"
-       - "https://www.encyclopediaofmath.org/index.php/Binomial_coefficients"
-      alias:
-       - combination
-    
-    - concept: binomial-distribution
-      arity: 2
-      en: binomial distribution $1 $2
-      property: function
-      area: "probability theory"
-      mathml:
-       - "<math><mrow intent='binomial-distribution($a1,$a2)'><mi>B</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>,</mo><mi arg='a2'>p</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BinomialDistribution.html"
-       - "https://en.wikipedia.org/wiki/Binomial_distribution"
-       - "https://www.encyclopediaofmath.org/index.php/Binomial_distribution"
-    
-    - concept: bit
-      arity: 0
+    property: symbol
+    subject-area: "coding theory"
+    mathml:
+     - "<math><msub intent='binary-golay-code'><mi>G</mi><mn>23</mn></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BinaryGolayCode.html"
+     - "https://ncatlab.org/nlab/show/binary+Golay+code"
+  
+  - concept: binomial-coefficient
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: binomial coefficient $a1 choose $a2
+    property: "indexed function"
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='binomial-coefficient($a1,$a2)'><mo>(</mo><mfrac linethickness='0pt'><mi arg='a1'>n</mi><mi arg='a2'>k</mi></mfrac><mo>)</mo></mrow></math>"
+     - "<math><mmultiscripts intent='binomial-coefficient($a1,$a2)'><mi>C</mi><mi arg='a2'>k</mi><mrow/><mprescripts/><mrow/><mi arg='a1'>n</mi></mmultiscripts></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BinomialCoefficient.html"
+     - "https://en.wikipedia.org/wiki/Binomial_coefficient"
+     - "https://dlmf.nist.gov/1.2#E1"
+     - "https://dlmf.nist.gov/26.3#SS1.p1"
+     - "https://www.encyclopediaofmath.org/index.php/Binomial_coefficients"
+    alias:
+     - combination
+  
+  - concept: binomial-distribution
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: binomial distribution $a1 $a2
+    property: function
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mrow intent='binomial-distribution($a1,$a2)'><mi>B</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>,</mo><mi arg='a2'>p</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BinomialDistribution.html"
+     - "https://en.wikipedia.org/wiki/Binomial_distribution"
+     - "https://www.encyclopediaofmath.org/index.php/Binomial_distribution"
+  
+  - concept: bit
+    arity: 0
+    arguments: []
+    speech:
       en: bit
-      property: symbol
-      area: "computer science"
-      mathml:
-       - "<math><mn intent='bit'>0</mn></math>"
-       - "<math><mn intent='bit'>1</mn></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Bit.html"
-       - "https://en.wikipedia.org/wiki/Bit"
-       - "https://www.encyclopediaofmath.org/index.php/Bit"
-    
-    - concept: bipolar-set
-      arity: 1
-      en: bipolar set of $1
-      property: msup
-      area: "functional analysis"
-      mathml:
-       - "<math><msup intent='bipolar-set($a1)'><mi arg='a1'>X</mi><mo>°°</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Polar_set"
-       - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)"
-       - "https://www.encyclopediaofmath.org/index.php/Polar_set"
-    
-    - concept: biquaternion
-      arity: 1
-      en: biquaternion of $1
-      property: mtable
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='biquaternion($a1)'><mo>(</mo><mtable rowspacing='4pt' columnspacing='1em'><mtr><mtd><mi>u</mi><mo>+</mo><mi>h</mi><mi>v</mi></mtd><mtd><mi>w</mi><mo>+</mo><mi>h</mi><mi arg='a1'>x</mi></mtd></mtr><mtr><mtd><mo>−</mo><mi>w</mi><mo>+</mo><mi>h</mi><mi arg='a1'>x</mi></mtd><mtd><mi>u</mi><mo>−</mo><mi>h</mi><mi>v</mi></mtd></mtr></mtable><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Biquaternion#Linear_representation"
-    
-    - concept: blaschke-product
-      arity: 1
-      en: blaschke product of $1
-      property: function
-      area: "complex analysis"
-      mathml:
-       - "<math><mrow intent='blaschke-product($a1)'><mi>B</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BlaschkeProduct.html"
-       - "https://en.wikipedia.org/wiki/Blaschke_product"
-       - "https://www.encyclopediaofmath.org/index.php/Blaschke_product"
-    
-    - concept: bloch-constant
-      arity: 0
+    property: symbol
+    subject-area: "computer science"
+    mathml:
+     - "<math><mn intent='bit'>0</mn></math>"
+     - "<math><mn intent='bit'>1</mn></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Bit.html"
+     - "https://en.wikipedia.org/wiki/Bit"
+     - "https://www.encyclopediaofmath.org/index.php/Bit"
+  
+  - concept: bipolar-set
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: bipolar set of $a1
+    property: msup
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><msup intent='bipolar-set($a1)'><mi arg='a1'>X</mi><mo>°°</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Polar_set"
+     - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)"
+     - "https://www.encyclopediaofmath.org/index.php/Polar_set"
+  
+  - concept: biquaternion
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: biquaternion of $a1
+    property: mtable
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='biquaternion($a1)'><mo>(</mo><mtable rowspacing='4pt' columnspacing='1em'><mtr><mtd><mi>u</mi><mo>+</mo><mi>h</mi><mi>v</mi></mtd><mtd><mi>w</mi><mo>+</mo><mi>h</mi><mi arg='a1'>x</mi></mtd></mtr><mtr><mtd><mo>−</mo><mi>w</mi><mo>+</mo><mi>h</mi><mi arg='a1'>x</mi></mtd><mtd><mi>u</mi><mo>−</mo><mi>h</mi><mi>v</mi></mtd></mtr></mtable><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Biquaternion#Linear_representation"
+  
+  - concept: blaschke-product
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: blaschke product of $a1
+    property: function
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mrow intent='blaschke-product($a1)'><mi>B</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BlaschkeProduct.html"
+     - "https://en.wikipedia.org/wiki/Blaschke_product"
+     - "https://www.encyclopediaofmath.org/index.php/Blaschke_product"
+  
+  - concept: bloch-constant
+    arity: 0
+    arguments: []
+    speech:
       en: bloch constant
-      property: symbol
-      area: "complex analysis"
-      mathml:
-       - "<math><mi intent='bloch-constant'>B</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BlochConstant.html"
-       - "https://www.encyclopediaofmath.org/index.php/Bloch_constant"
-    
-    - concept: boolean-domain
-      arity: 0
+    property: symbol
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mi intent='bloch-constant'>B</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BlochConstant.html"
+     - "https://www.encyclopediaofmath.org/index.php/Bloch_constant"
+  
+  - concept: boolean-domain
+    arity: 0
+    arguments: []
+    speech:
       en: boolean domain
-      property: symbol
-      area: "abstract algebra"
-      mathml:
-       - "<math><mi intent='boolean-domain'>𝔹</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Boolean_domain"
-       - "https://ncatlab.org/nlab/show/boolean+domain"
-    
-    - concept: bottom-type
-      arity: 0
+    property: symbol
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mi intent='boolean-domain'>𝔹</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Boolean_domain"
+     - "https://ncatlab.org/nlab/show/boolean+domain"
+  
+  - concept: bottom-type
+    arity: 0
+    arguments: []
+    speech:
       en: bottom type
-      property: symbol
-      area: "category theory"
-      mathml:
-       - "<math><mi intent='bottom-type'>⊥</mi></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/bottom"
-       - "https://en.wikipedia.org/wiki/Bottom_type"
-      alias:
-       - empty-type
-       - bottom
-    
-    - concept: bottom-element
-      arity: 0
+    property: symbol
+    subject-area: "category theory"
+    mathml:
+     - "<math><mi intent='bottom-type'>⊥</mi></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/bottom"
+     - "https://en.wikipedia.org/wiki/Bottom_type"
+    alias:
+     - empty-type
+     - bottom
+  
+  - concept: bottom-element
+    arity: 0
+    arguments: []
+    speech:
       en: bottom element
-      property: symbol
-      area: "order theory"
-      mathml:
-       - "<math><mi intent='bottom-element'>⊥</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Greatest_element_and_least_element"
-      alias:
-       - bottom
-       - least-element
-    
-    - concept: boundary
-      arity: 1
-      en: boundary of $1
-      property: function
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='boundary($a1)'><mi>bd</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='boundary($a1)'><mi>fr</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='boundary($a1)'><mi>∂</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Boundary.html"
-       - "https://en.wikipedia.org/wiki/Boundary_(topology)"
-       - "https://ncatlab.org/nlab/show/boundary"
-       - "https://www.encyclopediaofmath.org/index.php/Boundary"
-      alias:
-       - frontier
-    
-    - concept: bounded-variation
-      arity: 1
-      en: bounded variation of $1
-      property: function
-      area: "analysis"
-      mathml:
-       - "<math><mrow intent='bounded-variation($a1)'><mi>BV</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BoundedVariation.html"
-       - "https://en.wikipedia.org/wiki/Bounded_variation"
-    
-    - concept: box-product
-      arity: 2
-      en: $1 box product $2
-      property: infix
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='box-product($a1,$a2)'><mi arg='a1'>X</mi><mo>☐</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Cartesian_product_of_graphs"
-      alias:
-       - cartesian-product
-    
-    - concept: brauer-group
-      arity: 1
-      en: brauer group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='brauer-group($a1)'><mi>Br</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BrauerGroup.html"
-       - "https://en.wikipedia.org/wiki/Brauer_group"
-       - "https://ncatlab.org/nlab/show/Brauer+group"
-       - "https://www.encyclopediaofmath.org/index.php/Brauer_group"
-    
-    - concept: brun-constant
-      arity: 0
+    property: symbol
+    subject-area: "order theory"
+    mathml:
+     - "<math><mi intent='bottom-element'>⊥</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Greatest_element_and_least_element"
+    alias:
+     - bottom
+     - least-element
+  
+  - concept: boundary
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: boundary of $a1
+    property: function
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='boundary($a1)'><mi>bd</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='boundary($a1)'><mi>fr</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='boundary($a1)'><mi>∂</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Boundary.html"
+     - "https://en.wikipedia.org/wiki/Boundary_(topology)"
+     - "https://ncatlab.org/nlab/show/boundary"
+     - "https://www.encyclopediaofmath.org/index.php/Boundary"
+    alias:
+     - frontier
+  
+  - concept: bounded-variation
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: bounded variation of $a1
+    property: function
+    subject-area: "analysis"
+    mathml:
+     - "<math><mrow intent='bounded-variation($a1)'><mi>BV</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BoundedVariation.html"
+     - "https://en.wikipedia.org/wiki/Bounded_variation"
+  
+  - concept: box-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 box product $a2
+    property: infix
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='box-product($a1,$a2)'><mi arg='a1'>X</mi><mo>☐</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Cartesian_product_of_graphs"
+    alias:
+     - cartesian-product
+  
+  - concept: brauer-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: brauer group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='brauer-group($a1)'><mi>Br</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BrauerGroup.html"
+     - "https://en.wikipedia.org/wiki/Brauer_group"
+     - "https://ncatlab.org/nlab/show/Brauer+group"
+     - "https://www.encyclopediaofmath.org/index.php/Brauer_group"
+  
+  - concept: brun-constant
+    arity: 0
+    arguments: []
+    speech:
       en: brun constant
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='brun-constant'><mi>B</mi><mn>4</mn></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/BrunsConstant.html"
-       - "https://en.wikipedia.org/wiki/Brun%27s_theorem"
-    
-    - concept: burnside-group
-      arity: 1
-      en: burnside group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='burnside-group($a1)'><mi>B</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://www.encyclopediaofmath.org/index.php/Burnside_group"
-    
-    - concept: cahen-constant
-      arity: 0
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='brun-constant'><mi>B</mi><mn>4</mn></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/BrunsConstant.html"
+     - "https://en.wikipedia.org/wiki/Brun%27s_theorem"
+  
+  - concept: burnside-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: burnside group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='burnside-group($a1)'><mi>B</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://www.encyclopediaofmath.org/index.php/Burnside_group"
+  
+  - concept: cahen-constant
+    arity: 0
+    arguments: []
+    speech:
       en: cahen constant
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='cahen-constant'>C</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CahensConstant.html"
-       - "https://en.wikipedia.org/wiki/Cahen%27s_constant"
-    
-    - concept: calderon-toeplitz-operator
-      arity: 2
-      en: calderon toeplitz operator $1 $2
-      property: "indexed symbol"
-      area: "operator theory"
-      mathml:
-       - "<math><mrow intent='calderon-toeplitz-operator($a1,$a2)'><msub><mi>T</mi><mrow><mi arg='a1'>b</mi><mi arg='a2'>ψ</mi></mrow></msub></mrow></math>"
-      urls: 
-       - "https://www.encyclopediaofmath.org/index.php/Calderon-Toeplitz_operator"
-    
-    - concept: canonical-commutation-relation
-      arity: 2
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='cahen-constant'>C</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CahensConstant.html"
+     - "https://en.wikipedia.org/wiki/Cahen%27s_constant"
+  
+  - concept: calderon-toeplitz-operator
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: calderon toeplitz operator $a1 $a2
+    property: "indexed symbol"
+    subject-area: "operator theory"
+    mathml:
+     - "<math><mrow intent='calderon-toeplitz-operator($a1,$a2)'><msub><mi>T</mi><mrow><mi arg='a1'>b</mi><mi arg='a2'>ψ</mi></mrow></msub></mrow></math>"
+    urls: 
+     - "https://www.encyclopediaofmath.org/index.php/Calderon-Toeplitz_operator"
+  
+  - concept: canonical-commutation-relation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: canonical commutation relation
-      property: fenced
-      area: "quantum mechanics"
-      mathml:
-       - "<math><mrow intent='canonical-commutation-relation($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Canonical_commutation_relation"
-    
-    - concept: cap-product
-      arity: 2
-      en: $1 cap product $2
-      property: infix
-      area: "algebraic topology"
-      mathml:
-       - "<math><mrow intent='cap-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⌢</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Cap_product"
-       - "https://ncatlab.org/nlab/show/cap+product"
-    
-    - concept: cardinality
-      arity: 1
-      en: cardinality of $1
-      property: many
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='cardinality($a1)'><mo>#</mo><mi arg='a1'>X</mi></mrow></math>"
-       - "<math><mrow intent='cardinality($a1)'><mi>card</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Cardinality.html"
-       - "https://en.wikipedia.org/wiki/Cardinality"
-       - "https://www.encyclopediaofmath.org/index.php/Cardinality"
-      alias:
-       - size
-    
-    - concept: carmichael-function
-      arity: 1
-      en: carmichael function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='carmichael-function($a1)'><mi>λ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CarmichaelFunction.html"
-       - "https://en.wikipedia.org/wiki/Carmichael_function"
-    
-    - concept: cartesian-product
-      arity: 2
-      en: $1 cartesian product $2
-      property: infix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='cartesian-product($a1,$a2)'><mi arg='a1'>X</mi><mo>×</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CartesianProduct.html"
-       - "https://en.wikipedia.org/wiki/Cartesian_product"
-       - "https://en.wikipedia.org/wiki/Cartesian_product_of_graphs"
-       - "https://ncatlab.org/nlab/show/cartesian+product"
-       - "https://www.encyclopediaofmath.org/index.php/Cartesian_product"
-    
-    - concept: casimir-element
-      arity: 0
+    property: fenced
+    subject-area: "quantum mechanics"
+    mathml:
+     - "<math><mrow intent='canonical-commutation-relation($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Canonical_commutation_relation"
+  
+  - concept: cap-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 cap product $a2
+    property: infix
+    subject-area: "algebraic topology"
+    mathml:
+     - "<math><mrow intent='cap-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⌢</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Cap_product"
+     - "https://ncatlab.org/nlab/show/cap+product"
+  
+  - concept: cardinality
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cardinality of $a1
+    property: many
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='cardinality($a1)'><mo>#</mo><mi arg='a1'>X</mi></mrow></math>"
+     - "<math><mrow intent='cardinality($a1)'><mi>card</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Cardinality.html"
+     - "https://en.wikipedia.org/wiki/Cardinality"
+     - "https://www.encyclopediaofmath.org/index.php/Cardinality"
+    alias:
+     - size
+  
+  - concept: carmichael-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: carmichael function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='carmichael-function($a1)'><mi>λ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CarmichaelFunction.html"
+     - "https://en.wikipedia.org/wiki/Carmichael_function"
+  
+  - concept: cartesian-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 cartesian product $a2
+    property: infix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='cartesian-product($a1,$a2)'><mi arg='a1'>X</mi><mo>×</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CartesianProduct.html"
+     - "https://en.wikipedia.org/wiki/Cartesian_product"
+     - "https://en.wikipedia.org/wiki/Cartesian_product_of_graphs"
+     - "https://ncatlab.org/nlab/show/cartesian+product"
+     - "https://www.encyclopediaofmath.org/index.php/Cartesian_product"
+  
+  - concept: casimir-element
+    arity: 0
+    arguments: []
+    speech:
       en: casimir element
-      property: symbol
-      area: "lie algebra"
-      mathml:
-       - "<math><mi intent='casimir-element'>Ω</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Casimir_element"
-    
-    - concept: catalan-constant
-      arity: 0
+    property: symbol
+    subject-area: "lie algebra"
+    mathml:
+     - "<math><mi intent='casimir-element'>Ω</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Casimir_element"
+  
+  - concept: catalan-constant
+    arity: 0
+    arguments: []
+    speech:
       en: catalan constant
-      property: symbol
-      area: "combinatorics"
-      mathml:
-       - "<math><mi intent='catalan-constant'>G</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CatalansConstant.html"
-       - "https://en.wikipedia.org/wiki/Catalan%27s_constant"
-       - "https://www.encyclopediaofmath.org/index.php/Catalan_constant"
-    
-    - concept: catalan-number
-      arity: 1
-      en: $1<i>th</i> catalan number
-      property: "indexed symbol"
-      area: "combinatorics"
-      mathml:
-       - "<math><msub intent='catalan-number($a1)'><mi>C</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CatalanNumber.html"
-       - "https://en.wikipedia.org/wiki/Catalan_number"
-       - "https://dlmf.nist.gov/26.5#E1"
-    
-    - concept: category-of-algebraic-lattices
-      arity: 0
+    property: symbol
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mi intent='catalan-constant'>G</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CatalansConstant.html"
+     - "https://en.wikipedia.org/wiki/Catalan%27s_constant"
+     - "https://www.encyclopediaofmath.org/index.php/Catalan_constant"
+  
+  - concept: catalan-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> catalan number
+    property: "indexed symbol"
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><msub intent='catalan-number($a1)'><mi>C</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CatalanNumber.html"
+     - "https://en.wikipedia.org/wiki/Catalan_number"
+     - "https://dlmf.nist.gov/26.5#E1"
+  
+  - concept: category-of-algebraic-lattices
+    arity: 0
+    arguments: []
+    speech:
       en: category of algebraic lattices
-      property: symbol
-      area: "universal algebra"
-      mathml:
-       - "<math><mi intent='category-of-algebraic-lattices'>AlgCat</mi></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/algebraic+lattice"
-    
-    - concept: category-of-sets
-      arity: 0
+    property: symbol
+    subject-area: "universal algebra"
+    mathml:
+     - "<math><mi intent='category-of-algebraic-lattices'>AlgCat</mi></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/algebraic+lattice"
+  
+  - concept: category-of-sets
+    arity: 0
+    arguments: []
+    speech:
       en: category of sets
-      property: symbol
-      area: "category theory"
-      mathml:
-       - "<math><mi intent='category-of-sets'>Set</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Category_of_sets"
-       - "https://www.encyclopediaofmath.org/index.php/Category_of_a_set"
-       - "https://www.encyclopediaofmath.org/index.php/Category_of_sets"
-    
-    - concept: category-of-small-categories
-      arity: 0
+    property: symbol
+    subject-area: "category theory"
+    mathml:
+     - "<math><mi intent='category-of-sets'>Set</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Category_of_sets"
+     - "https://www.encyclopediaofmath.org/index.php/Category_of_a_set"
+     - "https://www.encyclopediaofmath.org/index.php/Category_of_sets"
+  
+  - concept: category-of-small-categories
+    arity: 0
+    arguments: []
+    speech:
       en: category of small categories
-      property: symbol
-      area: "category theory"
-      mathml:
-       - "<math><mi intent='category-of-small-categories'>Cat</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Category_of_small_categories"
-    
-    - concept: cauchy-principal-value
-      arity: 1
-      en: cauchy principal value of $1
-      property: function
-      area: "analysis"
-      mathml:
-       - "<math><mrow intent='cauchy-principal-value($a1)'><mi>p.v.</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CauchyPrincipalValue.html"
-       - "https://en.wikipedia.org/wiki/Cauchy_principal_value"
-       - "https://dlmf.nist.gov/1.4#E24"
-       - "https://ncatlab.org/nlab/show/Cauchy+principal+value"
-    
-    - concept: cauchy-product
-      arity: 2
-      en: $1 cauchy product $2
-      property: infix
-      area: "analysis"
-      mathml:
-       - "<math><mrow intent='cauchy-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⋅</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CauchyProduct.html"
-       - "https://en.wikipedia.org/wiki/Cauchy_product"
-    
-    - concept: cavitation-number
-      arity: 0
+    property: symbol
+    subject-area: "category theory"
+    mathml:
+     - "<math><mi intent='category-of-small-categories'>Cat</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Category_of_small_categories"
+  
+  - concept: cauchy-principal-value
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cauchy principal value of $a1
+    property: function
+    subject-area: "analysis"
+    mathml:
+     - "<math><mrow intent='cauchy-principal-value($a1)'><mi>p.v.</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CauchyPrincipalValue.html"
+     - "https://en.wikipedia.org/wiki/Cauchy_principal_value"
+     - "https://dlmf.nist.gov/1.4#E24"
+     - "https://ncatlab.org/nlab/show/Cauchy+principal+value"
+  
+  - concept: cauchy-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 cauchy product $a2
+    property: infix
+    subject-area: "analysis"
+    mathml:
+     - "<math><mrow intent='cauchy-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⋅</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CauchyProduct.html"
+     - "https://en.wikipedia.org/wiki/Cauchy_product"
+  
+  - concept: cavitation-number
+    arity: 0
+    arguments: []
+    speech:
       en: cavitation number
-      property: symbol
-      area: "physics"
-      mathml:
-       - "<math><mi intent='cavitation-number'>Ca</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Euler_number_(physics)#Cavitation_number"
-    
-    - concept: cayley-table
-      arity: 1
-      en: cayley table of $1
-      property: mtable
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='cayley-table($a1)'><mtable arg='a1'><mtr><mtd><mo>×</mo></mtd><mtd><mn>1</mn></mtd><mtd><mn>−1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>−1</mn></mtd></mtr><mtr><mtd><mn>−1</mn></mtd><mtd><mn>−1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CayleyTable.html"
-       - "https://en.wikipedia.org/wiki/Cayley_table"
-       - "https://www.encyclopediaofmath.org/index.php/Cayley_table"
-    
-    - concept: ceiling
-      arity: 1
-      en: ceiling of $1
-      property: fenced, function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='ceiling($a1)'><mo>⌈</mo><mi arg='a1'>X</mi><mo>⌉</mo></mrow></math>"
-       - "<math><mrow intent='ceiling($a1)'><mo>&#x27e7;</mo><mi arg='a1'>X</mi><mo>&#x27e6;</mo></mrow></math>"
-       - "<math><mrow intent='ceiling($a1)'><mo>]</mo><mi arg='a1'>X</mi><mo>[</mo></mrow></math>"
-       - "<math><mrow intent='ceiling($a1)'><mi>ceil</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions"
-       - "https://youtu.be/RxNs4SwP6lk"
-    
-    - concept: center
-      arity: 1
-      en: center of $1
-      property: function
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='center($a1)'><mi>Z</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Center_(group_theory)"
-       - "https://en.wikipedia.org/wiki/Center_(algebra)"
-       - "https://ncatlab.org/nlab/show/center"
-      alias:
-       - centre
-    
-    - concept: centralizer
-      arity: 1
-      en: centralizer of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='centralizer($a1)'><mi>C</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Centralizer.html"
-       - "https://en.wikipedia.org/wiki/Centralizer_and_normalizer"
-       - "https://ncatlab.org/nlab/show/centralizer"
-       - "https://www.encyclopediaofmath.org/index.php/Centralizer"
-    
-    - concept: chain
-      arity: 1
-      en: $1 chains
-      property: unit
-      area: "imperial units"
-      mathml:
-       - "<math><mrow intent='chain($a1)'><mi arg='a1'>x</mi><mo>&#x2009;</mo><mi>chain</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Chain_(unit)"
-    
-    - concept: champernowne-constant
-      arity: 0
+    property: symbol
+    subject-area: "physics"
+    mathml:
+     - "<math><mi intent='cavitation-number'>Ca</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Euler_number_(physics)#Cavitation_number"
+  
+  - concept: cayley-table
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cayley table of $a1
+    property: mtable
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='cayley-table($a1)'><mtable arg='a1'><mtr><mtd><mo>×</mo></mtd><mtd><mn>1</mn></mtd><mtd><mn>−1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>−1</mn></mtd></mtr><mtr><mtd><mn>−1</mn></mtd><mtd><mn>−1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CayleyTable.html"
+     - "https://en.wikipedia.org/wiki/Cayley_table"
+     - "https://www.encyclopediaofmath.org/index.php/Cayley_table"
+  
+  - concept: ceiling
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: ceiling of $a1
+    property: fenced, function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='ceiling($a1)'><mo>⌈</mo><mi arg='a1'>X</mi><mo>⌉</mo></mrow></math>"
+     - "<math><mrow intent='ceiling($a1)'><mo>&#x27e7;</mo><mi arg='a1'>X</mi><mo>&#x27e6;</mo></mrow></math>"
+     - "<math><mrow intent='ceiling($a1)'><mo>]</mo><mi arg='a1'>X</mi><mo>[</mo></mrow></math>"
+     - "<math><mrow intent='ceiling($a1)'><mi>ceil</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions"
+     - "https://youtu.be/RxNs4SwP6lk"
+  
+  - concept: center
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: center of $a1
+    property: function
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='center($a1)'><mi>Z</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Center_(group_theory)"
+     - "https://en.wikipedia.org/wiki/Center_(algebra)"
+     - "https://ncatlab.org/nlab/show/center"
+    alias:
+     - centre
+  
+  - concept: centralizer
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: centralizer of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='centralizer($a1)'><mi>C</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Centralizer.html"
+     - "https://en.wikipedia.org/wiki/Centralizer_and_normalizer"
+     - "https://ncatlab.org/nlab/show/centralizer"
+     - "https://www.encyclopediaofmath.org/index.php/Centralizer"
+  
+  - concept: chain
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1 chains
+    property: unit
+    subject-area: "imperial units"
+    mathml:
+     - "<math><mrow intent='chain($a1)'><mi arg='a1'>x</mi><mo>&#x2009;</mo><mi>chain</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Chain_(unit)"
+  
+  - concept: champernowne-constant
+    arity: 0
+    arguments: []
+    speech:
       en: champernowne constant
-      property: constant
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='champernowne-constant'>C</mi></math>"
-       - "<math><msup intent='champernowne-constant'><mi>C</mi><mn>10</mn></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ChampernowneConstant.html"
-       - "https://en.wikipedia.org/wiki/Champernowne_constant"
-    
-    - concept: character
-      arity: 1
-      en: character of $1
-      property: "indexed function"
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='character($a1)'><mi>χ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Character.html"
-       - "https://en.wikipedia.org/wiki/Character_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Event-driven_finite-state_machine"
-       - "https://en.wikipedia.org/wiki/Character_theory"
-       - "https://en.wikipedia.org/wiki/Multiplicative_character"
-       - "https://ncatlab.org/nlab/show/character"
-    
-    - concept: characteristic
-      arity: 1
-      en: characteristic of $1
-      property: function
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='characteristic($a1)'><mi>char</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Characteristic.html"
-       - "https://en.wikipedia.org/wiki/Characteristic_(algebra)"
-       - "https://ncatlab.org/nlab/show/characteristic"
-       - "https://www.encyclopediaofmath.org/index.php/Characteristic"
-    
-    - concept: characteristic-function
-      arity: 1
-      en: characteristic function of $1
-      property: "indexed function, function"
-      area: "probability theory"
-      mathml:
-       - "<math><msub intent='characteristic-function($a1)'><mi>𝟏</mi><mi arg='a1'>X</mi></msub></math>"
-       - "<math><mrow intent='characteristic-function($a1)'><mn>1</mn><mrow><mo>{</mo><mi arg='a1'>X</mi><mo>}</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CharacteristicFunction.html"
-       - "https://en.wikipedia.org/wiki/Characteristic_function_(probability_theory)"
-       - "https://en.wikipedia.org/wiki/Indicator_function"
-       - "https://en.wikipedia.org/wiki/Characteristic_function_(convex_analysis)"
-       - "https://ncatlab.org/nlab/show/characteristic+function"
-       - "https://www.encyclopediaofmath.org/index.php/Characteristic_function"
-       - "https://en.wikipedia.org/wiki/Expected_value#Interchanging_limits_and_expectation"
-      alias:
-       - indicator-function
-    
-    - concept: characteristic-subgroup
-      arity: 2
-      en: $1 characteristic subgroup $2
-      property: infix
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='characteristic-subgroup($a1,$a2)'><mi arg='a1'>X</mi><mo>char</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Characteristic_subgroup"
-       - "https://www.encyclopediaofmath.org/index.php/Characteristic_subgroup"
-    
-    - concept: charlier-polynomial
-      arity: 1
-      en: charlier polynomial of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='charlier-polynomial($a1)'><mi>C</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CharlierPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Charlier_polynomials"
-       - "https://dlmf.nist.gov/18.19#T1.t1.r11"
-       - "https://www.encyclopediaofmath.org/index.php/Charlier_polynomials"
-    
-    - concept: chebyshev-polynomial-of-first-kind
-      arity: 1
-      en: chebyshev polynomial of first kind of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='chebyshev-polynomial-of-first-kind($a1)'><mi>θ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='chebyshev-polynomial-of-first-kind($a1)'><mi>ϑ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='chebyshev-polynomial-of-first-kind($a1)'><mi>T</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html"
-       - "https://en.wikipedia.org/wiki/Chebyshev_polynomials"
-       - "https://dlmf.nist.gov/18.3#T1.t1.r8"
-      alias:
-       - first-chebyshev-function
-    
-    - concept: chebyshev-polynomial-of-second-kind
-      arity: 1
-      en: chebyshev polynomial of second kind of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='chebyshev-polynomial-of-second-kind($a1)'><mi>ψ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='chebyshev-polynomial-of-second-kind($a1)'><mi>U</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html"
-       - "https://en.wikipedia.org/wiki/Chebyshev_polynomials"
-       - "https://dlmf.nist.gov/18.3#T1.t1.r11"
-      alias:
-       - second-chebyshev-function
-    
-    - concept: cheeger-constant
-      arity: 1
-      en: cheeger constant of $1
-      property: function
-      area: "Riemannian geometry"
-      mathml:
-       - "<math><mrow intent='cheeger-constant($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Cheeger_constant"
-    
-    - concept: cheeger-number
-      arity: 1
-      en: cheeger number of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='cheeger-number($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Cheeger_constant_(graph_theory)"
-      alias:
-       - cheeger-constant
-       - isoperimetric-number
-    
-    - concept: chemical-equilibrium
-      arity: 2
-      en: $1 chemical equilibrium $2
-      property: infix
-      area: "chemistry"
-      mathml:
-       - "<math><mrow intent='chemical-equilibrium($a1,$a2)'><mi arg='a1'>X</mi><mo>⇌</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Chemical_equilibrium"
-      alias:
-       - equilibrium
-    
-    - concept: chi-squared-distribution
-      arity: 0
+    property: constant
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='champernowne-constant'>C</mi></math>"
+     - "<math><msup intent='champernowne-constant'><mi>C</mi><mn>10</mn></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ChampernowneConstant.html"
+     - "https://en.wikipedia.org/wiki/Champernowne_constant"
+  
+  - concept: character
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: character of $a1
+    property: "indexed function"
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='character($a1)'><mi>χ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Character.html"
+     - "https://en.wikipedia.org/wiki/Character_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Event-driven_finite-state_machine"
+     - "https://en.wikipedia.org/wiki/Character_theory"
+     - "https://en.wikipedia.org/wiki/Multiplicative_character"
+     - "https://ncatlab.org/nlab/show/character"
+  
+  - concept: characteristic
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: characteristic of $a1
+    property: function
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='characteristic($a1)'><mi>char</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Characteristic.html"
+     - "https://en.wikipedia.org/wiki/Characteristic_(algebra)"
+     - "https://ncatlab.org/nlab/show/characteristic"
+     - "https://www.encyclopediaofmath.org/index.php/Characteristic"
+  
+  - concept: characteristic-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: characteristic function of $a1
+    property: "indexed function, function"
+    subject-area: "probability theory"
+    mathml:
+     - "<math><msub intent='characteristic-function($a1)'><mi>𝟏</mi><mi arg='a1'>X</mi></msub></math>"
+     - "<math><mrow intent='characteristic-function($a1)'><mn>1</mn><mrow><mo>{</mo><mi arg='a1'>X</mi><mo>}</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CharacteristicFunction.html"
+     - "https://en.wikipedia.org/wiki/Characteristic_function_(probability_theory)"
+     - "https://en.wikipedia.org/wiki/Indicator_function"
+     - "https://en.wikipedia.org/wiki/Characteristic_function_(convex_analysis)"
+     - "https://ncatlab.org/nlab/show/characteristic+function"
+     - "https://www.encyclopediaofmath.org/index.php/Characteristic_function"
+     - "https://en.wikipedia.org/wiki/Expected_value#Interchanging_limits_and_expectation"
+    alias:
+     - indicator-function
+  
+  - concept: characteristic-subgroup
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 characteristic subgroup $a2
+    property: infix
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='characteristic-subgroup($a1,$a2)'><mi arg='a1'>X</mi><mo>char</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Characteristic_subgroup"
+     - "https://www.encyclopediaofmath.org/index.php/Characteristic_subgroup"
+  
+  - concept: charlier-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: charlier polynomial of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='charlier-polynomial($a1)'><mi>C</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CharlierPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Charlier_polynomials"
+     - "https://dlmf.nist.gov/18.19#T1.t1.r11"
+     - "https://www.encyclopediaofmath.org/index.php/Charlier_polynomials"
+  
+  - concept: chebyshev-polynomial-of-first-kind
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: chebyshev polynomial of first kind of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='chebyshev-polynomial-of-first-kind($a1)'><mi>θ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='chebyshev-polynomial-of-first-kind($a1)'><mi>ϑ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='chebyshev-polynomial-of-first-kind($a1)'><mi>T</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html"
+     - "https://en.wikipedia.org/wiki/Chebyshev_polynomials"
+     - "https://dlmf.nist.gov/18.3#T1.t1.r8"
+    alias:
+     - first-chebyshev-function
+  
+  - concept: chebyshev-polynomial-of-second-kind
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: chebyshev polynomial of second kind of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='chebyshev-polynomial-of-second-kind($a1)'><mi>ψ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='chebyshev-polynomial-of-second-kind($a1)'><mi>U</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html"
+     - "https://en.wikipedia.org/wiki/Chebyshev_polynomials"
+     - "https://dlmf.nist.gov/18.3#T1.t1.r11"
+    alias:
+     - second-chebyshev-function
+  
+  - concept: cheeger-constant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cheeger constant of $a1
+    property: function
+    subject-area: "Riemannian geometry"
+    mathml:
+     - "<math><mrow intent='cheeger-constant($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Cheeger_constant"
+  
+  - concept: cheeger-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cheeger number of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='cheeger-number($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Cheeger_constant_(graph_theory)"
+    alias:
+     - cheeger-constant
+     - isoperimetric-number
+  
+  - concept: chemical-equilibrium
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 chemical equilibrium $a2
+    property: infix
+    subject-area: "chemistry"
+    mathml:
+     - "<math><mrow intent='chemical-equilibrium($a1,$a2)'><mi arg='a1'>X</mi><mo>⇌</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Chemical_equilibrium"
+    alias:
+     - equilibrium
+  
+  - concept: chi-squared-distribution
+    arity: 0
+    arguments: []
+    speech:
       en: chi squared distribution
-      property: symbol
-      area: "probability theory"
-      mathml:
-       - "<math><msup intent='chi-squared-distribution'><mi>χ</mi><mn>2</mn></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Chi-SquaredDistribution.html"
-       - "https://en.wikipedia.org/wiki/Chi-squared_distribution"
-       - "https://www.encyclopediaofmath.org/index.php/Chi-squared_distribution"
-    
-    - concept: chord
-      arity: 1
-      en: chord of $1
-      property: function
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='chord($a1)'><mi>crd</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Chord_(geometry)"
-    
-    - concept: christoffel-symbol-of-first-kind
-      arity: 3
-      en: christoffel symbol of first kind of $1, $2, $3
-      property: "indexed symbol"
-      area: "Riemannian geometry"
-      mathml:
-       - "<math><mrow intent='christoffel-symbol-of-first-kind($a1,$a2,$a3)'><msub><mi>&#x0393;</mi><mrow><mi arg='a3'>k</mi><mi arg='a1'>i</mi><mi arg='a2'>j</mi></mrow></msub></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ChristoffelSymbol.html"
-       - "https://en.wikipedia.org/wiki/Christoffel_symbols"
-       - "https://ncatlab.org/nlab/show/Christoffel+symbols"
-       - "https://www.encyclopediaofmath.org/index.php/Christoffel_symbol"
-    
-    - concept: christoffel-symbol-of-second-kind
-      arity: 3
-      en: christoffel symbol of second kind of $1 $2 $3
-      property: "indexed symbol"
-      area: "Riemannian geometry"
-      mathml:
-       - "<math><mmultiscripts intent='christoffel-symbol-of-second-kind($a1,$a2,$a3)'><mi>&#x0393;</mi><mrow/><mi arg='a3'>k</mi><mi arg='a1'>i</mi><mrow/><mi arg='a2'>j</mi><mrow/></mmultiscripts></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ChristoffelSymbol.html"
-       - "https://en.wikipedia.org/wiki/Christoffel_symbols"
-       - "https://ncatlab.org/nlab/show/Christoffel+symbols"
-       - "https://www.encyclopediaofmath.org/index.php/Christoffel_symbol"
-    
-    - concept: chromatic-polynomial
-      arity: 1
-      en: chromatic polynomial of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><msub intent='chromatic-polynomial($a1)'><mi>P</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='chromatic-polynomial($a1)'><mi>π</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='chromatic-polynomial($a1)'><mi>χ</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ChromaticPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Chromatic_polynomial"
-    
-    - concept: classifying-space
-      arity: 1
-      en: classifying space of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='classifying-space($a1)'><mi>B</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='classifying-space($a1)'><mi>ℬ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Classifying_space"
-       - "https://ncatlab.org/nlab/show/classifying+space"
-       - "https://www.encyclopediaofmath.org/index.php/Classifying_space"
-    
-    - concept: clausen-function
-      arity: 1
-      en: clausen function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='clausen-function($a1)'><msub><mi>Cl</mi><mn>2</mn></msub><mrow><mo>(</mo><mi arg='a1'>&#x03c6;</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Clausen_function"
-    
-    - concept: clebsch-gordan-coefficient
-      arity: 8
-      en: clebsch gordan coefficient $1 $2 $3 $4 $5 $6 $7 $8
-      property: fenced
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='clebsch-gordan-coefficient($a1,$a2,$a3,$a4,$a5,$a6,$a7,$a8)'><mo>(</mo><msub arg='a1'><mi>j</mi><mn>1</mn></msub><msub arg='a2'><mi>j</mi><mn>2</mn></msub><msub arg='a3'><mi>m</mi><mn>1</mn></msub><msub arg='a4'><mi>m</mi><mn>2</mn></msub><mo>|</mo><msub arg='a5'><mi>j</mi><mn>1</mn></msub><msub arg='a6'><mi>j</mi><mn>2</mn></msub><mi arg='a7'>j</mi><mi arg='a8'>m</mi><mo>)</mo></mrow></math>"
-       - "<math><mrow intent='clebsch-gordan-coefficient($a1,$a2,$a3,$a4,$a5,$a6,$a7,$a8)'><mo>⟨</mo><msub arg='a1'><mi>j</mi><mn>1</mn></msub><msub arg='a2'><mi>j</mi><mn>2</mn></msub><msub arg='a3'><mi>m</mi><mn>1</mn></msub><msub arg='a4'><mi>m</mi><mn>2</mn></msub><mo>|</mo><msub arg='a5'><mi>j</mi><mn>1</mn></msub><msub arg='a6'><mi>j</mi><mn>2</mn></msub><mi arg='a7'>j</mi><mi arg='a8'>m</mi><mo>⟩</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Clebsch-GordanCoefficient.html"
-       - "https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients"
-       - "https://dlmf.nist.gov/34.1#p4"
-       - "https://ncatlab.org/nlab/show/Clebsch-Gordan+coefficient"
-    
-    - concept: clifford-algebra
-      arity: 1
-      en: clifford algebra of $1
-      property: function
-      area: "universal algebra"
-      mathml:
-       - "<math><mrow intent='clifford-algebra($a1)'><mi>Cl</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Clifford_algebra"
-    
-    - concept: clique
-      arity: 0
+    property: symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><msup intent='chi-squared-distribution'><mi>χ</mi><mn>2</mn></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Chi-SquaredDistribution.html"
+     - "https://en.wikipedia.org/wiki/Chi-squared_distribution"
+     - "https://www.encyclopediaofmath.org/index.php/Chi-squared_distribution"
+  
+  - concept: chord
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: chord of $a1
+    property: function
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='chord($a1)'><mi>crd</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Chord_(geometry)"
+  
+  - concept: christoffel-symbol-of-first-kind
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: christoffel symbol of first kind of $a1, $a2, $a3
+    property: "indexed symbol"
+    subject-area: "Riemannian geometry"
+    mathml:
+     - "<math><mrow intent='christoffel-symbol-of-first-kind($a1,$a2,$a3)'><msub><mi>&#x0393;</mi><mrow><mi arg='a3'>k</mi><mi arg='a1'>i</mi><mi arg='a2'>j</mi></mrow></msub></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ChristoffelSymbol.html"
+     - "https://en.wikipedia.org/wiki/Christoffel_symbols"
+     - "https://ncatlab.org/nlab/show/Christoffel+symbols"
+     - "https://www.encyclopediaofmath.org/index.php/Christoffel_symbol"
+  
+  - concept: christoffel-symbol-of-second-kind
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: christoffel symbol of second kind of $a1 $a2 $a3
+    property: "indexed symbol"
+    subject-area: "Riemannian geometry"
+    mathml:
+     - "<math><mmultiscripts intent='christoffel-symbol-of-second-kind($a1,$a2,$a3)'><mi>&#x0393;</mi><mrow/><mi arg='a3'>k</mi><mi arg='a1'>i</mi><mrow/><mi arg='a2'>j</mi><mrow/></mmultiscripts></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ChristoffelSymbol.html"
+     - "https://en.wikipedia.org/wiki/Christoffel_symbols"
+     - "https://ncatlab.org/nlab/show/Christoffel+symbols"
+     - "https://www.encyclopediaofmath.org/index.php/Christoffel_symbol"
+  
+  - concept: chromatic-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: chromatic polynomial of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><msub intent='chromatic-polynomial($a1)'><mi>P</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='chromatic-polynomial($a1)'><mi>π</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='chromatic-polynomial($a1)'><mi>χ</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ChromaticPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Chromatic_polynomial"
+  
+  - concept: classifying-space
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: classifying space of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='classifying-space($a1)'><mi>B</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='classifying-space($a1)'><mi>ℬ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Classifying_space"
+     - "https://ncatlab.org/nlab/show/classifying+space"
+     - "https://www.encyclopediaofmath.org/index.php/Classifying_space"
+  
+  - concept: clausen-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: clausen function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='clausen-function($a1)'><msub><mi>Cl</mi><mn>2</mn></msub><mrow><mo>(</mo><mi arg='a1'>&#x03c6;</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Clausen_function"
+  
+  - concept: clebsch-gordan-coefficient
+    arity: 8
+    arguments: [$a1, $a2, $a3, $a4, $a6, $a7, $a8]
+    speech:
+      en: clebsch gordan coefficient $a1 $a2 $a3 $a4 $a5 $a6 $a7 $a8
+    property: fenced
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='clebsch-gordan-coefficient($a1,$a2,$a3,$a4,$a5,$a6,$a7,$a8)'><mo>(</mo><msub arg='a1'><mi>j</mi><mn>1</mn></msub><msub arg='a2'><mi>j</mi><mn>2</mn></msub><msub arg='a3'><mi>m</mi><mn>1</mn></msub><msub arg='a4'><mi>m</mi><mn>2</mn></msub><mo>|</mo><msub arg='a5'><mi>j</mi><mn>1</mn></msub><msub arg='a6'><mi>j</mi><mn>2</mn></msub><mi arg='a7'>j</mi><mi arg='a8'>m</mi><mo>)</mo></mrow></math>"
+     - "<math><mrow intent='clebsch-gordan-coefficient($a1,$a2,$a3,$a4,$a5,$a6,$a7,$a8)'><mo>⟨</mo><msub arg='a1'><mi>j</mi><mn>1</mn></msub><msub arg='a2'><mi>j</mi><mn>2</mn></msub><msub arg='a3'><mi>m</mi><mn>1</mn></msub><msub arg='a4'><mi>m</mi><mn>2</mn></msub><mo>|</mo><msub arg='a5'><mi>j</mi><mn>1</mn></msub><msub arg='a6'><mi>j</mi><mn>2</mn></msub><mi arg='a7'>j</mi><mi arg='a8'>m</mi><mo>⟩</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Clebsch-GordanCoefficient.html"
+     - "https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients"
+     - "https://dlmf.nist.gov/34.1#p4"
+     - "https://ncatlab.org/nlab/show/Clebsch-Gordan+coefficient"
+  
+  - concept: clifford-algebra
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: clifford algebra of $a1
+    property: function
+    subject-area: "universal algebra"
+    mathml:
+     - "<math><mrow intent='clifford-algebra($a1)'><mi>Cl</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Clifford_algebra"
+  
+  - concept: clique
+    arity: 0
+    arguments: []
+    speech:
       en: clique
-      property: symbol
-      area: "graph theory"
-      mathml:
-       - "<math><mi intent='clique'>C</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Clique.html"
-       - "https://en.wikipedia.org/wiki/Clique_(graph_theory)"
-       - "https://ncatlab.org/nlab/show/clique"
-    
-    - concept: clique-number
-      arity: 1
-      en: clique number of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='clique-number($a1)'><mi>ω</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Clique_number"
-    
-    - concept: closed-ball
-      arity: 2
-      en: closed ball $1 $2
-      property: mixfix
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='closed-ball($a1,$a2)'><msub><mi>B</mi><mi arg='a1'>r</mi></msub><mrow><mo>[</mo><mi arg='a2'>p</mi><mo>]</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/OpenBall.html"
-       - "https://en.wikipedia.org/wiki/Ball_(mathematics)"
-      alias:
-       - closed-metric-ball
-    
-    - concept: closed-interval
-      arity: 2
+    property: symbol
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mi intent='clique'>C</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Clique.html"
+     - "https://en.wikipedia.org/wiki/Clique_(graph_theory)"
+     - "https://ncatlab.org/nlab/show/clique"
+  
+  - concept: clique-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: clique number of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='clique-number($a1)'><mi>ω</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Clique_number"
+  
+  - concept: closed-ball
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: closed ball $a1 $a2
+    property: mixfix
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='closed-ball($a1,$a2)'><msub><mi>B</mi><mi arg='a1'>r</mi></msub><mrow><mo>[</mo><mi arg='a2'>p</mi><mo>]</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/OpenBall.html"
+     - "https://en.wikipedia.org/wiki/Ball_(mathematics)"
+    alias:
+     - closed-metric-ball
+  
+  - concept: closed-interval
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: closed interval
-      property: fenced
-      area: "calculus"
-      mathml:
-       - "<math><mrow intent='closed-interval($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ClosedInterval.html"
-       - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r29"
-    
-    - concept: closed-neighbourhood
-      arity: 2
-      en: closed neighbourhood of $2 in $1
-      property: "indexed function, function"
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='closed-neighbourhood($a1,$a2)'><msub><mi>N</mi><mi arg='a2'>v</mi></msub><mrow><mo>[</mo><mi arg='a1'>G</mi><mo>]</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Neighbourhood_(graph_theory)"
-    
-    - concept: closure
-      arity: 1
-      en: closure of $1
-      property: "function, msup"
-      area: "abstract algebra,, topology"
-      mathml:
-       - "<math><mrow intent='closure($a1)'><mi>cl</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='closure($a1)'><mi>Cl</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><msup intent='closure($a1)'><mi arg='a1'>X</mi><mo>−</mo></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Closure.html"
-       - "https://en.wikipedia.org/wiki/Congruence_closure"
-       - "https://en.wikipedia.org/wiki/Closure_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Closure_(topology)"
-       - "https://en.wikipedia.org/wiki/Closure_problem"
-    
-    - concept: codimension
-      arity: 1
-      en: codimension of $1
-      property: function
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='codimension($a1)'><mi>codim</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Codimension.html"
-       - "https://en.wikipedia.org/wiki/Codimension"
-       - "https://ncatlab.org/nlab/show/codimension"
-       - "https://www.encyclopediaofmath.org/index.php/Codimension"
-    
-    - concept: cofinality
-      arity: 1
-      en: cofinality of $1
-      property: function
-      area: "order theory"
-      mathml:
-       - "<math><mrow intent='cofinality($a1)'><mi>cf</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Cofinality"
-       - "https://ncatlab.org/nlab/show/cofinality"
-    
-    - concept: cofinite-filter
-      arity: 0
+    property: fenced
+    subject-area: "calculus"
+    mathml:
+     - "<math><mrow intent='closed-interval($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ClosedInterval.html"
+     - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r29"
+  
+  - concept: closed-neighbourhood
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: closed neighbourhood of $a2 in $a1
+    property: "indexed function, function"
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='closed-neighbourhood($a1,$a2)'><msub><mi>N</mi><mi arg='a2'>v</mi></msub><mrow><mo>[</mo><mi arg='a1'>G</mi><mo>]</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Neighbourhood_(graph_theory)"
+  
+  - concept: closure
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: closure of $a1
+    property: "function, msup"
+    subject-area: "abstract algebra,, topology"
+    mathml:
+     - "<math><mrow intent='closure($a1)'><mi>cl</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='closure($a1)'><mi>Cl</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><msup intent='closure($a1)'><mi arg='a1'>X</mi><mo>−</mo></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Closure.html"
+     - "https://en.wikipedia.org/wiki/Congruence_closure"
+     - "https://en.wikipedia.org/wiki/Closure_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Closure_(topology)"
+     - "https://en.wikipedia.org/wiki/Closure_problem"
+  
+  - concept: codimension
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: codimension of $a1
+    property: function
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='codimension($a1)'><mi>codim</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Codimension.html"
+     - "https://en.wikipedia.org/wiki/Codimension"
+     - "https://ncatlab.org/nlab/show/codimension"
+     - "https://www.encyclopediaofmath.org/index.php/Codimension"
+  
+  - concept: cofinality
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cofinality of $a1
+    property: function
+    subject-area: "order theory"
+    mathml:
+     - "<math><mrow intent='cofinality($a1)'><mi>cf</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Cofinality"
+     - "https://ncatlab.org/nlab/show/cofinality"
+  
+  - concept: cofinite-filter
+    arity: 0
+    arguments: []
+    speech:
       en: cofinite filter
-      property: symbol
-      area: "order theory"
-      mathml:
-       - "<math><mi intent='cofinite-filter'>F</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CofiniteFilter.html"
-       - "https://en.wikipedia.org/wiki/Fr%C3%A9chet_filter"
-      alias:
-       - frechet-filter
-    
-    - concept: coherence
-      arity: 1
-      en: coherence of $1
-      property: "indexed function"
-      area: "signal processing, quantum physics"
-      mathml:
-       - "<math><mrow intent='coherence($a1)'><mi>C</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='coherence($a1)'><mi>γ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Coherence_(signal_processing)"
-       - "https://en.wikipedia.org/wiki/Coherence_(physics)"
-    
-    - concept: coimage
-      arity: 1
-      en: coimage of $1
-      property: function
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='coimage($a1)'><mi>coim</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Coimage"
-       - "https://ncatlab.org/nlab/show/coimage"
-    
-    - concept: cokernel
-      arity: 1
-      en: cokernel of $1
-      property: function
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='cokernel($a1)'><mi>coker</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Cokernel.html"
-       - "https://en.wikipedia.org/wiki/Cokernel"
-       - "https://ncatlab.org/nlab/show/cokernel"
-       - "https://www.encyclopediaofmath.org/index.php/Cokernel"
-    
-    - concept: column-vector
-      arity: ">=0"
-      en: column vector of $1 $2 ...
-      property: mtable
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='column-vector($a1,a2,a3)'><mo>(</mo><mtable><mtr><mtd><mi arg='a1'>x</mi></mtd></mtr><mtr><mtd><mi arg='a2'>y</mi></mtd></mtr><mtr><mtd><mi arg='a3'>z</mi></mtd></mtr></mtable><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ColumnVector.html"
-       - "https://en.wikipedia.org/wiki/Column_vector"
-    
-    - concept: comma-category
-      arity: 2
-      en: comma category $1 $2
-      property: mixfix
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='comma-category($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>↓</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Comma_category"
-    
-    - concept: commutator
-      arity: 2
+    property: symbol
+    subject-area: "order theory"
+    mathml:
+     - "<math><mi intent='cofinite-filter'>F</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CofiniteFilter.html"
+     - "https://en.wikipedia.org/wiki/Fr%C3%A9chet_filter"
+    alias:
+     - frechet-filter
+  
+  - concept: coherence
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: coherence of $a1
+    property: "indexed function"
+    subject-area: "signal processing, quantum physics"
+    mathml:
+     - "<math><mrow intent='coherence($a1)'><mi>C</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='coherence($a1)'><mi>γ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Coherence_(signal_processing)"
+     - "https://en.wikipedia.org/wiki/Coherence_(physics)"
+  
+  - concept: coimage
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: coimage of $a1
+    property: function
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='coimage($a1)'><mi>coim</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Coimage"
+     - "https://ncatlab.org/nlab/show/coimage"
+  
+  - concept: cokernel
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cokernel of $a1
+    property: function
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='cokernel($a1)'><mi>coker</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Cokernel.html"
+     - "https://en.wikipedia.org/wiki/Cokernel"
+     - "https://ncatlab.org/nlab/show/cokernel"
+     - "https://www.encyclopediaofmath.org/index.php/Cokernel"
+  
+  - concept: column-vector
+    arity: ">=0"
+    speech:
+      en: column vector of $a1 $a2 ...
+    property: mtable
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='column-vector($a1,$a2,$a3)'><mo>(</mo><mtable><mtr><mtd><mi arg='a1'>x</mi></mtd></mtr><mtr><mtd><mi arg='a2'>y</mi></mtd></mtr><mtr><mtd><mi arg='a3'>z</mi></mtd></mtr></mtable><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ColumnVector.html"
+     - "https://en.wikipedia.org/wiki/Column_vector"
+  
+  - concept: comma-category
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: comma category $a1 $a2
+    property: mixfix
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='comma-category($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>↓</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Comma_category"
+  
+  - concept: commutator
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: commutator
-      property: fenced
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='commutator($a1,$a2)'><mo>[</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Commutator.html"
-       - "https://en.wikipedia.org/wiki/Commutator"
-       - "https://ncatlab.org/nlab/show/commutator"
-       - "https://www.encyclopediaofmath.org/index.php/Commutator"
-    
-    - concept: commutator-subgroup
-      arity: 1
-      en: commutator subgroup of $1
-      property: msup, fenced
-      area: "abstract algebra"
-      mathml:
-       - "<math><msup intent='commutator-subgroup($a1)'><mi arg='a1'>X</mi><mo>'</mo></msup></math>"
-       - "<math><msup intent='commutator-subgroup($a1)'><mi arg='a1'>X</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math>"
-       - "<math><mrow intent='commutator-subgroup($a1)'><mo>[</mo><mi arg='a1'>X</mi><mo>,</mo><mi>X</mi><mo>]</mo></mrow></math>"
-      notationb: "msup $1 (1)"
-      notationa: "mrow [ $1, $1 ]"
-      urls: 
-       - "https://mathworld.wolfram.com/CommutatorSubgroup.html"
-       - "https://en.wikipedia.org/wiki/Commutator_subgroup"
-       - "https://en.wikipedia.org/wiki/Derived_series"
-       - "https://ncatlab.org/nlab/show/commutator+subgroup"
-       - "https://www.encyclopediaofmath.org/index.php/Commutator_subgroup"
-      alias:
-       - derived-subgroup
-    
-    - concept: companion-lehmer-number
-      arity: 1
-      en: companion lehmer number of $1
-      property: "indexed function"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='companion-lehmer-number($a1)'><mi>V</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LehmerNumber.html"
-       - "https://mathworld.wolfram.com/LehmersNumber.html"
-       - "https://en.wikipedia.org/wiki/Lehmer_number"
-    
-    - concept: comparability
-      arity: 2
-      en: $1 comparability $2
-      property: infix
-      area: "order theory"
-      mathml:
-       - "<math><mrow intent='comparability($a1,$a2)'><mi arg='a1'>X</mi><mo>⪋</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Comparability"
-      alias:
-       - comparable
-    
-    - concept: complement-of-interval
-      arity: 2
+    property: fenced
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='commutator($a1,$a2)'><mo>[</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Commutator.html"
+     - "https://en.wikipedia.org/wiki/Commutator"
+     - "https://ncatlab.org/nlab/show/commutator"
+     - "https://www.encyclopediaofmath.org/index.php/Commutator"
+  
+  - concept: commutator-subgroup
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: commutator subgroup of $a1
+    property: msup, fenced
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><msup intent='commutator-subgroup($a1)'><mi arg='a1'>X</mi><mo>'</mo></msup></math>"
+     - "<math><msup intent='commutator-subgroup($a1)'><mi arg='a1'>X</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math>"
+     - "<math><mrow intent='commutator-subgroup($a1)'><mo>[</mo><mi arg='a1'>X</mi><mo>,</mo><mi>X</mi><mo>]</mo></mrow></math>"
+    notationb: "msup $a1 (1)"
+    notationa: "mrow [ $a1, $a1 ]"
+    urls: 
+     - "https://mathworld.wolfram.com/CommutatorSubgroup.html"
+     - "https://en.wikipedia.org/wiki/Commutator_subgroup"
+     - "https://en.wikipedia.org/wiki/Derived_series"
+     - "https://ncatlab.org/nlab/show/commutator+subgroup"
+     - "https://www.encyclopediaofmath.org/index.php/Commutator_subgroup"
+    alias:
+     - derived-subgroup
+  
+  - concept: companion-lehmer-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: companion lehmer number of $a1
+    property: "indexed function"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='companion-lehmer-number($a1)'><mi>V</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LehmerNumber.html"
+     - "https://mathworld.wolfram.com/LehmersNumber.html"
+     - "https://en.wikipedia.org/wiki/Lehmer_number"
+  
+  - concept: comparability
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 comparability $a2
+    property: infix
+    subject-area: "order theory"
+    mathml:
+     - "<math><mrow intent='comparability($a1,$a2)'><mi arg='a1'>X</mi><mo>⪋</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Comparability"
+    alias:
+     - comparable
+  
+  - concept: complement-of-interval
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: complement of interval
-      property: fenced
-      area: "order theory"
-      mathml:
-       - "<math><mrow intent='complement-of-interval($a1,$a2)'><mo>]</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>[</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Interval_(mathematics)"
-    
-    - concept: complementary-nome
-      arity: 1
-      en: complementary nome of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='complementary-nome($a1)'><msub><mi>q</mi><mn>1</mn></msub><mrow><mo>(</mo><mi arg='a1'>k</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Nome.html"
-       - "https://en.wikipedia.org/wiki/Nome_(mathematics)"
-    
-    - concept: complete-graph
-      arity: 1
+    property: fenced
+    subject-area: "order theory"
+    mathml:
+     - "<math><mrow intent='complement-of-interval($a1,$a2)'><mo>]</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>[</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Interval_(mathematics)"
+  
+  - concept: complementary-nome
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: complementary nome of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='complementary-nome($a1)'><msub><mi>q</mi><mn>1</mn></msub><mrow><mo>(</mo><mi arg='a1'>k</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Nome.html"
+     - "https://en.wikipedia.org/wiki/Nome_(mathematics)"
+  
+  - concept: complete-graph
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: complete graph
-      property: symbol
-      area: "graph theory"
-      mathml:
-       - "<math><msub intent='complete-graph($a1)'><mi>K</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CompleteGraph.html"
-       - "https://en.wikipedia.org/wiki/Complete_graph"
-      alias:
-       - "Also complete bipartite graph: `K_{n,m}`"
-    
-    - concept: complex-conjugate
-      arity: 1
-      en: complex conjugate of $1
-      property: msup
-      area: "complex analysis"
-      mathml:
-       - "<math><msup intent='complex-conjugate($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
-      notationa: "mover $1 ¯"
-      urls: 
-       - "https://mathworld.wolfram.com/ComplexConjugate.html"
-       - "https://en.wikipedia.org/wiki/Complex_conjugate"
-       - "https://dlmf.nist.gov/1.9#E11"
-    
-    - concept: complex-projective-space
-      arity: 0
+    property: symbol
+    subject-area: "graph theory"
+    mathml:
+     - "<math><msub intent='complete-graph($a1)'><mi>K</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CompleteGraph.html"
+     - "https://en.wikipedia.org/wiki/Complete_graph"
+    alias:
+     - "Also complete bipartite graph: `K_{n,m}`"
+  
+  - concept: complex-conjugate
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: complex conjugate of $a1
+    property: msup
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><msup intent='complex-conjugate($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
+    notationa: "mover $a1 ¯"
+    urls: 
+     - "https://mathworld.wolfram.com/ComplexConjugate.html"
+     - "https://en.wikipedia.org/wiki/Complex_conjugate"
+     - "https://dlmf.nist.gov/1.9#E11"
+  
+  - concept: complex-projective-space
+    arity: 0
+    arguments: []
+    speech:
       en: complex projective space
-      property: symbol
-      area: "projective geometry"
-      mathml:
-       - "<math><mi intent='complex-projective-space'>ℂ⁢</mi><mi>ℙ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ProjectiveSpace.html"
-       - "https://en.wikipedia.org/wiki/Algebraic_geometry_of_projective_spaces"
-       - "https://en.wikipedia.org/wiki/Projective_space"
-       - "https://ncatlab.org/nlab/show/projective+space"
-       - "https://www.encyclopediaofmath.org/index.php/Projective_space"
-    
-    - concept: complexification
-      arity: 1
-      en: complexification of $1
-      property: msup
-      area: "complex manifolds"
-      mathml:
-       - "<math><msup intent='complexification($a1)'><mi arg='a1'>X</mi><mi>ℂ</mi></msup></math>"
-       - "<math><msup intent='complexification($a1)'><mi arg='a1'>X</mi><mi>C</mi></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Complexification"
-       - "https://ncatlab.org/nlab/show/complexification"
-       - "https://www.encyclopediaofmath.org/index.php/Complexification_of_a_vector_space"
-      alias:
-       - complexification-of-vector-space
-    
-    - concept: composition
-      arity: 2
-      en: $1 composition $2
-      property: infix
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='composition($a1,$a2)'><mi arg='a1'>X</mi><mo>∘</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Composition.html"
-       - "https://ncatlab.org/nlab/show/composition"
-       - "https://www.encyclopediaofmath.org/index.php/Composition"
-      alias:
-       - compose
-    
-    
-    
-    - concept: compound-interest-nominal-rate
-      arity: 1
+    property: symbol
+    subject-area: "projective geometry"
+    mathml:
+     - "<math><mi intent='complex-projective-space'>ℂ⁢</mi><mi>ℙ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ProjectiveSpace.html"
+     - "https://en.wikipedia.org/wiki/Algebraic_geometry_of_projective_spaces"
+     - "https://en.wikipedia.org/wiki/Projective_space"
+     - "https://ncatlab.org/nlab/show/projective+space"
+     - "https://www.encyclopediaofmath.org/index.php/Projective_space"
+  
+  - concept: complexification
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: complexification of $a1
+    property: msup
+    subject-area: "complex manifolds"
+    mathml:
+     - "<math><msup intent='complexification($a1)'><mi arg='a1'>X</mi><mi>ℂ</mi></msup></math>"
+     - "<math><msup intent='complexification($a1)'><mi arg='a1'>X</mi><mi>C</mi></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Complexification"
+     - "https://ncatlab.org/nlab/show/complexification"
+     - "https://www.encyclopediaofmath.org/index.php/Complexification_of_a_vector_space"
+    alias:
+     - complexification-of-vector-space
+  
+  - concept: composition
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 composition $a2
+    property: infix
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='composition($a1,$a2)'><mi arg='a1'>X</mi><mo>∘</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Composition.html"
+     - "https://ncatlab.org/nlab/show/composition"
+     - "https://www.encyclopediaofmath.org/index.php/Composition"
+    alias:
+     - compose
+  
+  
+  
+  - concept: compound-interest-nominal-rate
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: nominal rate
-      property: msup
-      area: "finance"
-      mathml:
-       - "<math><msup intent='compound-interest($a1)'><mi>i</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>)</mo></mrow></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CompoundInterest.html"
-       - "https://en.wikipedia.org/wiki/Compound_interest"
-    
-    - concept: concentration
-      arity: 1
-      en: concentration of $1
-      property: fenced
-      area: "chemistry"
-      mathml:
-       - "<math><mrow intent='concentration($a1)'><mo>[</mo><mi arg='a1'>x</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/04._Reactions_in_Aqueous_Solution/4.5%3A_Concentration_of_Solutions"
-    
-    - concept: condition-number
-      arity: 1
-      en: condition number of $1
-      property: function
-      area: "numerical analysis"
-      mathml:
-       - "<math><mrow intent='condition-number($a1)'><mi>κ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Condition_number"
-       - "https://dlmf.nist.gov/3.2#SS5.p1"
-       - "https://www.encyclopediaofmath.org/index.php/Condition_number"
-    
-    - concept: conditional-expectation
-      arity: 2
-      en: conditional expectation $1 $2
-      property: mixfix
-      area: "probability theory"
-      mathml:
-       - "<math><mrow intent='conditional-expectation($a1,$a2)'><mi>E</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Conditional_expectation"
-       - "https://ncatlab.org/nlab/show/conditional+expectation"
-    
-    - concept: conditional-probability
-      arity: 2
-      en: conditional probability $1 $2
-      property: mixfix
-      area: "probability theory"
-      mathml:
-       - "<math><mrow intent='conditional-probability($a1,$a2)'><mi>P</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ConditionalProbability.html"
-       - "https://en.wikipedia.org/wiki/Conditional_probability"
-       - "https://www.encyclopediaofmath.org/index.php/Conditional_probability"
-    
-    - concept: conductor
-      arity: 1
-      en: conductor of $1
-      property: function
-      area: "algebraic number theory"
-      mathml:
-       - "<math><mrow intent='conductor($a1)'><mi>𝔣⁢</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Conductor_(class_field_theory)"
-    
-    - concept: contraction-operator
-      arity: 2
-      en: $1 contraction operator $2
-      property: infix
-      area: "algebraic geometry"
-      mathml:
-       - "<math><mrow intent='contraction-operator($a1,$a2)'><mi arg='a1'>X</mi><mo>⌟</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://arxiv.org/abs/1104.1240"
-    
-    - concept: contrast-function
-      arity: 2
-      en: contrast function $1 $2
-      property: mixfix
-      area: "statistics"
-      mathml:
-       - "<math><mrow intent='contrast-function($a1,$a2)'><mi>D</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Divergence_(statistics)"
-      alias:
-       - divergence
-    
-    - concept: configuration
-      arity: 4
-      en: "configuration $1 sub $2, $3 sub $4"
-      property: mixfix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='configuration($a1,$a2,$a3,$a4)'><mo>(</mo><msub><mi arg='a1'>a</mi><mi arg='a2'>b</mi></msub><mo>,</mo><msub><mi arg='a3'>c</mi><mi arg='a4'>d</mi></msub><mo>)</mo></mrow></math>"     
-      urls: 
-       - "https://mathworld.wolfram.com/Configuration.html"
-       - "https://en.wikipedia.org/wiki/Configuration_(geometry)"
-       - "https://www.encyclopediaofmath.org/index.php/Configuration"
-    
-    - concept: congruence-relation
-      arity: 2
-      en: $1 congruence relation $2
-      property: infix
-      area: "algebra, geometry"
-      mathml:
-       - "<math><mrow intent='congruence-relation($a1,$a2)'><mi arg='a1'>x</mi><mo>≡</mo><mi arg='a2'>y</mi></mrow></math>"
-       - "<math><mrow intent='congruence-relation($a1,$a2)'><mi arg='a1'>x</mi><mo>≅</mo><mi arg='a2'>y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Congruence_relation"
-       - "https://mathworld.wolfram.com/Congruence.html"
-       - "https://en.wikipedia.org/wiki/Congruence_(general_relativity)"
-       - "https://en.wikipedia.org/wiki/Congruence_(manifolds)"
-       - "https://en.wikipedia.org/wiki/Congruence_(geometry)"
-       - "https://ncatlab.org/nlab/show/congruence"
-       - "https://www.encyclopediaofmath.org/index.php/Congruence"
-      alias:
-       - congruence
-       - congruent
-    
-    - concept: conjugacy-class
-      arity: 1
-      en: conjugacy class of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='conjugacy-class($a1)'><mi>Cl</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ConjugacyClass.html"
-       - "https://en.wikipedia.org/wiki/Conjugacy_class"
-       - "https://ncatlab.org/nlab/show/conjugacy+class"
-    
-    - concept: conjugate-transpose
-      arity: 1
-      en: conjugate transpose of $1
-      property: msup
-      area: "linear algebra"
-      mathml:
-       - "<math><msup intent='conjugate-transpose($a1)'><mi arg='a1'>X</mi><mi>H</mi></msup></math>"
-       - "<math><msup intent='conjugate-transpose($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ConjugateTranspose.html"
-       - "https://en.wikipedia.org/wiki/Conjugate_transpose"
-    
-    - concept: connected-sum
-      arity: 2
-      en: $1 connected sum $2
-      property: infix
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='connected-sum($a1,$a2)'><mi arg='a1'>X</mi><mo>#</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ConnectedSum.html"
-       - "https://en.wikipedia.org/wiki/Connected_sum"
-       - "https://www.encyclopediaofmath.org/index.php/Connected_sum"
-    
-    - concept: connectivity
-      arity: 1
-      en: connectivity of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='connectivity($a1)'><mi>κ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Connectivity.html"
-       - "https://en.wikipedia.org/wiki/Connectivity_(graph_theory)"
-       - "https://www.encyclopediaofmath.org/index.php/Connectivity"
-    
-    - concept: constant-of-integration
-      arity: 0
+    property: msup
+    subject-area: "finance"
+    mathml:
+     - "<math><msup intent='compound-interest($a1)'><mi>i</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>)</mo></mrow></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CompoundInterest.html"
+     - "https://en.wikipedia.org/wiki/Compound_interest"
+  
+  - concept: concentration
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: concentration of $a1
+    property: fenced
+    subject-area: "chemistry"
+    mathml:
+     - "<math><mrow intent='concentration($a1)'><mo>[</mo><mi arg='a1'>x</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/04._Reactions_in_Aqueous_Solution/4.5%3A_Concentration_of_Solutions"
+  
+  - concept: condition-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: condition number of $a1
+    property: function
+    subject-area: "numerical analysis"
+    mathml:
+     - "<math><mrow intent='condition-number($a1)'><mi>κ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Condition_number"
+     - "https://dlmf.nist.gov/3.2#SS5.p1"
+     - "https://www.encyclopediaofmath.org/index.php/Condition_number"
+  
+  - concept: conditional-expectation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: conditional expectation $a1 $a2
+    property: mixfix
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mrow intent='conditional-expectation($a1,$a2)'><mi>E</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Conditional_expectation"
+     - "https://ncatlab.org/nlab/show/conditional+expectation"
+  
+  - concept: conditional-probability
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: conditional probability $a1 $a2
+    property: mixfix
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mrow intent='conditional-probability($a1,$a2)'><mi>P</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ConditionalProbability.html"
+     - "https://en.wikipedia.org/wiki/Conditional_probability"
+     - "https://www.encyclopediaofmath.org/index.php/Conditional_probability"
+  
+  - concept: conductor
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: conductor of $a1
+    property: function
+    subject-area: "algebraic number theory"
+    mathml:
+     - "<math><mrow intent='conductor($a1)'><mi>𝔣⁢</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Conductor_(class_field_theory)"
+  
+  - concept: contraction-operator
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 contraction operator $a2
+    property: infix
+    subject-area: "algebraic geometry"
+    mathml:
+     - "<math><mrow intent='contraction-operator($a1,$a2)'><mi arg='a1'>X</mi><mo>⌟</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://arxiv.org/abs/1104.1240"
+  
+  - concept: contrast-function
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: contrast function $a1 $a2
+    property: mixfix
+    subject-area: "statistics"
+    mathml:
+     - "<math><mrow intent='contrast-function($a1,$a2)'><mi>D</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Divergence_(statistics)"
+    alias:
+     - divergence
+  
+  - concept: configuration
+    arity: 4
+    arguments: [$a1, $a2, $a3, $a4]
+    speech:
+      en: "configuration $a1 sub $a2, $a3 sub $a4"
+    property: mixfix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='configuration($a1,$a2,$a3,$a4)'><mo>(</mo><msub><mi arg='a1'>a</mi><mi arg='a2'>b</mi></msub><mo>,</mo><msub><mi arg='a3'>c</mi><mi arg='a4'>d</mi></msub><mo>)</mo></mrow></math>"     
+    urls: 
+     - "https://mathworld.wolfram.com/Configuration.html"
+     - "https://en.wikipedia.org/wiki/Configuration_(geometry)"
+     - "https://www.encyclopediaofmath.org/index.php/Configuration"
+  
+  - concept: congruence-relation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 congruence relation $a2
+    property: infix
+    subject-area: "algebra, geometry"
+    mathml:
+     - "<math><mrow intent='congruence-relation($a1,$a2)'><mi arg='a1'>x</mi><mo>≡</mo><mi arg='a2'>y</mi></mrow></math>"
+     - "<math><mrow intent='congruence-relation($a1,$a2)'><mi arg='a1'>x</mi><mo>≅</mo><mi arg='a2'>y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Congruence_relation"
+     - "https://mathworld.wolfram.com/Congruence.html"
+     - "https://en.wikipedia.org/wiki/Congruence_(general_relativity)"
+     - "https://en.wikipedia.org/wiki/Congruence_(manifolds)"
+     - "https://en.wikipedia.org/wiki/Congruence_(geometry)"
+     - "https://ncatlab.org/nlab/show/congruence"
+     - "https://www.encyclopediaofmath.org/index.php/Congruence"
+    alias:
+     - congruence
+     - congruent
+  
+  - concept: conjugacy-class
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: conjugacy class of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='conjugacy-class($a1)'><mi>Cl</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ConjugacyClass.html"
+     - "https://en.wikipedia.org/wiki/Conjugacy_class"
+     - "https://ncatlab.org/nlab/show/conjugacy+class"
+  
+  - concept: conjugate-transpose
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: conjugate transpose of $a1
+    property: msup
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><msup intent='conjugate-transpose($a1)'><mi arg='a1'>X</mi><mi>H</mi></msup></math>"
+     - "<math><msup intent='conjugate-transpose($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ConjugateTranspose.html"
+     - "https://en.wikipedia.org/wiki/Conjugate_transpose"
+  
+  - concept: connected-sum
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 connected sum $a2
+    property: infix
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='connected-sum($a1,$a2)'><mi arg='a1'>X</mi><mo>#</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ConnectedSum.html"
+     - "https://en.wikipedia.org/wiki/Connected_sum"
+     - "https://www.encyclopediaofmath.org/index.php/Connected_sum"
+  
+  - concept: connectivity
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: connectivity of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='connectivity($a1)'><mi>κ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Connectivity.html"
+     - "https://en.wikipedia.org/wiki/Connectivity_(graph_theory)"
+     - "https://www.encyclopediaofmath.org/index.php/Connectivity"
+  
+  - concept: constant-of-integration
+    arity: 0
+    arguments: []
+    speech:
       en: constant of integration
-      property: constant
-      area: "calculus"
-      mathml:
-       - "<math><mi intent='constant-of-integration'>C</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ConstantofIntegration.html"
-       - "https://en.wikipedia.org/wiki/Constant_of_integration"
-    
-    - concept: containment
-      arity: 2
-      en: $1 containment $2
-      property: infix
-      area: "computer science"
-      mathml:
-       - "<math><mrow intent='containment($a1,$a2)'><mi arg='a1'>X</mi><mo>≤</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Encompassment_ordering"
-       - "https://en.wikipedia.org/wiki/Subset"
-       - "https://en.wikipedia.org/wiki/%E2%8A%83"
-      alias:
-       - encompassment
-    
-    - concept: contingency-table
-      arity: 1
-      en: contingency table of $1
-      property: mtable
-      area: "statistics"
-      mathml:
-       - "<math><mrow intent='contingency-table($a1)'><mtable arg='a1'><mtr><mtd><mtext>...</mtext></mtd></mtr><mtr><mtd><mtext>...</mtext></mtd></mtr></mtable></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ContingencyTable.html"
-       - "https://en.wikipedia.org/wiki/Contingency_table"
-      alias:
-       - two-way-frequency-table
-    
-    - concept: continued-fraction
-      arity: 1
-      en: continued fraction $1
-      property: mixfix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='periodic-continued-fraction($a1)'><msub><mi>a</mi><mn>0</mn></msub><mo>+</mo><mfrac arg='a1'><mn>1</mn><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>+</mo><mo>⋱</mo></mrow></mfrac></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ContinuedFraction.html"
-       - "https://en.wikipedia.org/wiki/Continued_fraction"
-       - "https://dlmf.nist.gov/1.12#i"
-       - "https://ncatlab.org/nlab/show/continued+fraction"
-       - "https://www.encyclopediaofmath.org/index.php/Continued_fraction"
-      alias:
-       - anthyphairetic-ratio
-       - chain-fraction
-    
-    - concept: continuum
-      arity: 0
+    property: constant
+    subject-area: "calculus"
+    mathml:
+     - "<math><mi intent='constant-of-integration'>C</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ConstantofIntegration.html"
+     - "https://en.wikipedia.org/wiki/Constant_of_integration"
+  
+  - concept: containment
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 containment $a2
+    property: infix
+    subject-area: "computer science"
+    mathml:
+     - "<math><mrow intent='containment($a1,$a2)'><mi arg='a1'>X</mi><mo>≤</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Encompassment_ordering"
+     - "https://en.wikipedia.org/wiki/Subset"
+     - "https://en.wikipedia.org/wiki/%E2%8A%83"
+    alias:
+     - encompassment
+  
+  - concept: contingency-table
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: contingency table of $a1
+    property: mtable
+    subject-area: "statistics"
+    mathml:
+     - "<math><mrow intent='contingency-table($a1)'><mtable arg='a1'><mtr><mtd><mtext>...</mtext></mtd></mtr><mtr><mtd><mtext>...</mtext></mtd></mtr></mtable></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ContingencyTable.html"
+     - "https://en.wikipedia.org/wiki/Contingency_table"
+    alias:
+     - two-way-frequency-table
+  
+  - concept: continued-fraction
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: continued fraction $a1
+    property: mixfix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='periodic-continued-fraction($a1)'><msub><mi>a</mi><mn>0</mn></msub><mo>+</mo><mfrac arg='a1'><mn>1</mn><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>+</mo><mo>⋱</mo></mrow></mfrac></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ContinuedFraction.html"
+     - "https://en.wikipedia.org/wiki/Continued_fraction"
+     - "https://dlmf.nist.gov/1.12#i"
+     - "https://ncatlab.org/nlab/show/continued+fraction"
+     - "https://www.encyclopediaofmath.org/index.php/Continued_fraction"
+    alias:
+     - anthyphairetic-ratio
+     - chain-fraction
+  
+  - concept: continuum
+    arity: 0
+    arguments: []
+    speech:
       en: continuum
-      property: constant
-      area: "set theory"
-      mathml:
-       - "<math><mi intent='continuum'>𝔠</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Continuum.html"
-       - "https://en.wikipedia.org/wiki/List_of_continuity-related_topics"
-       - "https://en.wikipedia.org/wiki/Linear_continuum"
-       - "https://en.wikipedia.org/wiki/Continuum_(set_theory)"
-       - "https://en.wikipedia.org/wiki/Continuum_(topology)"
-       - "https://ncatlab.org/nlab/show/continuum"
-       - "https://www.encyclopediaofmath.org/index.php/Continuum"
-    
-    - concept: contradiction
-      arity: 0
+    property: constant
+    subject-area: "set theory"
+    mathml:
+     - "<math><mi intent='continuum'>𝔠</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Continuum.html"
+     - "https://en.wikipedia.org/wiki/List_of_continuity-related_topics"
+     - "https://en.wikipedia.org/wiki/Linear_continuum"
+     - "https://en.wikipedia.org/wiki/Continuum_(set_theory)"
+     - "https://en.wikipedia.org/wiki/Continuum_(topology)"
+     - "https://ncatlab.org/nlab/show/continuum"
+     - "https://www.encyclopediaofmath.org/index.php/Continuum"
+  
+  - concept: contradiction
+    arity: 0
+    arguments: []
+    speech:
       en: contradiction
-      property: constant
-      area: "logic"
-      mathml:
-       - "<math><mo intent='contradiction'>⊥</mo></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Contradiction.html"
-       - "https://en.wikipedia.org/wiki/Contradiction"
-       - "https://ncatlab.org/nlab/show/contradiction"
-    
-    - concept: converge
-      arity: 1
-      en: $1 converges
-      property: postfix
-      area: "computer science"
-      mathml:
-       - "<math><mrow intent='converge($a1)'><mi arg='a1'>x</mi><mo>↓</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Divergence_(computer_science)"
-      alias:
-       - convergence
-    
-    - concept: converse
-      arity: 1
-      en: converse of $1
-      property: msup
-      area: "relational algebra"
-      mathml:
-       - "<math><msup intent='converse($a1)'><mi arg='a1'>X</mi><mo>˘</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Relation_algebra"
-      alias:
-       - reciprocal
-    
-    - concept: converse-graph
-      arity: 1
-      en: converse graph of $1
-      property: msup
-      area: "graph theory"
-      mathml:
-       - "<math><msup intent='converse-graph($a1)'><mi arg='a1'>X</mi><mo>'</mo></msup></math>"
-       - "<math><msup intent='converse-graph($a1)'><mi arg='a1'>X</mi><mi>T</mi></msup></math>"
-       - "<math><msup intent='converse-graph($a1)'><mi arg='a1'>X</mi><mi>R</mi></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Transpose_graph"
-      alias:
-       - transpose-graph
-       - reverse-graph
-    
-    - concept: convolution
-      arity: 2
-      en: $1 convolution $2
-      property: infix
-      area: "functional analysis"
-      mathml:
-       - "<math><mrow intent='convolution($a1,$a2)'><mi arg='a1'>X</mi><mo>∗</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Convolution.html"
-       - "https://en.wikipedia.org/wiki/List_of_convolutions_of_probability_distributions"
-       - "https://en.wikipedia.org/wiki/Convolution_(computer_science)"
-       - "https://en.wikipedia.org/wiki/Convolution"
-      alias:
-       - convolve
-    
-    - concept: conway-group
-      arity: 0
+    property: constant
+    subject-area: "logic"
+    mathml:
+     - "<math><mo intent='contradiction'>⊥</mo></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Contradiction.html"
+     - "https://en.wikipedia.org/wiki/Contradiction"
+     - "https://ncatlab.org/nlab/show/contradiction"
+  
+  - concept: converge
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1 converges
+    property: postfix
+    subject-area: "computer science"
+    mathml:
+     - "<math><mrow intent='converge($a1)'><mi arg='a1'>x</mi><mo>↓</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Divergence_(computer_science)"
+    alias:
+     - convergence
+  
+  - concept: converse
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: converse of $a1
+    property: msup
+    subject-area: "relational algebra"
+    mathml:
+     - "<math><msup intent='converse($a1)'><mi arg='a1'>X</mi><mo>˘</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Relation_algebra"
+    alias:
+     - reciprocal
+  
+  - concept: converse-graph
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: converse graph of $a1
+    property: msup
+    subject-area: "graph theory"
+    mathml:
+     - "<math><msup intent='converse-graph($a1)'><mi arg='a1'>X</mi><mo>'</mo></msup></math>"
+     - "<math><msup intent='converse-graph($a1)'><mi arg='a1'>X</mi><mi>T</mi></msup></math>"
+     - "<math><msup intent='converse-graph($a1)'><mi arg='a1'>X</mi><mi>R</mi></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Transpose_graph"
+    alias:
+     - transpose-graph
+     - reverse-graph
+  
+  - concept: convolution
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 convolution $a2
+    property: infix
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><mrow intent='convolution($a1,$a2)'><mi arg='a1'>X</mi><mo>∗</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Convolution.html"
+     - "https://en.wikipedia.org/wiki/List_of_convolutions_of_probability_distributions"
+     - "https://en.wikipedia.org/wiki/Convolution_(computer_science)"
+     - "https://en.wikipedia.org/wiki/Convolution"
+    alias:
+     - convolve
+  
+  - concept: conway-group
+    arity: 0
+    arguments: []
+    speech:
       en: conway group
-      property: symbol
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='conway-group'><mi>Co</mi><mn>0</mn></msub></math>"
-       - "<math><msub intent='conway-group'><mi>Co</mi><mn>1</mn></msub></math>"
-       - "<math><msub intent='conway-group'><mi>Co</mi><mn>2</mn></msub></math>"
-       - "<math><msub intent='conway-group'><mi>Co</mi><mn>3</mn></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ConwayGroups.html"
-       - "https://en.wikipedia.org/wiki/Conway_group"
-       - "https://en.wikipedia.org/wiki/Conway_group_Co1"
-       - "https://en.wikipedia.org/wiki/Conway_group_Co2"
-       - "https://en.wikipedia.org/wiki/Conway_group_Co3"
-    
-    - concept: coprime
-      arity: 2
-      en: $1 coprime $2
-      property: infix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='coprime($a1,$a2)'><mi arg='a1'>X</mi><mo>⊥</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Coprime.html"
-       - "https://en.wikipedia.org/wiki/Coprime_integers"
-      alias:
-       - relatively-prime
-       - mutually-prime
-    
-    - concept: coproduct
-      arity: 2
-      en: coproduct of $1 and $2
-      property: indexed
-      area: "topology, category theory"
-      mathml:
-       - "<math><mrow intent='coproduct($a1,$a2)'><mi arg='a1'>X</mi><mo>⊔</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Coproduct.html"
-       - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)"
-       - "https://en.wikipedia.org/wiki/Coproduct"
-       - "https://ncatlab.org/nlab/show/coproduct"
-       - "https://www.encyclopediaofmath.org/index.php/Coproduct"
-    
-    - concept: correlation
-      arity: 1
-      en: correlation of $1
-      property: function
-      area: "statistics"
-      mathml:
-       - "<math><mrow intent='correlation($a1)'><mi>corr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Correlation_and_dependence"
-    
-    - concept: correlation-ratio
-      arity: 0
+    property: symbol
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='conway-group'><mi>Co</mi><mn>0</mn></msub></math>"
+     - "<math><msub intent='conway-group'><mi>Co</mi><mn>1</mn></msub></math>"
+     - "<math><msub intent='conway-group'><mi>Co</mi><mn>2</mn></msub></math>"
+     - "<math><msub intent='conway-group'><mi>Co</mi><mn>3</mn></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ConwayGroups.html"
+     - "https://en.wikipedia.org/wiki/Conway_group"
+     - "https://en.wikipedia.org/wiki/Conway_group_Co1"
+     - "https://en.wikipedia.org/wiki/Conway_group_Co2"
+     - "https://en.wikipedia.org/wiki/Conway_group_Co3"
+  
+  - concept: coprime
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 coprime $a2
+    property: infix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='coprime($a1,$a2)'><mi arg='a1'>X</mi><mo>⊥</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Coprime.html"
+     - "https://en.wikipedia.org/wiki/Coprime_integers"
+    alias:
+     - relatively-prime
+     - mutually-prime
+  
+  - concept: coproduct
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: coproduct of $a1 and $a2
+    property: indexed
+    subject-area: "topology, category theory"
+    mathml:
+     - "<math><mrow intent='coproduct($a1,$a2)'><mi arg='a1'>X</mi><mo>⊔</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Coproduct.html"
+     - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)"
+     - "https://en.wikipedia.org/wiki/Coproduct"
+     - "https://ncatlab.org/nlab/show/coproduct"
+     - "https://www.encyclopediaofmath.org/index.php/Coproduct"
+  
+  - concept: correlation
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: correlation of $a1
+    property: function
+    subject-area: "statistics"
+    mathml:
+     - "<math><mrow intent='correlation($a1)'><mi>corr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Correlation_and_dependence"
+  
+  - concept: correlation-ratio
+    arity: 0
+    arguments: []
+    speech:
       en: correlation ratio
-      property: symbol
-      area: "statistics"
-      mathml:
-       - "<math><mi intent='correlation-ratio'>η</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CorrelationRatio.html"
-       - "https://en.wikipedia.org/wiki/Correlation_ratio"
-       - "https://www.encyclopediaofmath.org/index.php/Correlation_ratio"
-    
-    - concept: cosine-integral
-      arity: 1
-      en: cosine integral of $1
-      property: operator
-      area: "special-functions"
-      mathml:
-       - "<math><mrow intent='cosine-integral($a1)'><mi>Ci</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CosineIntegral.html"
-       - "https://dlmf.nist.gov/6.2#ii"
-       - "https://dlmf.nist.gov/6.2#E11"
-       - "https://dlmf.nist.gov/6.2#E12"
-    
-    - concept: coupling-constant
-      arity: 0
+    property: symbol
+    subject-area: "statistics"
+    mathml:
+     - "<math><mi intent='correlation-ratio'>η</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CorrelationRatio.html"
+     - "https://en.wikipedia.org/wiki/Correlation_ratio"
+     - "https://www.encyclopediaofmath.org/index.php/Correlation_ratio"
+  
+  - concept: cosine-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cosine integral of $a1
+    property: operator
+    subject-area: "special-functions"
+    mathml:
+     - "<math><mrow intent='cosine-integral($a1)'><mi>Ci</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CosineIntegral.html"
+     - "https://dlmf.nist.gov/6.2#ii"
+     - "https://dlmf.nist.gov/6.2#E11"
+     - "https://dlmf.nist.gov/6.2#E12"
+  
+  - concept: coupling-constant
+    arity: 0
+    arguments: []
+    speech:
       en: coupling constant
-      property: symbol
-      area: "gauge theory"
-      mathml:
-       - "<math><mi intent='coupling-constant'>g</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Coupling_constant"
-      alias:
-       - gauge-coupling-parameter
-       - coupling
-    
-    - concept: covariance
-      arity: 1
-      en: covariance of $1
-      property: function
-      area: "statistics"
-      mathml:
-       - "<math><mrow intent='covariance($a1)'><mi>cov</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Covariance.html"
-       - "https://en.wikipedia.org/wiki/Covariance_operator"
-       - "https://en.wikipedia.org/wiki/Covariance"
-       - "https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors"
-       - "https://www.encyclopediaofmath.org/index.php/Covariance"
-    
-    - concept: covariant-derivative
-      arity: 1
-      en: covariant derivative of $1
-      property: "indexed operator"
-      area: "differential geometry"
-      mathml:
-       - "<math><msub intent='covariant-derivative($a1)'><mi>∇</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CovariantDerivative.html"
-       - "https://en.wikipedia.org/wiki/Covariant_derivative"
-       - "https://ncatlab.org/nlab/show/covariant+derivative"
-       - "https://www.encyclopediaofmath.org/index.php/Covariant_derivative"
-    
-    - concept: covariation
-      arity: 3
-      en: covariation of $1 and $2 over $3
-      property: indexed fenced
-      area: "stochastic processes"
-      mathml:
-       - "<math><mrow intent='covariation($a1,$a2,$a3)'><msub><mrow><mo>[</mo><mi arg='a1'>X</mi><mo>,</mo><mi arg='a2'>Y</mi><mo>]</mo></mrow><mi arg='a3'>t</mi></msub></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Quadratic_variation"
-      alias:
-       - cross-variance
-    
-    - concept: covering-relation
-      arity: 2
-      en: $1 covering relation $2
-      property: infix
-      area: "order theory"
-      mathml:
-       - "<math><mrow intent='covering-relation($a1,$a2)'><mi arg='a1'>X</mi><mo>⋖</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='covering-relation($a1,$a2)'><mi arg='a1'>X</mi><mo>&lt;:</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Partially_ordered_set"
-       - "https://en.wikipedia.org/wiki/Covering_relation"
-    
-    - concept: cross-product
-      arity: 2
-      en: $1 cross product $2
-      property: infix
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='cross-product($a1,$a2)'><mi arg='a1'>X</mi><mo>×</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CrossProduct.html"
-       - "https://en.wikipedia.org/wiki/Cross_product"
-       - "https://ncatlab.org/nlab/show/cross+product"
-       - "https://www.encyclopediaofmath.org/index.php/Cross_product"
-      alias:
-       - vector-product
-    
-    - concept: cross-ratio
-      arity: 4
-      en: "cross ratio of $1, $2, $3, $4"
-      property: fenced
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='cross-ratio($a1,$a2,$a3,$a4)'><mo>(</mo><mi arg='a1'>A</mi><mo>,</mo><mi arg='a2'>B</mi><mo>;</mo><mi arg='a3'>C</mi><mo>,</mo><mi arg='a4'>D</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Cross-Ratio.html"
-       - "https://en.wikipedia.org/wiki/Cross-ratio"
-      alias:
-       - double-ratio
-    
-    - concept: crossing-number
-      arity: 1
-      en: crossing number of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='crossing-number($a1)'><mi>Cr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Crossing_number_(graph_theory)"
-       - "https://en.wikipedia.org/wiki/Crossing_number_(knot_theory)"
-       - "https://ncatlab.org/nlab/show/crossing+number"
-    
-    - concept: cullen-number
-      arity: 1
-      en: $1<i>th</i> cullen number
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='cullen-number($a1)'><mi>C</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CullenNumber.html"
-       - "https://en.wikipedia.org/wiki/Cullen_number"
-    
-    - concept: cumulant
-      arity: 1
-      en: cumulant of $1
-      property: "indexed symbol"
-      area: "probability theory"
-      mathml:
-       - "<math><msub intent='cumulant($a1)'><mi>κ</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Cumulant.html"
-       - "https://en.wikipedia.org/wiki/Cumulant"
-       - "https://en.wikipedia.org/wiki/Cumulant-generating_function"
-       - "https://ncatlab.org/nlab/show/cumulant"
-       - "https://www.encyclopediaofmath.org/index.php/Cumulant"
-    
-    - concept: cumulative-distribution-function
-      arity: 1
-      en: cumulative distribution function of $1
-      property: "indexed symbol"
-      area: "probability theory"
-      mathml:
-       - "<math><msub intent='cumulative-distribution-function($a1)'><mi>F</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CumulativeDistributionFunction.html"
-       - "https://en.wikipedia.org/wiki/Cumulative_distribution_function"
-      alias:
-       - cdf
-       - distribution-function
-    
-    - concept: cup-product
-      arity: 2
-      en: $1 cup product $2
-      property: infix
-      area: "algebraic topology"
-      mathml:
-       - "<math><mrow intent='cup-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⌣</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Cup_product"
-       - "https://ncatlab.org/nlab/show/cup+product"
-    
-    - concept: curl
-      arity: 1
-      en: curl of $1
-      property: function
-      area: "vector calculus"
-      mathml:
-       - "<math><mrow intent='curl($a1)'><mi>curl</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='curl($a1)'><mi>rot</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      notationa: "mrow ∇ × $1"
-      urls: 
-       - "https://mathworld.wolfram.com/Curl.html"
-       - "https://en.wikipedia.org/wiki/Curl_(mathematics)"
-       - "https://ncatlab.org/nlab/show/curl"
-       - "https://www.encyclopediaofmath.org/index.php/Curl"
-    
-    - concept: current
-      arity: 1
-      en: current of $1
-      property: fenced
-      area: "differential topology"
-      mathml:
-       - "<math><mrow intent='current($a1)'><mo>[</mo><mi arg='a1'>M</mi><mo>]</mo></mrow></math>"
-       - "<math><mrow intent='current($a1)'><mo>⟦</mo><mi arg='a1'>M</mi><mo>⟧</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Current.html"
-       - "https://en.wikipedia.org/wiki/Current_(mathematics)"
-       - "https://www.encyclopediaofmath.org/index.php/Current"
-    
-    - concept: curvature
-      arity: 1
-      en: curvature of $1
-      property: function
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='curvature($a1)'><mi>κ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Curvature.html"
-       - "https://en.wikipedia.org/wiki/Geodesic_curvature"
-       - "https://en.wikipedia.org/wiki/Curvature"
-       - "https://ncatlab.org/nlab/show/curvature"
-       - "https://www.encyclopediaofmath.org/index.php/Curvature"
-    
-    - concept: cycle
-      arity: 1
-      en: cycle $1
-      property: fenced
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='cycle($a1)'><mrow arg='a1'><mrow><mo>(</mo><mn>1</mn><mn>2</mn><mn>6</mn><mo>)</mo></mrow><mrow><mo>(</mo><mn>3</mn><mn>5</mn><mo>)</mo></mrow></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Permutation#Cycle_notation"
-       - "https://en.wikipedia.org/wiki/Transposition_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Cycles_and_fixed_points"
-    
-    - concept: cycle-gene
-      arity: 0
+    property: symbol
+    subject-area: "gauge theory"
+    mathml:
+     - "<math><mi intent='coupling-constant'>g</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Coupling_constant"
+    alias:
+     - gauge-coupling-parameter
+     - coupling
+  
+  - concept: covariance
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: covariance of $a1
+    property: function
+    subject-area: "statistics"
+    mathml:
+     - "<math><mrow intent='covariance($a1)'><mi>cov</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Covariance.html"
+     - "https://en.wikipedia.org/wiki/Covariance_operator"
+     - "https://en.wikipedia.org/wiki/Covariance"
+     - "https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors"
+     - "https://www.encyclopediaofmath.org/index.php/Covariance"
+  
+  - concept: covariant-derivative
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: covariant derivative of $a1
+    property: "indexed operator"
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><msub intent='covariant-derivative($a1)'><mi>∇</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CovariantDerivative.html"
+     - "https://en.wikipedia.org/wiki/Covariant_derivative"
+     - "https://ncatlab.org/nlab/show/covariant+derivative"
+     - "https://www.encyclopediaofmath.org/index.php/Covariant_derivative"
+  
+  - concept: covariation
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: covariation of $a1 and $a2 over $a3
+    property: indexed fenced
+    subject-area: "stochastic processes"
+    mathml:
+     - "<math><mrow intent='covariation($a1,$a2,$a3)'><msub><mrow><mo>[</mo><mi arg='a1'>X</mi><mo>,</mo><mi arg='a2'>Y</mi><mo>]</mo></mrow><mi arg='a3'>t</mi></msub></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Quadratic_variation"
+    alias:
+     - cross-variance
+  
+  - concept: covering-relation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 covering relation $a2
+    property: infix
+    subject-area: "order theory"
+    mathml:
+     - "<math><mrow intent='covering-relation($a1,$a2)'><mi arg='a1'>X</mi><mo>⋖</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='covering-relation($a1,$a2)'><mi arg='a1'>X</mi><mo>&lt;:</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Partially_ordered_set"
+     - "https://en.wikipedia.org/wiki/Covering_relation"
+  
+  - concept: cross-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 cross product $a2
+    property: infix
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='cross-product($a1,$a2)'><mi arg='a1'>X</mi><mo>×</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CrossProduct.html"
+     - "https://en.wikipedia.org/wiki/Cross_product"
+     - "https://ncatlab.org/nlab/show/cross+product"
+     - "https://www.encyclopediaofmath.org/index.php/Cross_product"
+    alias:
+     - vector-product
+  
+  - concept: cross-ratio
+    arity: 4
+    arguments: [$a1, $a2, $a3, $a4]
+    speech:
+      en: "cross ratio of $a1, $a2, $a3, $a4"
+    property: fenced
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='cross-ratio($a1,$a2,$a3,$a4)'><mo>(</mo><mi arg='a1'>A</mi><mo>,</mo><mi arg='a2'>B</mi><mo>;</mo><mi arg='a3'>C</mi><mo>,</mo><mi arg='a4'>D</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Cross-Ratio.html"
+     - "https://en.wikipedia.org/wiki/Cross-ratio"
+    alias:
+     - double-ratio
+  
+  - concept: crossing-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: crossing number of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='crossing-number($a1)'><mi>Cr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Crossing_number_(graph_theory)"
+     - "https://en.wikipedia.org/wiki/Crossing_number_(knot_theory)"
+     - "https://ncatlab.org/nlab/show/crossing+number"
+  
+  - concept: cullen-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> cullen number
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='cullen-number($a1)'><mi>C</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CullenNumber.html"
+     - "https://en.wikipedia.org/wiki/Cullen_number"
+  
+  - concept: cumulant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cumulant of $a1
+    property: "indexed symbol"
+    subject-area: "probability theory"
+    mathml:
+     - "<math><msub intent='cumulant($a1)'><mi>κ</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Cumulant.html"
+     - "https://en.wikipedia.org/wiki/Cumulant"
+     - "https://en.wikipedia.org/wiki/Cumulant-generating_function"
+     - "https://ncatlab.org/nlab/show/cumulant"
+     - "https://www.encyclopediaofmath.org/index.php/Cumulant"
+  
+  - concept: cumulative-distribution-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cumulative distribution function of $a1
+    property: "indexed symbol"
+    subject-area: "probability theory"
+    mathml:
+     - "<math><msub intent='cumulative-distribution-function($a1)'><mi>F</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CumulativeDistributionFunction.html"
+     - "https://en.wikipedia.org/wiki/Cumulative_distribution_function"
+    alias:
+     - cdf
+     - distribution-function
+  
+  - concept: cup-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 cup product $a2
+    property: infix
+    subject-area: "algebraic topology"
+    mathml:
+     - "<math><mrow intent='cup-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⌣</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Cup_product"
+     - "https://ncatlab.org/nlab/show/cup+product"
+  
+  - concept: curl
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: curl of $a1
+    property: function
+    subject-area: "vector calculus"
+    mathml:
+     - "<math><mrow intent='curl($a1)'><mi>curl</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='curl($a1)'><mi>rot</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    notationa: "mrow ∇ × $a1"
+    urls: 
+     - "https://mathworld.wolfram.com/Curl.html"
+     - "https://en.wikipedia.org/wiki/Curl_(mathematics)"
+     - "https://ncatlab.org/nlab/show/curl"
+     - "https://www.encyclopediaofmath.org/index.php/Curl"
+  
+  - concept: current
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: current of $a1
+    property: fenced
+    subject-area: "differential topology"
+    mathml:
+     - "<math><mrow intent='current($a1)'><mo>[</mo><mi arg='a1'>M</mi><mo>]</mo></mrow></math>"
+     - "<math><mrow intent='current($a1)'><mo>⟦</mo><mi arg='a1'>M</mi><mo>⟧</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Current.html"
+     - "https://en.wikipedia.org/wiki/Current_(mathematics)"
+     - "https://www.encyclopediaofmath.org/index.php/Current"
+  
+  - concept: curvature
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: curvature of $a1
+    property: function
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='curvature($a1)'><mi>κ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Curvature.html"
+     - "https://en.wikipedia.org/wiki/Geodesic_curvature"
+     - "https://en.wikipedia.org/wiki/Curvature"
+     - "https://ncatlab.org/nlab/show/curvature"
+     - "https://www.encyclopediaofmath.org/index.php/Curvature"
+  
+  - concept: cycle
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cycle $a1
+    property: fenced
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='cycle($a1)'><mrow arg='a1'><mrow><mo>(</mo><mn>1</mn><mn>2</mn><mn>6</mn><mo>)</mo></mrow><mrow><mo>(</mo><mn>3</mn><mn>5</mn><mo>)</mo></mrow></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Permutation#Cycle_notation"
+     - "https://en.wikipedia.org/wiki/Transposition_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Cycles_and_fixed_points"
+  
+  - concept: cycle-gene
+    arity: 0
+    arguments: []
+    speech:
       en: cycle gene
-      property: symbol
-      area: "genetics"
-      mathml:
-       - "<math><mi intent='cycle-gene'>cyc</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Cycle_(gene)"
-    
-    - concept: cyclotomic-field
-      arity: 1
-      en: cyclotomic field of $1
-      property: embellished symbol
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='cyclotomic-field($a1)'><mi>𝐐</mi><mrow><mo>(</mo><msub><mi>ζ</mi><mi arg='a1'>n</mi></msub><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CyclotomicField.html"
-       - "https://en.wikipedia.org/wiki/Cyclotomic_field"
-       - "https://ncatlab.org/nlab/show/cyclotomic+field"
-       - "https://www.encyclopediaofmath.org/index.php/Cyclotomic_field"
-    
-    - concept: cyclotomic-polynomial
-      arity: 1
-      en: $1<i>th</i> cyclotomic polynomial
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='cyclotomic-polynomial($a1)'><mi>Φ</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CyclotomicPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Cyclotomic_polynomial"
-       - "https://www.encyclopediaofmath.org/index.php/Cyclotomic_polynomials"
-    
-    - concept: dalembert-operator
-      arity: 1
-      en: dalembert operator of $1
-      property: prefix
-      area: "partial differential equations"
-      mathml:
-       - "<math><mrow intent='dalembert-operator($a1)'><mo>☐</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/D%27Alembert_operator"
-       - "https://www.encyclopediaofmath.org/index.php/D'Alembert_operator"
-      alias:
-       - dalembertian
-       - wave-operator
-       - box-operator
-    
-    - concept: davenport-constant
-      arity: 1
-      en: davenport constant of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='davenport-constant($a1)'><mi>D</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DavenportConstant.html"
-       - "https://en.wikipedia.org/wiki/Davenport_constant"
-       - "https://www.encyclopediaofmath.org/index.php/Davenport_constant"
-    
-    - concept: dawson-function
-      arity: 1
-      en: dawson function of $1
-      property: function
-      area: "special-functions"
-      mathml:
-       - "<math><mrow intent='dawson-function($a1)'><mi>F</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='dawson-function($a1)'><mi>D</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      notationb: "mi sub D -"
-      notationa: "mi sub D +"
-      urls: 
-       - "https://mathworld.wolfram.com/DawsonsIntegral.html"
-       - "https://en.wikipedia.org/wiki/Dawson_function"
-       - "https://dlmf.nist.gov/7.2#ii"
-       - "https://dlmf.nist.gov/7.2#E5"
-      alias:
-       - dawson-integral
-    
-    - concept: decrease
-      arity: 1
-      en: decrease of $1
-      property: postfix
-      area: "physics"
-      mathml:
-       - "<math><mrow intent='decrease($a1)'><mi arg='a1'>x</mi><mo>↓</mo></mrow></math>"
-      urls: 
-       - "https://youtu.be/HZ7a9YkF204?t=4705"
-    
-    - concept: decrease-tends-to
-      arity: 2
-      en: $1 decrease tends to $2
-      property: infix
-      area: "calculus"
-      mathml:
-       - "<math><mrow intent='decrease-tends-to($a1,$a2)'><mi arg='a1'>X</mi><mo>↘</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://math.stackexchange.com/questions/1886232/what-does-this-notation-mean-limes-from-left-right"
-       - "http://pi.math.cornell.edu/~web6720/MATH%206710%20notes.pdf"
-    
-    - concept: dedekind-eta-function
-      arity: 1
-      en: dedekind eta function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='dedekind-eta-function($a1)'><mi>η</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DedekindEtaFunction.html"
-       - "https://en.wikipedia.org/wiki/Dedekind_eta_function"
-       - "https://ncatlab.org/nlab/show/Dedekind+eta+function"
-    
-    - concept: dedekind-zeta-function
-      arity: 1
-      en: dedekind zeta function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='dedekind-zeta-function($a1)'><mi>ζ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Dedekind_zeta_function"
-    
-    - concept: deductive-closure
-      arity: 1
-      en: deductive closure of $1
-      property: function
-      area: "logic"
-      mathml:
-       - "<math><mrow intent='deductive-closure($a1)'><mi>Ded</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='deductive-closure($a1)'><mi>Th</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Deductive_closure"
-    
-    - concept: defined-as
-      arity: 2
-      en: $1 defined as $2
-      property: infix
-      area: "general"
-      mathml:
-       - "<math><mrow intent='defined-as($a1,$a2)'><mi arg='a1'>X</mi><mo>≜</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='defined-as($a1,$a2)'><mi arg='a1'>X</mi><mo>≝</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='defined-as($a1,$a2)'><mi arg='a1'>X</mi><mo>:=</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='defined-as($a1,$a2)'><mi arg='a1'>X</mi><mover><mo>=</mo><mi>def</mi></mover><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='defined-as($a1,$a2)'><mi arg='a1'>X</mi><mo>:</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://math.stackexchange.com/questions/522864/what-is-the-symbol-triangleq"
-       - "https://drive.google.com/file/d/1z_dcQ6lsOA_0CsH55fwcg4hQF_w22olM/view"
-      alias:
-       - defined-to-be-equal-to
-       - equal-to-by-definition
-    
-    - concept: degree
-      arity: 1
-      en: degree of $1
-      property: prefix, postfix
-      area: "physics, geometry"
-      mathml:
-       - "<math><mrow intent='degree($a1)'><mi arg='a1'>x</mi><mo>°</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Degree.html"
-       - "https://en.wikipedia.org/wiki/Degree_(angle)"
-       - "https://en.wikipedia.org/wiki/Degree_(temperature)"
-       - "https://ncatlab.org/nlab/show/degree"
-       - "https://www.encyclopediaofmath.org/index.php/Degree"
-    
-    - concept: degree-of-graph
-      arity: 1
-      en: degree of graph of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='degree-of-graph($a1)'><mi>deg</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Degree_(graph_theory)"
-      alias:
-       - valency
-       - degree
-    
-    - concept: degree-of-freedom
-      arity: 0
+    property: symbol
+    subject-area: "genetics"
+    mathml:
+     - "<math><mi intent='cycle-gene'>cyc</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Cycle_(gene)"
+  
+  - concept: cyclotomic-field
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: cyclotomic field of $a1
+    property: embellished symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='cyclotomic-field($a1)'><mi>𝐐</mi><mrow><mo>(</mo><msub><mi>ζ</mi><mi arg='a1'>n</mi></msub><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CyclotomicField.html"
+     - "https://en.wikipedia.org/wiki/Cyclotomic_field"
+     - "https://ncatlab.org/nlab/show/cyclotomic+field"
+     - "https://www.encyclopediaofmath.org/index.php/Cyclotomic_field"
+  
+  - concept: cyclotomic-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> cyclotomic polynomial
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='cyclotomic-polynomial($a1)'><mi>Φ</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CyclotomicPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Cyclotomic_polynomial"
+     - "https://www.encyclopediaofmath.org/index.php/Cyclotomic_polynomials"
+  
+  - concept: dalembert-operator
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dalembert operator of $a1
+    property: prefix
+    subject-area: "partial differential equations"
+    mathml:
+     - "<math><mrow intent='dalembert-operator($a1)'><mo>☐</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/D%27Alembert_operator"
+     - "https://www.encyclopediaofmath.org/index.php/D'Alembert_operator"
+    alias:
+     - dalembertian
+     - wave-operator
+     - box-operator
+  
+  - concept: davenport-constant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: davenport constant of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='davenport-constant($a1)'><mi>D</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DavenportConstant.html"
+     - "https://en.wikipedia.org/wiki/Davenport_constant"
+     - "https://www.encyclopediaofmath.org/index.php/Davenport_constant"
+  
+  - concept: dawson-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dawson function of $a1
+    property: function
+    subject-area: "special-functions"
+    mathml:
+     - "<math><mrow intent='dawson-function($a1)'><mi>F</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='dawson-function($a1)'><mi>D</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    notationb: "mi sub D -"
+    notationa: "mi sub D +"
+    urls: 
+     - "https://mathworld.wolfram.com/DawsonsIntegral.html"
+     - "https://en.wikipedia.org/wiki/Dawson_function"
+     - "https://dlmf.nist.gov/7.2#ii"
+     - "https://dlmf.nist.gov/7.2#E5"
+    alias:
+     - dawson-integral
+  
+  - concept: decrease
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: decrease of $a1
+    property: postfix
+    subject-area: "physics"
+    mathml:
+     - "<math><mrow intent='decrease($a1)'><mi arg='a1'>x</mi><mo>↓</mo></mrow></math>"
+    urls: 
+     - "https://youtu.be/HZ7a9YkF204?t=4705"
+  
+  - concept: decrease-tends-to
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 decrease tends to $a2
+    property: infix
+    subject-area: "calculus"
+    mathml:
+     - "<math><mrow intent='decrease-tends-to($a1,$a2)'><mi arg='a1'>X</mi><mo>↘</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://math.stackexchange.com/questions/1886232/what-does-this-notation-mean-limes-from-left-right"
+     - "http://pi.math.cornell.edu/~web6720/MATH%206710%20notes.pdf"
+  
+  - concept: dedekind-eta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dedekind eta function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='dedekind-eta-function($a1)'><mi>η</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DedekindEtaFunction.html"
+     - "https://en.wikipedia.org/wiki/Dedekind_eta_function"
+     - "https://ncatlab.org/nlab/show/Dedekind+eta+function"
+  
+  - concept: dedekind-zeta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dedekind zeta function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='dedekind-zeta-function($a1)'><mi>ζ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Dedekind_zeta_function"
+  
+  - concept: deductive-closure
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: deductive closure of $a1
+    property: function
+    subject-area: "logic"
+    mathml:
+     - "<math><mrow intent='deductive-closure($a1)'><mi>Ded</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='deductive-closure($a1)'><mi>Th</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Deductive_closure"
+  
+  - concept: defined-as
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 defined as $a2
+    property: infix
+    subject-area: "general"
+    mathml:
+     - "<math><mrow intent='defined-as($a1,$a2)'><mi arg='a1'>X</mi><mo>≜</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='defined-as($a1,$a2)'><mi arg='a1'>X</mi><mo>≝</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='defined-as($a1,$a2)'><mi arg='a1'>X</mi><mo>:=</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='defined-as($a1,$a2)'><mi arg='a1'>X</mi><mover><mo>=</mo><mi>def</mi></mover><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='defined-as($a1,$a2)'><mi arg='a1'>X</mi><mo>:</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://math.stackexchange.com/questions/522864/what-is-the-symbol-triangleq"
+     - "https://drive.google.com/file/d/1z_dcQ6lsOA_0CsH55fwcg4hQF_w22olM/view"
+    alias:
+     - defined-to-be-equal-to
+     - equal-to-by-definition
+  
+  - concept: degree
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: degree of $a1
+    property: prefix, postfix
+    subject-area: "physics, geometry"
+    mathml:
+     - "<math><mrow intent='degree($a1)'><mi arg='a1'>x</mi><mo>°</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Degree.html"
+     - "https://en.wikipedia.org/wiki/Degree_(angle)"
+     - "https://en.wikipedia.org/wiki/Degree_(temperature)"
+     - "https://ncatlab.org/nlab/show/degree"
+     - "https://www.encyclopediaofmath.org/index.php/Degree"
+  
+  - concept: degree-of-graph
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: degree of graph of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='degree-of-graph($a1)'><mi>deg</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Degree_(graph_theory)"
+    alias:
+     - valency
+     - degree
+  
+  - concept: degree-of-freedom
+    arity: 0
+    arguments: []
+    speech:
       en: degree of freedom
-      property: symbol
-      area: "statistics"
-      mathml:
-       - "<math><mi intent='degree-of-freedom'>ν</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DegreeofFreedom.html"
-       - "https://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)#Notation"
-    
-    - concept: degree-of-mapping
-      arity: 1
-      en: degree of mapping of $1
-      property: function
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='degree-of-mapping($a1)'><mi>deg</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Degree_of_a_continuous_mapping"
-      alias:
-       - degree
-    
-    - concept: degree-of-polynomial
-      arity: 1
-      en: degree of polynomial of $1
-      property: function
-      area: "polynomials"
-      mathml:
-       - "<math><mrow intent='degree-of-polynomial($a1)'><mi>deg</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Degree_of_a_polynomial"
-      alias:
-       - degree
-    
-    - concept: dependence-relation
-      arity: 2
-      en: $1 dependence relation $2
-      property: infix
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='dependence-relation($a1,$a2)'><mi arg='a1'>X</mi><mo>◃</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Dependence_relation"
-    
-    - concept: dereference
-      arity: 1
-      en: dereference of $1
-      property: prefix
-      area: "programming languages"
-      mathml:
-       - "<math><mrow intent='dereference($a1)'><mo>!</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://arxiv.org/pdf/1208.5915.pdf"
-    
-    - concept: derivation-tree
-      arity: 2
-      en: derivation  $1, $2
-      property: mfrac
-      area: "logic"
-      mathml:
-       - "<math><mfrac intent='derivation-tree($a1,$a2)'><mrow arg='a1'><mi>P</mi><mi>Q</mi></mrow><mi arg='a2'>R</mi></mfrac></math>"
-      urls: 
-       - "https://www.encyclopediaofmath.org/index.php/Derivation_tree"
-    
-    - concept: derived-category
-      arity: 1
-      en: derived category of $1
-      property: function
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='derived-category($a1)'><mi>D</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Derived_category"
-       - "https://ncatlab.org/nlab/show/derived+category"
-       - "https://www.encyclopediaofmath.org/index.php/Derived_category"
-    
-    - concept: diagonal-functor
-      arity: 0
+    property: symbol
+    subject-area: "statistics"
+    mathml:
+     - "<math><mi intent='degree-of-freedom'>ν</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DegreeofFreedom.html"
+     - "https://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)#Notation"
+  
+  - concept: degree-of-mapping
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: degree of mapping of $a1
+    property: function
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='degree-of-mapping($a1)'><mi>deg</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Degree_of_a_continuous_mapping"
+    alias:
+     - degree
+  
+  - concept: degree-of-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: degree of polynomial of $a1
+    property: function
+    subject-area: "polynomials"
+    mathml:
+     - "<math><mrow intent='degree-of-polynomial($a1)'><mi>deg</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Degree_of_a_polynomial"
+    alias:
+     - degree
+  
+  - concept: dependence-relation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 dependence relation $a2
+    property: infix
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='dependence-relation($a1,$a2)'><mi arg='a1'>X</mi><mo>◃</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Dependence_relation"
+  
+  - concept: dereference
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dereference of $a1
+    property: prefix
+    subject-area: "programming languages"
+    mathml:
+     - "<math><mrow intent='dereference($a1)'><mo>!</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://arxiv.org/pdf/1208.5915.pdf"
+  
+  - concept: derivation-tree
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: derivation  $a1, $a2
+    property: mfrac
+    subject-area: "logic"
+    mathml:
+     - "<math><mfrac intent='derivation-tree($a1,$a2)'><mrow arg='a1'><mi>P</mi><mi>Q</mi></mrow><mi arg='a2'>R</mi></mfrac></math>"
+    urls: 
+     - "https://www.encyclopediaofmath.org/index.php/Derivation_tree"
+  
+  - concept: derived-category
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: derived category of $a1
+    property: function
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='derived-category($a1)'><mi>D</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Derived_category"
+     - "https://ncatlab.org/nlab/show/derived+category"
+     - "https://www.encyclopediaofmath.org/index.php/Derived_category"
+  
+  - concept: diagonal-functor
+    arity: 0
+    arguments: []
+    speech:
       en: diagonal functor
-      property: symbol
-      area: "category theory"
-      mathml:
-       - "<math><mi intent='diagonal-functor'>Δ</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Diagonal_functor"
-       - "https://ncatlab.org/nlab/show/diagonal+functor"
-    
-    - concept: diagonal-intersection
-      arity: 1
-      en: diagonal intersection of $1
-      property: function
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='diagonal-intersection($a1)'><mi>Δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Diagonal_intersection"
-    
-    - concept: diagonal-matrix
-      arity: 1
-      en: diagonal matrix of $1
-      property: function
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='diagonal-matrix($a1)'><mi>diag</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Diagonal_matrix"
-    
-    - concept: diameter
-      arity: 1
-      en: diameter of $1
-      property: symbol, prefix unit
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='diameter($a1)'><mi>d</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='diameter($a1)'><mo>⌀</mo><mi arg='a1'>x</mi></mrow></math>"
-      notationb: "mi DIA"
-      notationa: "mi dia"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Diameter#Symbol"
-    
-    - concept: dickman-function
-      arity: 1
-      en: dickman function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='dickman-function($a1)'><mi>ρ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DickmanFunction.html"
-       - "https://en.wikipedia.org/wiki/Dickman_function"
-       - "https://www.encyclopediaofmath.org/index.php/Dickman_function"
-      alias:
-       - dickman-de-bruijn-function
-    
-    - concept: different-ideal
-      arity: 1
-      en: different ideal of $1
-      property: function
-      area: "algebraic number theory"
-      mathml:
-       - "<math><msub intent='different-ideal($a1)'><mi>δ</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Different_ideal"
-      alias:
-       - different
-    
-    - concept: differential-entropy
-      arity: 1
-      en: differential entropy of $1
-      property: function
-      area: "information theory"
-      mathml:
-       - "<math><mrow intent='differential-entropy($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DifferentialEntropy.html"
-       - "https://en.wikipedia.org/wiki/Differential_entropy"
-       - "https://www.encyclopediaofmath.org/index.php/Differential_entropy"
-      alias:
-       - continuous-entropy
-    
-    - concept: differential-operator
-      arity: 1
-      en: differential operator with respect to $1
-      property: prefix
-      area: "calculus"
-      mathml:
-       - "<math><msub intent='differential-operator($a1)'><mi>D</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='differential-operator($a1)'><mo>∂</mo><mi arg='a1'>x</mi></msub></math>"
-       - "<math><mfrac intent='differential-operator($a1)'><mi>d</mi><mrow><mi>d</mi><mi arg='a1'>x</mi></mrow></mfrac></math>"
-      notationa: "mfrac d mrow d $1"
-      urls: 
-       - "https://mathworld.wolfram.com/DifferentialOperator.html"
-       - "https://en.wikipedia.org/wiki/Differential_operator"
-       - "https://ncatlab.org/nlab/show/differential+operator"
-       - "https://www.encyclopediaofmath.org/index.php/Differential_operator"
-      alias:
-       - newton-leibniz-operator
-       - differential
-       - diff
-    
-    - concept: digamma-function
-      arity: 0
+    property: symbol
+    subject-area: "category theory"
+    mathml:
+     - "<math><mi intent='diagonal-functor'>Δ</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Diagonal_functor"
+     - "https://ncatlab.org/nlab/show/diagonal+functor"
+  
+  - concept: diagonal-intersection
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: diagonal intersection of $a1
+    property: function
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='diagonal-intersection($a1)'><mi>Δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Diagonal_intersection"
+  
+  - concept: diagonal-matrix
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: diagonal matrix of $a1
+    property: function
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='diagonal-matrix($a1)'><mi>diag</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Diagonal_matrix"
+  
+  - concept: diameter
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: diameter of $a1
+    property: symbol, prefix unit
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='diameter($a1)'><mi>d</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='diameter($a1)'><mo>⌀</mo><mi arg='a1'>x</mi></mrow></math>"
+    notationb: "mi DIA"
+    notationa: "mi dia"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Diameter#Symbol"
+  
+  - concept: dickman-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dickman function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='dickman-function($a1)'><mi>ρ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DickmanFunction.html"
+     - "https://en.wikipedia.org/wiki/Dickman_function"
+     - "https://www.encyclopediaofmath.org/index.php/Dickman_function"
+    alias:
+     - dickman-de-bruijn-function
+  
+  - concept: different-ideal
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: different ideal of $a1
+    property: function
+    subject-area: "algebraic number theory"
+    mathml:
+     - "<math><msub intent='different-ideal($a1)'><mi>δ</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Different_ideal"
+    alias:
+     - different
+  
+  - concept: differential-entropy
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: differential entropy of $a1
+    property: function
+    subject-area: "information theory"
+    mathml:
+     - "<math><mrow intent='differential-entropy($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DifferentialEntropy.html"
+     - "https://en.wikipedia.org/wiki/Differential_entropy"
+     - "https://www.encyclopediaofmath.org/index.php/Differential_entropy"
+    alias:
+     - continuous-entropy
+  
+  - concept: differential-operator
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: differential operator with respect to $a1
+    property: prefix
+    subject-area: "calculus"
+    mathml:
+     - "<math><msub intent='differential-operator($a1)'><mi>D</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='differential-operator($a1)'><mo>∂</mo><mi arg='a1'>x</mi></msub></math>"
+     - "<math><mfrac intent='differential-operator($a1)'><mi>d</mi><mrow><mi>d</mi><mi arg='a1'>x</mi></mrow></mfrac></math>"
+    notationa: "mfrac d mrow d $a1"
+    urls: 
+     - "https://mathworld.wolfram.com/DifferentialOperator.html"
+     - "https://en.wikipedia.org/wiki/Differential_operator"
+     - "https://ncatlab.org/nlab/show/differential+operator"
+     - "https://www.encyclopediaofmath.org/index.php/Differential_operator"
+    alias:
+     - newton-leibniz-operator
+     - differential
+     - diff
+  
+  - concept: digamma-function
+    arity: 0
+    arguments: []
+    speech:
       en: digamma function
-      property: symbol
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='digamma-function'><mi>ψ</mi><mn>0</mn></msub></math>"
-       - "<math><msup intent='digamma-function'><mi>ψ</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msup></math>"
-       - "<math><mi intent='digamma-function'>F</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DigammaFunction.html"
-       - "https://en.wikipedia.org/wiki/Digamma_function"
-    
-    - concept: dihedral-group
-      arity: 1
-      en: $1<i>th</i> dihedral group
-      property: symbol
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='dihedral-group'><mi>D</mi><mi arg='a1'>n</mi></msub></math>"
-       - "<math><msub intent='dihedral-group'><mi>Dih</mi><mi arg='a1'>n</mi></msub></math>"
-       - "<math><msub intent='dihedral-group'><mi>D</mi><mrow><mn>2</mn><mi arg='a1'>n</mi></mrow></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DihedralGroup.html"
-       - "https://en.wikipedia.org/wiki/Dihedral_group"
-    
-    - concept: dilation
-      arity: 2
-      en: $1 dilation $2
-      property: infix
-      area: "mathematical morphology"
-      mathml:
-       - "<math><mrow intent='dilation($a1,$a2)'><mi arg='a1'>X</mi><mo>⊕</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Dilation_(morphology)"
-    
-    - concept: dilogarithm
-      arity: 1
-      en: dilogarithm of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='dilogarithm($a1)'><msub><mi>L</mi><mn>2</mn></msub><mi arg='a1'>z</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Dilogarithm.html"
-       - "https://en.wikipedia.org/wiki/Spence%27s_function"
-       - "https://dlmf.nist.gov/25.12#E1"
-       - "https://ncatlab.org/nlab/show/dilogarithm"
-       - "https://ncatlab.org/nlab/show/dilogarithm"
-      alias:
-       - spence-function
-    
-    - concept: dimension
-      arity: 1
-      en: dimension of $1
-      property: "function, fenced"
-      area: "linear algebra, graph theory"
-      mathml:
-       - "<math><mrow intent='dimension($a1)'><mi>dim</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='dimension($a1)'><mo>[</mo><mi arg='a1'>x</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Dimension.html"
-       - "https://en.wikipedia.org/wiki/Dimension_(mathematics_and_physics)"
-       - "https://en.wikipedia.org/wiki/Dimension_(graph_theory)"
-       - "https://en.wikipedia.org/wiki/Order_dimension"
-       - "https://en.wikipedia.org/wiki/Dimensions_(animation)"
-       - "https://en.wikipedia.org/wiki/Dimension_(vector_space)"
-       - "https://en.wikipedia.org/wiki/Dimension_of_an_algebraic_variety"
-       - "https://en.wikipedia.org/wiki/Slowly_changing_dimension"
-       - "https://en.wikipedia.org/wiki/Scaling_dimension"
-       - "https://ncatlab.org/nlab/show/dimension"
-       - "https://www.encyclopediaofmath.org/index.php/Dimension"
-       - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions"
-       - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions"
-       - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values"
-    
-    - concept: dirac-delta-function
-      arity: 1
-      en: dirac delta function of $1
-      property: function
-      area: "analysis"
-      mathml:
-       - "<math><mrow intent='dirac-delta-function($a1)'><mi>δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DiracDeltaFunction.html"
-       - "https://en.wikipedia.org/wiki/Dirac_delta_function"
-      alias:
-       - delta-function
-    
-    - concept: dirac-matrix
-      arity: 0
+    property: symbol
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='digamma-function'><mi>ψ</mi><mn>0</mn></msub></math>"
+     - "<math><msup intent='digamma-function'><mi>ψ</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msup></math>"
+     - "<math><mi intent='digamma-function'>F</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DigammaFunction.html"
+     - "https://en.wikipedia.org/wiki/Digamma_function"
+  
+  - concept: dihedral-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> dihedral group
+    property: symbol
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='dihedral-group'><mi>D</mi><mi arg='a1'>n</mi></msub></math>"
+     - "<math><msub intent='dihedral-group'><mi>Dih</mi><mi arg='a1'>n</mi></msub></math>"
+     - "<math><msub intent='dihedral-group'><mi>D</mi><mrow><mn>2</mn><mi arg='a1'>n</mi></mrow></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DihedralGroup.html"
+     - "https://en.wikipedia.org/wiki/Dihedral_group"
+  
+  - concept: dilation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 dilation $a2
+    property: infix
+    subject-area: "mathematical morphology"
+    mathml:
+     - "<math><mrow intent='dilation($a1,$a2)'><mi arg='a1'>X</mi><mo>⊕</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Dilation_(morphology)"
+  
+  - concept: dilogarithm
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dilogarithm of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='dilogarithm($a1)'><msub><mi>L</mi><mn>2</mn></msub><mi arg='a1'>z</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Dilogarithm.html"
+     - "https://en.wikipedia.org/wiki/Spence%27s_function"
+     - "https://dlmf.nist.gov/25.12#E1"
+     - "https://ncatlab.org/nlab/show/dilogarithm"
+     - "https://ncatlab.org/nlab/show/dilogarithm"
+    alias:
+     - spence-function
+  
+  - concept: dimension
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dimension of $a1
+    property: "function, fenced"
+    subject-area: "linear algebra, graph theory"
+    mathml:
+     - "<math><mrow intent='dimension($a1)'><mi>dim</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='dimension($a1)'><mo>[</mo><mi arg='a1'>x</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Dimension.html"
+     - "https://en.wikipedia.org/wiki/Dimension_(mathematics_and_physics)"
+     - "https://en.wikipedia.org/wiki/Dimension_(graph_theory)"
+     - "https://en.wikipedia.org/wiki/Order_dimension"
+     - "https://en.wikipedia.org/wiki/Dimensions_(animation)"
+     - "https://en.wikipedia.org/wiki/Dimension_(vector_space)"
+     - "https://en.wikipedia.org/wiki/Dimension_of_an_algebraic_variety"
+     - "https://en.wikipedia.org/wiki/Slowly_changing_dimension"
+     - "https://en.wikipedia.org/wiki/Scaling_dimension"
+     - "https://ncatlab.org/nlab/show/dimension"
+     - "https://www.encyclopediaofmath.org/index.php/Dimension"
+     - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions"
+     - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions"
+     - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values"
+  
+  - concept: dirac-delta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dirac delta function of $a1
+    property: function
+    subject-area: "analysis"
+    mathml:
+     - "<math><mrow intent='dirac-delta-function($a1)'><mi>δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DiracDeltaFunction.html"
+     - "https://en.wikipedia.org/wiki/Dirac_delta_function"
+    alias:
+     - delta-function
+  
+  - concept: dirac-matrix
+    arity: 0
+    arguments: []
+    speech:
       en: dirac matrix
-      property: constant
-      area: "mathematical physics"
-      mathml:
-       - "<math><msup intent='dirac-matrix'><mi>γ</mi><mn>0</mn></msup></math>"
-       - "<math><msup intent='dirac-matrix'><mi>γ</mi><mn>1</mn></msup></math>"
-       - "<math><msup intent='dirac-matrix'><mi>γ</mi><mn>2</mn></msup></math>"
-       - "<math><msup intent='dirac-matrix'><mi>γ</mi><mn>3</mn></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DiracMatrices.html"
-       - "https://en.wikipedia.org/wiki/Gamma_matrices"
-       - "https://www.encyclopediaofmath.org/index.php/Dirac_matrices"
-      alias:
-       - gamma-matrix
-    
-    - concept: dirac-measure
-      arity: 1
-      en: dirac measure of $1
-      property: function
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='dirac-measure($a1)'><mi>δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Dirac_measure"
-    
-    - concept: dirac-operator
-      arity: 1
-      en: dirac operator of $1
-      property: function
-      area: "differential operators"
-      mathml:
-       - "<math><mrow intent='dirac-operator($a1)'><mi>D</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DiracOperator.html"
-       - "https://en.wikipedia.org/wiki/Dirac_operator"
-       - "https://ncatlab.org/nlab/show/Dirac+operator"
-    
-    - concept: direct-limit
-      arity: 1
-      en: direct limit of $1
-      property: prefix
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='direct-limit($a1)'><munder><mi>lim</mi><mo>→</mo></munder><mi arg='a1'>A</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DirectLimit.html"
-       - "https://en.wikipedia.org/wiki/Direct_limit"
-       - "https://ncatlab.org/nlab/show/direct+limit"
-    
-    - concept: direct-product
-      arity: 2
-      en: $1 direct product $2
-      property: infix
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='direct-product($a1,$a2)'><mi arg='a1'>X</mi><mo>×</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DirectProduct.html"
-       - "https://en.wikipedia.org/wiki/Direct_product"
-       - "https://en.wikipedia.org/wiki/Direct_product_of_groups"
-       - "https://ncatlab.org/nlab/show/direct+product"
-       - "https://www.encyclopediaofmath.org/index.php/Direct_product"
-    
-    - concept: direct-sum
-      arity: 2
-      en: $1 direct sum $2
-      property: infix
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='direct-sum($a1,$a2)'><mi arg='a1'>X</mi><mo>⊕</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DirectSum.html"
-       - "https://en.wikipedia.org/wiki/Direct_sum"
-       - "https://en.wikipedia.org/wiki/Direct_sum_of_modules"
-       - "https://en.wikipedia.org/wiki/Skew_and_direct_sums_of_permutations"
-       - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)"
-       - "https://en.wikipedia.org/wiki/Direct_sum_of_groups"
-       - "https://ncatlab.org/nlab/show/direct+sum"
-       - "https://www.encyclopediaofmath.org/index.php/Direct_sum"
-    
-    - concept: directional-derivative
-      arity: 1
-      en: directional derivative of $1
-      property: "function, mixfix"
-      area: "differential calculus"
-      mathml:
-       - "<math><msup intent='directional-derivative($a1)'><mi>∇</mi><mi>v</mi></msup><mi arg='a1'>f</mi></math>"
-       - "<math><msup intent='directional-derivative($a1)'><mi>D</mi><mi>v</mi></msup><mi arg='a1'>f</mi></math>"
-       - "<math><mrow intent='directional-derivative($a1)'><mi>v</mi><mo>⋅</mo><mi>∇</mi></mrow><mi arg='a1'>f</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DirectionalDerivative.html"
-       - "https://en.wikipedia.org/wiki/Directional_derivative"
-       - "https://ncatlab.org/nlab/show/directional+derivative"
-    
-    - concept: dirichlet-character
-      arity: 1
-      en: dirichlet character of $1
-      property: function
-      area: "special-functions"
-      mathml:
-       - "<math><mrow intent='dirichlet-character($a1)'><mi>χ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DirichletCharacter.html"
-       - "https://en.wikipedia.org/wiki/Dirichlet_character"
-       - "https://dlmf.nist.gov/27.8"
-       - "https://www.encyclopediaofmath.org/index.php/Dirichlet_character"
-    
-    - concept: dirichlet-convolution
-      arity: 2
-      en: $1 dirichlet convolution $2
-      property: infix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='dirichlet-convolution($a1,$a2)'><mi arg='a1'>X</mi><mo>∗</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Dirichlet_convolution"
-       - "https://www.encyclopediaofmath.org/index.php/Dirichlet_convolution"
-    
-    - concept: dirichlet-distribution
-      arity: 0
+    property: constant
+    subject-area: "mathematical physics"
+    mathml:
+     - "<math><msup intent='dirac-matrix'><mi>γ</mi><mn>0</mn></msup></math>"
+     - "<math><msup intent='dirac-matrix'><mi>γ</mi><mn>1</mn></msup></math>"
+     - "<math><msup intent='dirac-matrix'><mi>γ</mi><mn>2</mn></msup></math>"
+     - "<math><msup intent='dirac-matrix'><mi>γ</mi><mn>3</mn></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DiracMatrices.html"
+     - "https://en.wikipedia.org/wiki/Gamma_matrices"
+     - "https://www.encyclopediaofmath.org/index.php/Dirac_matrices"
+    alias:
+     - gamma-matrix
+  
+  - concept: dirac-measure
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dirac measure of $a1
+    property: function
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='dirac-measure($a1)'><mi>δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Dirac_measure"
+  
+  - concept: dirac-operator
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dirac operator of $a1
+    property: function
+    subject-area: "differential operators"
+    mathml:
+     - "<math><mrow intent='dirac-operator($a1)'><mi>D</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DiracOperator.html"
+     - "https://en.wikipedia.org/wiki/Dirac_operator"
+     - "https://ncatlab.org/nlab/show/Dirac+operator"
+  
+  - concept: direct-limit
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: direct limit of $a1
+    property: prefix
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='direct-limit($a1)'><munder><mi>lim</mi><mo>→</mo></munder><mi arg='a1'>A</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DirectLimit.html"
+     - "https://en.wikipedia.org/wiki/Direct_limit"
+     - "https://ncatlab.org/nlab/show/direct+limit"
+  
+  - concept: direct-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 direct product $a2
+    property: infix
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='direct-product($a1,$a2)'><mi arg='a1'>X</mi><mo>×</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DirectProduct.html"
+     - "https://en.wikipedia.org/wiki/Direct_product"
+     - "https://en.wikipedia.org/wiki/Direct_product_of_groups"
+     - "https://ncatlab.org/nlab/show/direct+product"
+     - "https://www.encyclopediaofmath.org/index.php/Direct_product"
+  
+  - concept: direct-sum
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 direct sum $a2
+    property: infix
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='direct-sum($a1,$a2)'><mi arg='a1'>X</mi><mo>⊕</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DirectSum.html"
+     - "https://en.wikipedia.org/wiki/Direct_sum"
+     - "https://en.wikipedia.org/wiki/Direct_sum_of_modules"
+     - "https://en.wikipedia.org/wiki/Skew_and_direct_sums_of_permutations"
+     - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)"
+     - "https://en.wikipedia.org/wiki/Direct_sum_of_groups"
+     - "https://ncatlab.org/nlab/show/direct+sum"
+     - "https://www.encyclopediaofmath.org/index.php/Direct_sum"
+  
+  - concept: directional-derivative
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: directional derivative of $a1
+    property: "function, mixfix"
+    subject-area: "differential calculus"
+    mathml:
+     - "<math><msup intent='directional-derivative($a1)'><mi>∇</mi><mi>v</mi></msup><mi arg='a1'>f</mi></math>"
+     - "<math><msup intent='directional-derivative($a1)'><mi>D</mi><mi>v</mi></msup><mi arg='a1'>f</mi></math>"
+     - "<math><mrow intent='directional-derivative($a1)'><mi>v</mi><mo>⋅</mo><mi>∇</mi></mrow><mi arg='a1'>f</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DirectionalDerivative.html"
+     - "https://en.wikipedia.org/wiki/Directional_derivative"
+     - "https://ncatlab.org/nlab/show/directional+derivative"
+  
+  - concept: dirichlet-character
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dirichlet character of $a1
+    property: function
+    subject-area: "special-functions"
+    mathml:
+     - "<math><mrow intent='dirichlet-character($a1)'><mi>χ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DirichletCharacter.html"
+     - "https://en.wikipedia.org/wiki/Dirichlet_character"
+     - "https://dlmf.nist.gov/27.8"
+     - "https://www.encyclopediaofmath.org/index.php/Dirichlet_character"
+  
+  - concept: dirichlet-convolution
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 dirichlet convolution $a2
+    property: infix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='dirichlet-convolution($a1,$a2)'><mi arg='a1'>X</mi><mo>∗</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Dirichlet_convolution"
+     - "https://www.encyclopediaofmath.org/index.php/Dirichlet_convolution"
+  
+  - concept: dirichlet-distribution
+    arity: 0
+    arguments: []
+    speech:
       en: dirichlet distribution
-      property: symbol
-      area: "statistics"
-      mathml:
-       - "<math><mi intent='dirichlet-distribution'>Dir</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DirichletDistribution.html"
-       - "https://en.wikipedia.org/wiki/Dirichlet_distribution"
-       - "https://www.encyclopediaofmath.org/index.php/Dirichlet_distribution"
-    
-    - concept: dirichlet-eta-function
-      arity: 1
-      en: dirichlet eta function of $1
-      property: function
-      area: "analytic number theory"
-      mathml:
-       - "<math><mrow intent='dirichlet-eta-function($a1)'><mi>η</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DirichletEtaFunction.html"
-       - "https://en.wikipedia.org/wiki/%CE%97(x)"
-       - "https://en.wikipedia.org/wiki/Dirichlet_eta_function"
-    
-    - concept: dirichlet-kernel
-      arity: 1
-      en: dirichlet kernel of $1
-      property: function
-      area: "mathematical analysis"
-      mathml:
-       - "<math><msup intent='dirichlet-kernel($a1)'><mi>D</mi><mi>n</mi></msup><mi arg='a1'>f</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DirichletKernel.html"
-       - "https://en.wikipedia.org/wiki/Dirichlet_kernel"
-       - "https://www.encyclopediaofmath.org/index.php/Dirichlet_kernel"
-    
-    - concept: dirichlet-l-function
-      arity: 1
-      en: dirichlet l function of $1
-      property: function
-      area: "special-functions"
-      mathml:
-       - "<math><mrow intent='dirichlet-l-function($a1)'><mi>L</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DirichletL-Function.html"
-       - "https://en.wikipedia.org/wiki/Dirichlet_L-function"
-      alias:
-       - dirichlet-l-series
-    
-    - concept: discrete-valuation
-      arity: 1
-      en: discrete valuation of $1
-      property: function
-      area: "commutative algebra"
-      mathml:
-       - "<math><mrow intent='discrete-valuation($a1)'><mi>ν</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Discrete_valuation"
-       - "https://ncatlab.org/nlab/show/discrete+valuation"
-    
-    - concept: discriminant
-      arity: 1
-      en: discriminant of $1
-      property: function
-      area: "polynomials"
-      mathml:
-       - "<math><mrow intent='discriminant($a1)'><mi>Disc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='discriminant($a1)'><mi>D</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='discriminant($a1)'><mi>Δ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Discriminant.html"
-       - "https://en.wikipedia.org/wiki/Discriminant"
-       - "https://ncatlab.org/nlab/show/discriminant"
-       - "https://www.encyclopediaofmath.org/index.php/Discriminant"
-    
-    - concept: disjoint-union
-      arity: 1
-      en: disjoint union of $1
-      property: indexed
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='disjoint-union($a1)'><msub><mo>&#x2a06;</mo><mrow><mi>i</mi><mo>&#x2208;</mo><mi>A</mi></mrow></msub><msup><mi arg='a1'>A</mi><mi>i</mi></msup></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DisjointUnion.html"
-       - "https://en.wikipedia.org/wiki/Disjoint_union"
-       - "https://en.wikipedia.org/wiki/Tagged_union"
-       - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)"
-       - "https://ncatlab.org/nlab/show/disjoint+union"
+    property: symbol
+    subject-area: "statistics"
+    mathml:
+     - "<math><mi intent='dirichlet-distribution'>Dir</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DirichletDistribution.html"
+     - "https://en.wikipedia.org/wiki/Dirichlet_distribution"
+     - "https://www.encyclopediaofmath.org/index.php/Dirichlet_distribution"
+  
+  - concept: dirichlet-eta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dirichlet eta function of $a1
+    property: function
+    subject-area: "analytic number theory"
+    mathml:
+     - "<math><mrow intent='dirichlet-eta-function($a1)'><mi>η</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DirichletEtaFunction.html"
+     - "https://en.wikipedia.org/wiki/%CE%97(x)"
+     - "https://en.wikipedia.org/wiki/Dirichlet_eta_function"
+  
+  - concept: dirichlet-kernel
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dirichlet kernel of $a1
+    property: function
+    subject-area: "mathematical analysis"
+    mathml:
+     - "<math><msup intent='dirichlet-kernel($a1)'><mi>D</mi><mi>n</mi></msup><mi arg='a1'>f</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DirichletKernel.html"
+     - "https://en.wikipedia.org/wiki/Dirichlet_kernel"
+     - "https://www.encyclopediaofmath.org/index.php/Dirichlet_kernel"
+  
+  - concept: dirichlet-l-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dirichlet l function of $a1
+    property: function
+    subject-area: "special-functions"
+    mathml:
+     - "<math><mrow intent='dirichlet-l-function($a1)'><mi>L</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DirichletL-Function.html"
+     - "https://en.wikipedia.org/wiki/Dirichlet_L-function"
+    alias:
+     - dirichlet-l-series
+  
+  - concept: discrete-valuation
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: discrete valuation of $a1
+    property: function
+    subject-area: "commutative algebra"
+    mathml:
+     - "<math><mrow intent='discrete-valuation($a1)'><mi>ν</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Discrete_valuation"
+     - "https://ncatlab.org/nlab/show/discrete+valuation"
+  
+  - concept: discriminant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: discriminant of $a1
+    property: function
+    subject-area: "polynomials"
+    mathml:
+     - "<math><mrow intent='discriminant($a1)'><mi>Disc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='discriminant($a1)'><mi>D</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='discriminant($a1)'><mi>Δ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Discriminant.html"
+     - "https://en.wikipedia.org/wiki/Discriminant"
+     - "https://ncatlab.org/nlab/show/discriminant"
+     - "https://www.encyclopediaofmath.org/index.php/Discriminant"
+  
+  - concept: disjoint-union
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: disjoint union of $a1
+    property: indexed
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='disjoint-union($a1)'><msub><mo>&#x2a06;</mo><mrow><mi>i</mi><mo>&#x2208;</mo><mi>A</mi></mrow></msub><msup><mi arg='a1'>A</mi><mi>i</mi></msup></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DisjointUnion.html"
+     - "https://en.wikipedia.org/wiki/Disjoint_union"
+     - "https://en.wikipedia.org/wiki/Tagged_union"
+     - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)"
+     - "https://ncatlab.org/nlab/show/disjoint+union"
 
-    - concept: disjoint-union
-      arity: 2
-      en: disjoint union of $1 and $2
-      property: infix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='disjoint-union($a1,$a2)'><mi arg='a1'>A</mi><msup><mi></mi><mo>*</mo></msup><mi arg='a2'>B</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DisjointUnion.html"
-       - "https://en.wikipedia.org/wiki/Disjoint_union"
-       - "https://en.wikipedia.org/wiki/Tagged_union"
-       - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)"
-       - "https://ncatlab.org/nlab/show/disjoint+union"
-    
-    - concept: distance
-      arity: 2
+  - concept: disjoint-union
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: disjoint union of $a1 and $a2
+    property: infix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='disjoint-union($a1,$a2)'><mi arg='a1'>A</mi><msup><mi></mi><mo>*</mo></msup><mi arg='a2'>B</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DisjointUnion.html"
+     - "https://en.wikipedia.org/wiki/Disjoint_union"
+     - "https://en.wikipedia.org/wiki/Tagged_union"
+     - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)"
+     - "https://ncatlab.org/nlab/show/disjoint+union"
+  
+  - concept: distance
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: distance
-      property: fenced
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='distance($a1,$a2)'><mo>|</mo><mi arg='a1'>X</mi><mo>&#x2009;</mo><mi arg='a2'>Y</mi><mo>|</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Distance"
-    
-    - concept: diverge
-      arity: 1
-      en: $1 diverges
-      property: postfix
-      area: "computer science"
-      mathml:
-       - "<math><mrow intent='diverge($a1)'><mi arg='a1'>x</mi><mo>↑</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Divergence_(computer_science)"
-      alias:
-       - divergence
-    
-    - concept: divergence
-      arity: 1
-      en: divergence of $1
-      property: "function, mixfix"
-      area: "vector calculus"
-      mathml:
-       - "<math><mrow intent='divergence($a1)'><mi>div</mi><mi arg='a1'>f</mi></mrow></math>"
-       - "<math><mrow intent='divergence($a1)'><mi>∇</mi><mo>⋅</mo><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Divergence.html"
-       - "https://en.wikipedia.org/wiki/Divergence_(computer_science)"
-       - "https://en.wikipedia.org/wiki/Divergence"
-       - "https://en.wikipedia.org/wiki/Divergence_(statistics)"
-       - "https://ncatlab.org/nlab/show/divergence"
-       - "https://www.encyclopediaofmath.org/index.php/Divergence"
-    
-    - concept: divided-difference
-      arity: ">=0"
-      en: divided difference of $1 ..
-      property: "fenced, mixfix"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='divided-difference($a1)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>,</mo><mi arg='a3'>z</mi><mo>]</mo></mrow></math>"
-       - "<math><mrow intent='divided-difference($a1)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>,</mo><mi arg='a3'>z</mi><mo>]</mo></mrow></math>"
-       - "<math><mrow intent='divided-difference($a1)'><mi>f</mi><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>,</mo><mi arg='a3'>z</mi><mo>]</mo></mrow></math>"
-       - "<math><mrow intent='divided-difference($a1)'><mi>D</mi><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>,</mo><mi arg='a3'>z</mi><mo>]</mo><mi>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DividedDifference.html"
-       - "https://en.wikipedia.org/wiki/Divided_differences"
-       - "https://dlmf.nist.gov/3.3#SS3.p1"
-    
-    - concept: divisible-by
-      arity: 2
-      en: $1 divisible by $2
-      property: infix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='divisible-by($a1,$a2)'><mi arg='a1'>X</mi><mo>|</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='divisible-by($a1,$a2)'><mi arg='a2'>Y</mi><mo>⋮</mo><mi arg='a1'>X</mi></mrow></math>"
-       - "<math><mrow intent='divisible-by($a1,$a2)'><mi arg='a2'>Y</mi><mo>/</mo><mi arg='a1'>X</mi></mrow></math>"
-      urls: 
-       - "https://youtu.be/9dyK_op-Ocw?t=251"
-       - "https://en.wikipedia.org/wiki/Divisor"
-       - "https://ru.wikipedia.org/wiki/%D0%94%D0%B5%D0%BB%D0%B8%D0%BC%D0%BE%D1%81%D1%82%D1%8C"
-       - "https://youtu.be/a3wyG2mkmxc?t=32"
-      alias:
-       - divides
-    
-    
-    - concept: divisor-function
-      arity: 1
-      en: divisor function of $1
-      property: indexed
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='divisor-function($a1)'><mi>σ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DivisorFunction.html"
-       - "https://en.wikipedia.org/wiki/D(n)"
-       - "https://en.wikipedia.org/wiki/%CE%A3(n)"
-       - "https://en.wikipedia.org/wiki/Divisor_function"
-       - "https://dlmf.nist.gov/27.2#E9"
-       - "https://dlmf.nist.gov/27.2#SS1.p4"
-    
-    - concept: domain
-      arity: 1
-      en: domain of $1
-      property: function
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='domain($a1)'><mi>dom</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Domain_of_a_function"
-    
-    - concept: domain-of-discourse
-      arity: 0
+    property: fenced
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='distance($a1,$a2)'><mo>|</mo><mi arg='a1'>X</mi><mo>&#x2009;</mo><mi arg='a2'>Y</mi><mo>|</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Distance"
+  
+  - concept: diverge
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1 diverges
+    property: postfix
+    subject-area: "computer science"
+    mathml:
+     - "<math><mrow intent='diverge($a1)'><mi arg='a1'>x</mi><mo>↑</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Divergence_(computer_science)"
+    alias:
+     - divergence
+  
+  - concept: divergence
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: divergence of $a1
+    property: "function, mixfix"
+    subject-area: "vector calculus"
+    mathml:
+     - "<math><mrow intent='divergence($a1)'><mi>div</mi><mi arg='a1'>f</mi></mrow></math>"
+     - "<math><mrow intent='divergence($a1)'><mi>∇</mi><mo>⋅</mo><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Divergence.html"
+     - "https://en.wikipedia.org/wiki/Divergence_(computer_science)"
+     - "https://en.wikipedia.org/wiki/Divergence"
+     - "https://en.wikipedia.org/wiki/Divergence_(statistics)"
+     - "https://ncatlab.org/nlab/show/divergence"
+     - "https://www.encyclopediaofmath.org/index.php/Divergence"
+  
+  - concept: divided-difference
+    arity: ">=0"
+    speech:
+      en: divided difference of $a1 ..
+    property: "fenced, mixfix"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='divided-difference($a1)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>,</mo><mi arg='a3'>z</mi><mo>]</mo></mrow></math>"
+     - "<math><mrow intent='divided-difference($a1)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>,</mo><mi arg='a3'>z</mi><mo>]</mo></mrow></math>"
+     - "<math><mrow intent='divided-difference($a1)'><mi>f</mi><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>,</mo><mi arg='a3'>z</mi><mo>]</mo></mrow></math>"
+     - "<math><mrow intent='divided-difference($a1)'><mi>D</mi><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>,</mo><mi arg='a3'>z</mi><mo>]</mo><mi>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DividedDifference.html"
+     - "https://en.wikipedia.org/wiki/Divided_differences"
+     - "https://dlmf.nist.gov/3.3#SS3.p1"
+  
+  - concept: divisible-by
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 divisible by $a2
+    property: infix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='divisible-by($a1,$a2)'><mi arg='a1'>X</mi><mo>|</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='divisible-by($a1,$a2)'><mi arg='a2'>Y</mi><mo>⋮</mo><mi arg='a1'>X</mi></mrow></math>"
+     - "<math><mrow intent='divisible-by($a1,$a2)'><mi arg='a2'>Y</mi><mo>/</mo><mi arg='a1'>X</mi></mrow></math>"
+    urls: 
+     - "https://youtu.be/9dyK_op-Ocw?t=251"
+     - "https://en.wikipedia.org/wiki/Divisor"
+     - "https://ru.wikipedia.org/wiki/%D0%94%D0%B5%D0%BB%D0%B8%D0%BC%D0%BE%D1%81%D1%82%D1%8C"
+     - "https://youtu.be/$a3wyG2mkmxc?t=32"
+    alias:
+     - divides
+  
+  
+  - concept: divisor-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: divisor function of $a1
+    property: indexed
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='divisor-function($a1)'><mi>σ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DivisorFunction.html"
+     - "https://en.wikipedia.org/wiki/D(n)"
+     - "https://en.wikipedia.org/wiki/%CE%A3(n)"
+     - "https://en.wikipedia.org/wiki/Divisor_function"
+     - "https://dlmf.nist.gov/27.2#E9"
+     - "https://dlmf.nist.gov/27.2#SS1.p4"
+  
+  - concept: domain
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: domain of $a1
+    property: function
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='domain($a1)'><mi>dom</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Domain_of_a_function"
+  
+  - concept: domain-of-discourse
+    arity: 0
+    arguments: []
+    speech:
       en: domain of discourse
-      property: symbol
-      area: "formal semantics"
-      mathml:
-       - "<math><mi intent='domain-of-discourse'>𝔻</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Domain_of_discourse"
-      alias:
-       - universe-of-discourse
-    
-    - concept: domination-number
-      arity: 1
-      en: domination number of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='domination-number($a1)'><mi>γ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DominationNumber.html"
-       - "https://en.wikipedia.org/wiki/Dominating_set"
-       - "https://en.wikipedia.org/wiki/Domination_number"
-       - "https://en.wikipedia.org/wiki/Independent_domination_number"
-       - "https://en.wikipedia.org/wiki/Domination_analysis"
-       - "https://en.wikipedia.org/wiki/Domination_perfect_graph"
-    
-    - concept: dot-product
-      arity: 2
-      en: $1 dot product $2
-      property: infix
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='dot-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⋅</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DotProduct.html"
-       - "https://en.wikipedia.org/wiki/Dot_product"
-      alias:
-       - scalar-product
-    
-    - concept: double-bond
-      arity: 2
-      en: $1 double bond $2
-      property: infix
-      area: "chemistry"
-      mathml:
-       - "<math><mrow intent='double-bond($a1,$a2)'><mi arg='a1'>X</mi><mo>=</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Double_bond"
-    
-    - concept: double-category
-      arity: 2
-      en: $1 double category $2
-      property: infix
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='double-category($a1,$a2)'><mi arg='a1'>X</mi><mo>⇉</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/double+category"
-    
-    - concept: double-factorial
-      arity: 1
-      en: double factorial of $1
-      property: postfix
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='double-factorial($a1)'><mn arg='a1'>10</mn><mo>&#x203c;</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DoubleFactorial.html"
-       - "https://en.wikipedia.org/wiki/Double_factorial"
-       - "https://arxiv.org/pdf/0806.2334.pdf"
-      alias:
-       - semifactorial
-    
-    - concept: double-mersenne-number
-      arity: 0
+    property: symbol
+    subject-area: "formal semantics"
+    mathml:
+     - "<math><mi intent='domain-of-discourse'>𝔻</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Domain_of_discourse"
+    alias:
+     - universe-of-discourse
+  
+  - concept: domination-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: domination number of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='domination-number($a1)'><mi>γ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DominationNumber.html"
+     - "https://en.wikipedia.org/wiki/Dominating_set"
+     - "https://en.wikipedia.org/wiki/Domination_number"
+     - "https://en.wikipedia.org/wiki/Independent_domination_number"
+     - "https://en.wikipedia.org/wiki/Domination_analysis"
+     - "https://en.wikipedia.org/wiki/Domination_perfect_graph"
+  
+  - concept: dot-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 dot product $a2
+    property: infix
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='dot-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⋅</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DotProduct.html"
+     - "https://en.wikipedia.org/wiki/Dot_product"
+    alias:
+     - scalar-product
+  
+  - concept: double-bond
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 double bond $a2
+    property: infix
+    subject-area: "chemistry"
+    mathml:
+     - "<math><mrow intent='double-bond($a1,$a2)'><mi arg='a1'>X</mi><mo>=</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Double_bond"
+  
+  - concept: double-category
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 double category $a2
+    property: infix
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='double-category($a1,$a2)'><mi arg='a1'>X</mi><mo>⇉</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/double+category"
+  
+  - concept: double-factorial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: double factorial of $a1
+    property: postfix
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='double-factorial($a1)'><mn arg='a1'>10</mn><mo>&#x203c;</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DoubleFactorial.html"
+     - "https://en.wikipedia.org/wiki/Double_factorial"
+     - "https://arxiv.org/pdf/0806.2334.pdf"
+    alias:
+     - semifactorial
+  
+  - concept: double-mersenne-number
+    arity: 0
+    arguments: []
+    speech:
       en: double mersenne number
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='double-mersenne-number'><mi>M</mi><msub><mi>M</mi><mi>p</mi></msub></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DoubleMersenneNumber.html"
-       - "https://en.wikipedia.org/wiki/Double_Mersenne_number"
-       - "https://en.wikipedia.org/wiki/Double_Mersenne_prime"
-       - "https://en.wikipedia.org/wiki/Catalan%27s_Mersenne_conjecture"
-    
-    - concept: drinfeld-center
-      arity: 1
-      en: drinfeld center of $1
-      property: prefix
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='drinfeld-center($a1)'><mi>𝒵</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Center_(category_theory)"
-      alias:
-       - center
-    
-    - concept: dual-basis
-      arity: 1
-      en: dual basis of $1
-      property: msup
-      area: "linear algebra"
-      mathml:
-       - "<math><msup intent='dual-basis($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DualBasis.html"
-       - "https://en.wikipedia.org/wiki/Dual_basis"
-       - "https://ncatlab.org/nlab/show/dual+basis"
-       - "https://www.encyclopediaofmath.org/index.php/Dual_basis"
-      alias:
-       - dual-set
-       - reciprocal-basis
-    
-    - concept: dual-bundle
-      arity: 1
-      en: dual bundle of $1
-      property: msup
-      area: "vector bundles"
-      mathml:
-       - "<math><msup intent='dual-bundle($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DualBundle.html"
-       - "https://en.wikipedia.org/wiki/Dual_bundle"
-       - "https://www.encyclopediaofmath.org/index.php/Dual_bundle"
-      alias:
-       - dual
-    
-    - concept: dual-space
-      arity: 1
-      en: dual space of $1
-      property: msup
-      area: "linear algebra"
-      mathml:
-       - "<math><msup intent='dual-space($a1)'><mi arg='a1'>V</mi><mo>*</mo></msup></math>"
-       - "<math><msup intent='dual-space($a1)'><mi arg='a1'>V</mi><mo>&#x2032;</mo></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DualSpace.html"
-       - "https://en.wikipedia.org/wiki/Dual_space"
-       - "https://ncatlab.org/nlab/show/dual+space"
-      alias:
-       - dual
-    
-    - concept: duodecimal
-      arity: 1
-      en: duodecimal of $1
-      property: unit
-      area: "arithmetic"
-      mathml:
-       - "<math><msub intent='duodecimal($a1)'><mi arg='a1'>n</mi><mi>z</mi></msub></math>"
-       - "<math><msub intent='duodecimal($a1)'><mi arg='a1'>n</mi><mn>12</mn></msub></math>"
-       - "<math><msub intent='duodecimal($a1)'><mi arg='a1'>n</mi><mi>doz</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Duodecimal.html"
-       - "https://en.wikipedia.org/wiki/Duodecimal#Base_notation"
-      alias:
-       - base-twelve
-       - dozenal
-    
-    - concept: e-function
-      arity: 1
-      en: e function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='e-function($a1)'><mi>E</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/E-Function.html"
-       - "https://en.wikipedia.org/wiki/E-function"
-       - "https://en.wikipedia.org/wiki/MacRobert_E_function"
-       - "https://www.encyclopediaofmath.org/index.php/E-function"
-    
-    - concept: eccentricity
-      arity: 0
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='double-mersenne-number'><mi>M</mi><msub><mi>M</mi><mi>p</mi></msub></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DoubleMersenneNumber.html"
+     - "https://en.wikipedia.org/wiki/Double_Mersenne_number"
+     - "https://en.wikipedia.org/wiki/Double_Mersenne_prime"
+     - "https://en.wikipedia.org/wiki/Catalan%27s_Mersenne_conjecture"
+  
+  - concept: drinfeld-center
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: drinfeld center of $a1
+    property: prefix
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='drinfeld-center($a1)'><mi>𝒵</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Center_(category_theory)"
+    alias:
+     - center
+  
+  - concept: dual-basis
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dual basis of $a1
+    property: msup
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><msup intent='dual-basis($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DualBasis.html"
+     - "https://en.wikipedia.org/wiki/Dual_basis"
+     - "https://ncatlab.org/nlab/show/dual+basis"
+     - "https://www.encyclopediaofmath.org/index.php/Dual_basis"
+    alias:
+     - dual-set
+     - reciprocal-basis
+  
+  - concept: dual-bundle
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dual bundle of $a1
+    property: msup
+    subject-area: "vector bundles"
+    mathml:
+     - "<math><msup intent='dual-bundle($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DualBundle.html"
+     - "https://en.wikipedia.org/wiki/Dual_bundle"
+     - "https://www.encyclopediaofmath.org/index.php/Dual_bundle"
+    alias:
+     - dual
+  
+  - concept: dual-space
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: dual space of $a1
+    property: msup
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><msup intent='dual-space($a1)'><mi arg='a1'>V</mi><mo>*</mo></msup></math>"
+     - "<math><msup intent='dual-space($a1)'><mi arg='a1'>V</mi><mo>&#x2032;</mo></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DualSpace.html"
+     - "https://en.wikipedia.org/wiki/Dual_space"
+     - "https://ncatlab.org/nlab/show/dual+space"
+    alias:
+     - dual
+  
+  - concept: duodecimal
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: duodecimal of $a1
+    property: unit
+    subject-area: "arithmetic"
+    mathml:
+     - "<math><msub intent='duodecimal($a1)'><mi arg='a1'>n</mi><mi>z</mi></msub></math>"
+     - "<math><msub intent='duodecimal($a1)'><mi arg='a1'>n</mi><mn>12</mn></msub></math>"
+     - "<math><msub intent='duodecimal($a1)'><mi arg='a1'>n</mi><mi>doz</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Duodecimal.html"
+     - "https://en.wikipedia.org/wiki/Duodecimal#Base_notation"
+    alias:
+     - base-twelve
+     - dozenal
+  
+  - concept: e-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: e function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='e-function($a1)'><mi>E</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/E-Function.html"
+     - "https://en.wikipedia.org/wiki/E-function"
+     - "https://en.wikipedia.org/wiki/MacRobert_E_function"
+     - "https://www.encyclopediaofmath.org/index.php/E-function"
+  
+  - concept: eccentricity
+    arity: 0
+    arguments: []
+    speech:
       en: eccentricity
-      property: symbol
-      area: "analytic geometry, graph theory"
-      mathml:
-       - "<math><mi intent='eccentricity'>e</mi></math>"
-       - "<math><mi intent='eccentricity'>ϵ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Eccentricity.html"
-       - "https://en.wikipedia.org/wiki/Eccentricity_(mathematics)"
-       - "https://www.encyclopediaofmath.org/index.php/Eccentricity"
-    
-    - concept: edge-cover-number
-      arity: 1
-      en: edge cover number of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='edge-cover-number($a1)'><mi>ρ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EdgeCoverNumber.html"
-       - "https://en.wikipedia.org/wiki/Edge_covering_number"
-    
-    - concept: effective-domain
-      arity: 1
-      en: effective domain of $1
-      property: function
-      area: "convex analysis"
-      mathml:
-       - "<math><mrow intent='effective-domain($a1)'><mi>dom</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Effective_domain"
-    
-    - concept: efficiency
-      arity: 1
-      en: efficiency of $1
-      property: function
-      area: "statistics"
-      mathml:
-       - "<math><mrow intent='efficiency($a1)'><mi>e</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Antenna_efficiency"
-       - "https://en.wikipedia.org/wiki/Efficiency_(statistics)"
-       - "https://en.wikipedia.org/wiki/Efficiency"
-    
-    - concept: einstein-tensor
-      arity: 0
+    property: symbol
+    subject-area: "analytic geometry, graph theory"
+    mathml:
+     - "<math><mi intent='eccentricity'>e</mi></math>"
+     - "<math><mi intent='eccentricity'>ϵ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Eccentricity.html"
+     - "https://en.wikipedia.org/wiki/Eccentricity_(mathematics)"
+     - "https://www.encyclopediaofmath.org/index.php/Eccentricity"
+  
+  - concept: edge-cover-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: edge cover number of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='edge-cover-number($a1)'><mi>ρ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EdgeCoverNumber.html"
+     - "https://en.wikipedia.org/wiki/Edge_covering_number"
+  
+  - concept: effective-domain
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: effective domain of $a1
+    property: function
+    subject-area: "convex analysis"
+    mathml:
+     - "<math><mrow intent='effective-domain($a1)'><mi>dom</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Effective_domain"
+  
+  - concept: efficiency
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: efficiency of $a1
+    property: function
+    subject-area: "statistics"
+    mathml:
+     - "<math><mrow intent='efficiency($a1)'><mi>e</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Antenna_efficiency"
+     - "https://en.wikipedia.org/wiki/Efficiency_(statistics)"
+     - "https://en.wikipedia.org/wiki/Efficiency"
+  
+  - concept: einstein-tensor
+    arity: 0
+    arguments: []
+    speech:
       en: einstein tensor
-      property: symbol
-      area: "general relativity"
-      mathml:
-       - "<math><mi intent='einstein-tensor'>G</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EinsteinTensor.html"
-       - "https://en.wikipedia.org/wiki/Einstein_tensor"
-       - "https://ncatlab.org/nlab/show/Einstein+tensor"
-    
-    - concept: elliptic-function
-      arity: 1
-      en: elliptic function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='elliptic-function($a1)'><mi>cn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='elliptic-function($a1)'><mi>sn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='elliptic-function($a1)'><mi>dn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EllipticFunction.html"
-       - "https://en.wikipedia.org/wiki/Elliptic_function"
-       - "https://ncatlab.org/nlab/show/elliptic+function"
-       - "https://www.encyclopediaofmath.org/index.php/Elliptic_function"
-       - "https://mathworld.wolfram.com/JacobiEllipticFunctions.html"
-    
-    - concept: end
-      arity: 0
+    property: symbol
+    subject-area: "general relativity"
+    mathml:
+     - "<math><mi intent='einstein-tensor'>G</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EinsteinTensor.html"
+     - "https://en.wikipedia.org/wiki/Einstein_tensor"
+     - "https://ncatlab.org/nlab/show/Einstein+tensor"
+  
+  - concept: elliptic-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: elliptic function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='elliptic-function($a1)'><mi>cn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='elliptic-function($a1)'><mi>sn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='elliptic-function($a1)'><mi>dn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EllipticFunction.html"
+     - "https://en.wikipedia.org/wiki/Elliptic_function"
+     - "https://ncatlab.org/nlab/show/elliptic+function"
+     - "https://www.encyclopediaofmath.org/index.php/Elliptic_function"
+     - "https://mathworld.wolfram.com/JacobiEllipticFunctions.html"
+  
+  - concept: end
+    arity: 0
+    arguments: []
+    speech:
       en: end
-      property: symbol
-      area: "category theory"
-      mathml:
-       - "<math><mi intent='end'>e</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/End_(category_theory)"
-       - "https://ncatlab.org/nlab/show/end"
-    
-    - concept: endomorphism-monoid
-      arity: 1
-      en: endomorphism monoid of $1
-      property: function
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='endomorphism-monoid($a1)'><mi>End</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Endomorphism.html"
-       - "https://en.wikipedia.org/wiki/Endomorphism"
-       - "https://ncatlab.org/nlab/show/endomorphism"
-       - "https://www.encyclopediaofmath.org/index.php/Endomorphism"
-    
-    - concept: energy
-      arity: 0
+    property: symbol
+    subject-area: "category theory"
+    mathml:
+     - "<math><mi intent='end'>e</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/End_(category_theory)"
+     - "https://ncatlab.org/nlab/show/end"
+  
+  - concept: endomorphism-monoid
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: endomorphism monoid of $a1
+    property: function
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='endomorphism-monoid($a1)'><mi>End</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Endomorphism.html"
+     - "https://en.wikipedia.org/wiki/Endomorphism"
+     - "https://ncatlab.org/nlab/show/endomorphism"
+     - "https://www.encyclopediaofmath.org/index.php/Endomorphism"
+  
+  - concept: energy
+    arity: 0
+    arguments: []
+    speech:
       en: energy
-      property: symbol
-      area: "physics"
-      mathml:
-       - "<math><mi intent='energy'>E</mi></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/energy"
-    
-    - concept: energy-of-signal
-      arity: 0
+    property: symbol
+    subject-area: "physics"
+    mathml:
+     - "<math><mi intent='energy'>E</mi></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/energy"
+  
+  - concept: energy-of-signal
+    arity: 0
+    arguments: []
+    speech:
       en: energy of signal
-      property: symbol
-      area: "signal processing"
-      mathml:
-       - "<math><msub intent='energy-of-signal'><mi>E</mi><mi>s</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Energy_(signal_processing)"
-       - "https://en.wikipedia.org/wiki/Energy_(signal_processing)"
-    
-    - concept: entropy
-      arity: 1
-      en: entropy of $1
-      property: unit
-      area: "physics"
-      mathml:
-       - "<math><mrow intent='entropy($a1)'><mi>S</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Entropy"
-       - "https://en.wikipedia.org/wiki/Entropy_(arrow_of_time)"
-       - "https://en.wikipedia.org/wiki/Entropy_(classical_thermodynamics)"
-       - "https://en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics)"
-       - "https://en.wikipedia.org/wiki/History_of_entropy"
-    
-    - concept: epigraph
-      arity: 1
-      en: epigraph of $1
-      property: function
-      area: "analysis"
-      mathml:
-       - "<math><mrow intent='epigraph($a1)'><mi>epi</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Epigraph_(mathematics)"
-    
-    - concept: epsilon-number
-      arity: 0
+    property: symbol
+    subject-area: "signal processing"
+    mathml:
+     - "<math><msub intent='energy-of-signal'><mi>E</mi><mi>s</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Energy_(signal_processing)"
+     - "https://en.wikipedia.org/wiki/Energy_(signal_processing)"
+  
+  - concept: entropy
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: entropy of $a1
+    property: unit
+    subject-area: "physics"
+    mathml:
+     - "<math><mrow intent='entropy($a1)'><mi>S</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Entropy"
+     - "https://en.wikipedia.org/wiki/Entropy_(arrow_of_time)"
+     - "https://en.wikipedia.org/wiki/Entropy_(classical_thermodynamics)"
+     - "https://en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics)"
+     - "https://en.wikipedia.org/wiki/History_of_entropy"
+  
+  - concept: epigraph
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: epigraph of $a1
+    property: function
+    subject-area: "analysis"
+    mathml:
+     - "<math><mrow intent='epigraph($a1)'><mi>epi</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Epigraph_(mathematics)"
+  
+  - concept: epsilon-number
+    arity: 0
+    arguments: []
+    speech:
       en: epsilon number
-      property: symbol
-      area: "ordinal numbers"
-      mathml:
-       - "<math><mi intent='epsilon-number'>ε</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Epsilon_numbers_(mathematics)"
-    
-    - concept: equalizer
-      arity: 1
-      en: equalizer of $1
-      property: function
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='equalizer($a1)'><mi>Eq</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Equalizer.html"
-       - "https://en.wikipedia.org/wiki/Equaliser_(mathematics)"
-       - "https://ncatlab.org/nlab/show/equalizer"
-      alias:
-       - difference-kernel
-       - equaliser
-    
-    - concept: equivalence-class
-      arity: 1
-      en: equivalence class of $1
-      property: fenced
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='equivalence-class($a1)'><mo>[</mo><mi arg='a1'>X</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EquivalenceClass.html"
-       - "https://en.wikipedia.org/wiki/Equivalence_class"
-       - "https://en.wikipedia.org/wiki/Equivalence_class_(music)"
-       - "https://ncatlab.org/nlab/show/equivalence+class"
-       - "https://www.encyclopediaofmath.org/index.php/Equivalence_class"
-    
-    - concept: equivalence-relation
-      arity: 2
-      en: $1 equivalence relation $2
-      property: infix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='equivalence-relation($a1,$a2)'><mi arg='a1'>X</mi><mo>~</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EquivalenceRelation.html"
-       - "https://en.wikipedia.org/wiki/Equivalence_relation"
-       - "https://ncatlab.org/nlab/show/equivalence+relation"
-       - "https://www.encyclopediaofmath.org/index.php/Equivalence_relation"
-      alias:
-       - equivalence
-    
-    - concept: equivariant-cohomology
-      arity: 2
-      en: equivariant cohomology $1 $2
-      property: function
-      area: "algebraic topology"
-      mathml:
-       - "<math><mrow intent='equivariant-cohomology($a1,$a2)'><msubsup><mi>H</mi><mi>G</mi><mo>*</mo></msubsup><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>;</mo><mo arg='a2'>&#x039b;</mo><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Equivariant_cohomology"
-       - "https://ncatlab.org/nlab/show/equivariant+cohomology"
-       - "https://www.encyclopediaofmath.org/index.php/Equivariant_cohomology"
-    
-    - concept: erdos-borwein-constant
-      arity: 0
+    property: symbol
+    subject-area: "ordinal numbers"
+    mathml:
+     - "<math><mi intent='epsilon-number'>ε</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Epsilon_numbers_(mathematics)"
+  
+  - concept: equalizer
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: equalizer of $a1
+    property: function
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='equalizer($a1)'><mi>Eq</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Equalizer.html"
+     - "https://en.wikipedia.org/wiki/Equaliser_(mathematics)"
+     - "https://ncatlab.org/nlab/show/equalizer"
+    alias:
+     - difference-kernel
+     - equaliser
+  
+  - concept: equivalence-class
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: equivalence class of $a1
+    property: fenced
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='equivalence-class($a1)'><mo>[</mo><mi arg='a1'>X</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EquivalenceClass.html"
+     - "https://en.wikipedia.org/wiki/Equivalence_class"
+     - "https://en.wikipedia.org/wiki/Equivalence_class_(music)"
+     - "https://ncatlab.org/nlab/show/equivalence+class"
+     - "https://www.encyclopediaofmath.org/index.php/Equivalence_class"
+  
+  - concept: equivalence-relation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 equivalence relation $a2
+    property: infix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='equivalence-relation($a1,$a2)'><mi arg='a1'>X</mi><mo>~</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EquivalenceRelation.html"
+     - "https://en.wikipedia.org/wiki/Equivalence_relation"
+     - "https://ncatlab.org/nlab/show/equivalence+relation"
+     - "https://www.encyclopediaofmath.org/index.php/Equivalence_relation"
+    alias:
+     - equivalence
+  
+  - concept: equivariant-cohomology
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: equivariant cohomology $a1 $a2
+    property: function
+    subject-area: "algebraic topology"
+    mathml:
+     - "<math><mrow intent='equivariant-cohomology($a1,$a2)'><msubsup><mi>H</mi><mi>G</mi><mo>*</mo></msubsup><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>;</mo><mo arg='a2'>&#x039b;</mo><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Equivariant_cohomology"
+     - "https://ncatlab.org/nlab/show/equivariant+cohomology"
+     - "https://www.encyclopediaofmath.org/index.php/Equivariant_cohomology"
+  
+  - concept: erdos-borwein-constant
+    arity: 0
+    arguments: []
+    speech:
       en: erdos borwein constant
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='erdos-borwein-constant'>E</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Erdos-BorweinConstant.html"
-       - "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Borwein_constant"
-    
-    - concept: error-function
-      arity: 1
-      en: error function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='error-function($a1)'><mi>erf</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='error-function($a1)'><mi>erfc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='error-function($a1)'><mi>w</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ErrorFunction.html"
-       - "https://en.wikipedia.org/wiki/Error_function"
-       - "https://dlmf.nist.gov/7.2#i"
-       - "https://dlmf.nist.gov/7.2#E1"
-    
-    - concept: essential-extension
-      arity: 2
-      en: $1 essential extension $2
-      property: infix
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='essential-extension($a1,$a2)'><mi arg='a1'>X</mi><msub><mo>⊆</mo><mi>e</mi></msub><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='essential-extension($a1,$a2)'><mi arg='a1'>X</mi><mo>⊴</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='essential-extension($a1,$a2)'><mi arg='a1'>X</mi><mo>⊂</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Essential_extension"
-      alias:
-       - essential-submodule
-       - large-submodule
-    
-    - concept: essential-infimum
-      arity: 1
-      en: essential infimum of $1
-      property: function
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='essential-infimum($a1)'><mi>ess inf</mi><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/essentialsupremum.html"
-       - "https://en.wikipedia.org/wiki/essential_supremum_and_essential_infimum"
-       - "https://ncatlab.org/nlab/show/essential+supremum"
-    
-    - concept: essential-supremum
-      arity: 1
-      en: essential supremum of $1
-      property: function
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='essential-supremum($a1)'><mi>ess sup</mi><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EssentialSupremum.html"
-       - "https://en.wikipedia.org/wiki/Essential_supremum_and_essential_infimum"
-       - "https://ncatlab.org/nlab/show/essential+supremum"
-    
-    - concept: estimated
-      arity: 0
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='erdos-borwein-constant'>E</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Erdos-BorweinConstant.html"
+     - "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Borwein_constant"
+  
+  - concept: error-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: error function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='error-function($a1)'><mi>erf</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='error-function($a1)'><mi>erfc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='error-function($a1)'><mi>w</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ErrorFunction.html"
+     - "https://en.wikipedia.org/wiki/Error_function"
+     - "https://dlmf.nist.gov/7.2#i"
+     - "https://dlmf.nist.gov/7.2#E1"
+  
+  - concept: essential-extension
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 essential extension $a2
+    property: infix
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='essential-extension($a1,$a2)'><mi arg='a1'>X</mi><msub><mo>⊆</mo><mi>e</mi></msub><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='essential-extension($a1,$a2)'><mi arg='a1'>X</mi><mo>⊴</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='essential-extension($a1,$a2)'><mi arg='a1'>X</mi><mo>⊂</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Essential_extension"
+    alias:
+     - essential-submodule
+     - large-submodule
+  
+  - concept: essential-infimum
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: essential infimum of $a1
+    property: function
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='essential-infimum($a1)'><mi>ess inf</mi><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/essentialsupremum.html"
+     - "https://en.wikipedia.org/wiki/essential_supremum_and_essential_infimum"
+     - "https://ncatlab.org/nlab/show/essential+supremum"
+  
+  - concept: essential-supremum
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: essential supremum of $a1
+    property: function
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='essential-supremum($a1)'><mi>ess sup</mi><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EssentialSupremum.html"
+     - "https://en.wikipedia.org/wiki/Essential_supremum_and_essential_infimum"
+     - "https://ncatlab.org/nlab/show/essential+supremum"
+  
+  - concept: estimated
+    arity: 0
+    arguments: []
+    speech:
       en: estimated
-      property: symbol
-      area: "symbols"
-      mathml:
-       - "<math><mi intent='estimated'>℮</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Estimation"
-      alias:
-       - estimated-sign
-       - e-mark
-    
-    - concept: etale-cohomology
-      arity: 1
-      en: etale cohomology of $1
-      property: function
-      area: "algebraic topology"
-      mathml:
-       - "<math><mrow intent='etale-cohomology($a1)'><msubsup><mi>H</mi><mi>et</mi><mo>*</mo></msubsup><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/%C3%89tale_cohomology"
-       - "https://ncatlab.org/nlab/show/etale+cohomology"
-       - "https://www.encyclopediaofmath.org/index.php/Etale_cohomology"
-    
-    - concept: euclid-number
-      arity: 1
-      en: euclid number $1
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='euclid-number($a1)'><mi>E</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EuclidNumber.html"
-       - "https://en.wikipedia.org/wiki/Euclid_number"
-    
-    - concept: euclidean-distance
-      arity: 1
-      en: euclidean distance of $1
-      property: function
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='euclidean-distance($a1)'><mi>d</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><msub intent='euclidean-distance($a1)'><mi>d</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Euclidean_distance"
-      alias:
-       - euclidean-metric
-    
-    - concept: euclidean-plane
-      arity: 0
+    property: symbol
+    subject-area: "symbols"
+    mathml:
+     - "<math><mi intent='estimated'>℮</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Estimation"
+    alias:
+     - estimated-sign
+     - e-mark
+  
+  - concept: etale-cohomology
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: etale cohomology of $a1
+    property: function
+    subject-area: "algebraic topology"
+    mathml:
+     - "<math><mrow intent='etale-cohomology($a1)'><msubsup><mi>H</mi><mi>et</mi><mo>*</mo></msubsup><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/%C3%89tale_cohomology"
+     - "https://ncatlab.org/nlab/show/etale+cohomology"
+     - "https://www.encyclopediaofmath.org/index.php/Etale_cohomology"
+  
+  - concept: euclid-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: euclid number $a1
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='euclid-number($a1)'><mi>E</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EuclidNumber.html"
+     - "https://en.wikipedia.org/wiki/Euclid_number"
+  
+  - concept: euclidean-distance
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: euclidean distance of $a1
+    property: function
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='euclidean-distance($a1)'><mi>d</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><msub intent='euclidean-distance($a1)'><mi>d</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Euclidean_distance"
+    alias:
+     - euclidean-metric
+  
+  - concept: euclidean-plane
+    arity: 0
+    arguments: []
+    speech:
       en: euclidean plane
-      property: symbol
-      area: "geometry"
-      mathml:
-       - "<math><msup intent='euclidean-plane'><mi>ℝ</mi><mn>2</mn></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EuclideanPlane.html"
-      alias:
-       - euclidean-space
-    
-    - concept: euler-characteristic
-      arity: 1
-      en: euler characteristic of $1
-      property: function
-      area: "algebraic topology"
-      mathml:
-       - "<math><mrow intent='euler-characteristic($a1)'><mi>χ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EulerCharacteristic.html"
-       - "https://en.wikipedia.org/wiki/Euler_characteristic"
-       - "https://ncatlab.org/nlab/show/Euler+characteristic"
-       - "https://www.encyclopediaofmath.org/index.php/Euler_characteristic"
-    
-    - concept: euler-class
-      arity: 1
-      en: euler class of $1
-      property: function
-      area: "algebraic topology"
-      mathml:
-       - "<math><mrow intent='euler-class($a1)'><mi>e</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Euler_class"
-       - "https://ncatlab.org/nlab/show/Euler+class"
-       - "https://www.encyclopediaofmath.org/index.php/Euler_class"
-    
-    - concept: euler-constant
-      arity: 0
+    property: symbol
+    subject-area: "geometry"
+    mathml:
+     - "<math><msup intent='euclidean-plane'><mi>ℝ</mi><mn>2</mn></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EuclideanPlane.html"
+    alias:
+     - euclidean-space
+  
+  - concept: euler-characteristic
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: euler characteristic of $a1
+    property: function
+    subject-area: "algebraic topology"
+    mathml:
+     - "<math><mrow intent='euler-characteristic($a1)'><mi>χ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EulerCharacteristic.html"
+     - "https://en.wikipedia.org/wiki/Euler_characteristic"
+     - "https://ncatlab.org/nlab/show/Euler+characteristic"
+     - "https://www.encyclopediaofmath.org/index.php/Euler_characteristic"
+  
+  - concept: euler-class
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: euler class of $a1
+    property: function
+    subject-area: "algebraic topology"
+    mathml:
+     - "<math><mrow intent='euler-class($a1)'><mi>e</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Euler_class"
+     - "https://ncatlab.org/nlab/show/Euler+class"
+     - "https://www.encyclopediaofmath.org/index.php/Euler_class"
+  
+  - concept: euler-constant
+    arity: 0
+    arguments: []
+    speech:
       en: euler constant
-      property: symbol
-      area: "analysis"
-      mathml:
-       - "<math><mi intent='euler-constant'>γ</mi></math>"
-       - "<math><mi intent='euler-constant'>𝛾</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Euler-MascheroniConstant.html"
-       - "https://en.wikipedia.org/wiki/%CE%93%27(1)"
-       - "https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant"
-       - "https://dlmf.nist.gov/5.2#E3"
-       - "https://www.encyclopediaofmath.org/index.php/Euler_constant"
-      alias:
-       - euler-mascheroni-constant
-    
-    - concept: euler-number
-      arity: 0
+    property: symbol
+    subject-area: "analysis"
+    mathml:
+     - "<math><mi intent='euler-constant'>γ</mi></math>"
+     - "<math><mi intent='euler-constant'>𝛾</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Euler-MascheroniConstant.html"
+     - "https://en.wikipedia.org/wiki/%CE%93%27(1)"
+     - "https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant"
+     - "https://dlmf.nist.gov/5.2#E3"
+     - "https://www.encyclopediaofmath.org/index.php/Euler_constant"
+    alias:
+     - euler-mascheroni-constant
+  
+  - concept: euler-number
+    arity: 0
+    arguments: []
+    speech:
       en: euler number
-      property: symbol
-      area: "physics"
-      mathml:
-       - "<math><mi intent='euler-number'>Eu</mi></math>"
-       - "<math><mi intent='euler-number'>e</mi></math>"
-       - "<math><mi intent='euler-number'>𝑒</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EulerNumber.html"
-       - "https://en.wikipedia.org/wiki/Euler_number"
-       - "https://en.wikipedia.org/wiki/Euler_number_(physics)"
-       - "https://dlmf.nist.gov/24.1#P2"
-       - "https://dlmf.nist.gov/24.2#ii"
-       - "https://ncatlab.org/nlab/show/Euler+number"
-       - "https://www.encyclopediaofmath.org/index.php/Euler_numbers"
-      alias:
-       - napier-constant
-    
-    - concept: euler-polynomial
-      arity: 1
-      en: euler polynomial of $1
-      property: function
-      area: "special-functions"
-      mathml:
-       - "<math><msub intent='euler-polynomial($a1)'><mi>E</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EulerPolynomial.html"
-       - "https://dlmf.nist.gov/24.1#P2"
-       - "https://dlmf.nist.gov/24.2#ii"
-       - "https://www.encyclopediaofmath.org/index.php/Euler_polynomials"
-    
-    - concept: euler-totient-function
-      arity: 1
-      en: euler totient function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='euler-totient-function($a1)'><mi>φ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='euler-totient-function($a1)'><mi>ϕ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EulerTotientFunction.html"
-       - "https://en.wikipedia.org/wiki/Euler%27s_totient_function"
-      alias:
-       - totient-function
-    
-    - concept: euler-mascheroni-constant
-      arity: 0
+    property: symbol
+    subject-area: "physics"
+    mathml:
+     - "<math><mi intent='euler-number'>Eu</mi></math>"
+     - "<math><mi intent='euler-number'>e</mi></math>"
+     - "<math><mi intent='euler-number'>𝑒</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EulerNumber.html"
+     - "https://en.wikipedia.org/wiki/Euler_number"
+     - "https://en.wikipedia.org/wiki/Euler_number_(physics)"
+     - "https://dlmf.nist.gov/24.1#P2"
+     - "https://dlmf.nist.gov/24.2#ii"
+     - "https://ncatlab.org/nlab/show/Euler+number"
+     - "https://www.encyclopediaofmath.org/index.php/Euler_numbers"
+    alias:
+     - napier-constant
+  
+  - concept: euler-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: euler polynomial of $a1
+    property: function
+    subject-area: "special-functions"
+    mathml:
+     - "<math><msub intent='euler-polynomial($a1)'><mi>E</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EulerPolynomial.html"
+     - "https://dlmf.nist.gov/24.1#P2"
+     - "https://dlmf.nist.gov/24.2#ii"
+     - "https://www.encyclopediaofmath.org/index.php/Euler_polynomials"
+  
+  - concept: euler-totient-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: euler totient function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='euler-totient-function($a1)'><mi>φ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='euler-totient-function($a1)'><mi>ϕ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EulerTotientFunction.html"
+     - "https://en.wikipedia.org/wiki/Euler%27s_totient_function"
+    alias:
+     - totient-function
+  
+  - concept: euler-mascheroni-constant
+    arity: 0
+    arguments: []
+    speech:
       en: euler mascheroni constant
-      property: constant
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='euler-mascheroni-constant'>γ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Euler-MascheroniConstant.html"
-       - "https://en.wikipedia.org/wiki/%CE%93%27(1)"
-       - "https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant"
-    
-    - concept: eulerian-number
-      arity: 1
-      en: eulerian number of $1
-      property: function
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='eulerian-number($a1)'><mi>A</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EulerianNumber.html"
-       - "https://en.wikipedia.org/wiki/Eulerian_number"
-       - "https://dlmf.nist.gov/26.14#SS1.p3"
-    
-    - concept: exclusive-or
-      arity: 2
-      en: $1 exclusive or $2
-      property: infix
-      area: "logic"
-      mathml:
-       - "<math><mrow intent='exclusive-or($a1,$a2)'><mi arg='a1'>X</mi><mo>⊻</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='exclusive-or($a1,$a2)'><mi arg='a1'>X</mi><mo>⊕</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='exclusive-or($a1,$a2)'><mi arg='a1'>X</mi><mo>↮</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='exclusive-or($a1,$a2)'><mi arg='a1'>X</mi><mo>≢</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='exclusive-or($a1,$a2)'><mi arg='a1'>X</mi><mi>XOR</mi><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ExclusiveDisjunction.html"
-       - "https://ncatlab.org/nlab/show/exclusive+disjunction"
-       - "https://www.encyclopediaofmath.org/index.php/Exclusive_disjunction"
-       - "https://en.wikipedia.org/wiki/Exclusive_or"
-      alias:
-       - exclusive-disjunction
-       - xor
-    
-    - concept: expectation-value
-      arity: 1
-      en: expectation value of $1
-      property: fenced
-      area: "quantum physics"
-      mathml:
-       - "<math><mrow intent='expectation-value($a1)'><mo>⟨</mo><mi arg='a1'>X</mi><mo>⟩</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ExpectationValue.html"
-       - "https://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics)"
-       - "https://ncatlab.org/nlab/show/expectation+value"
-    
-    - concept: expected-value
-      arity: 1
-      en: expected value of $1
-      property: function
-      area: "probability theory"
-      mathml:
-       - "<math><mrow intent='expected-value($a1)'><mi>E</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='expected-value($a1)'><mi>M</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><msub intent='expected-value($a1)'><mi>μ</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Expected_value#Notations"
-      alias:
-       - mathematical-expectation
-       - expectation
-       - mean
-       - average
-       - first-moment
-    
-    - concept: exponential-factorial
-      arity: 1
-      en: exponential factorial of $1
-      property: postfix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='exponential-factorial($a1)'><mi arg='a1'>x</mi><mo>$</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ExponentialFactorial.html"
-       - "https://en.wikipedia.org/wiki/Exponential_factorial"
-    
-    - concept: exponential-integral
-      arity: 1
-      en: exponential integral of $1
-      property: 
-      area: 
-      mathml:
-       - "<math><mrow intent='exponential-integral($a1)'><mi>Ei</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ExponentialIntegral.html"
-       - "https://en.wikipedia.org/wiki/Exponential_integral"
-       - "https://dlmf.nist.gov/6.2#i"
-       - "https://dlmf.nist.gov/6.2#E1"
-       - "https://dlmf.nist.gov/6.2#SS1.p3"
-      alias:
-       - ei
-    
-    - concept: exterior
-      arity: 1
-      en: exterior of $1
-      property: "function, msup"
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='exterior($a1)'><mi>ext</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><msup intent='exterior($a1)'><mi arg='a1'>X</mi><mi>e</mi></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Exterior.html"
-       - "https://en.wikipedia.org/wiki/Exterior_(topology)"
-    
-    - concept: exterior-derivative
-      arity: 1
-      en: exterior derivative of $1
-      property: operator
-      area: "differential forms"
-      mathml:
-       - "<math><mrow intent='exterior-derivative($a1)'><mi>d</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ExteriorDerivative.html"
-       - "https://en.wikipedia.org/wiki/Exterior_derivative"
-    
-    - concept: exterior-algebra
-      arity: 1
-      en: exterior algebra of $1
-      property: function
-      area: "multilinear algebra"
-      mathml:
-       - "<math><mrow intent='exterior-algebra($a1)'><mi>Λ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Exterior_algebra"
-    
-    - concept: exterior-product
-      arity: 2
-      en: $1 exterior product $2
-      property: infix
-      area: "multilinear algebra"
-      mathml:
-       - "<math><mrow intent='exterior-product($a1,$a2)'><mi arg='a1'>X</mi><mo>∧</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ExteriorProduct.html"
-       - "https://www.encyclopediaofmath.org/index.php/Exterior_product"
-      alias:
-       - wedge-product
-    
-    - concept: f-distribution
-      arity: 1
-      en: f distribution of $1
-      property: "indexed symbol"
-      area: "probability theory"
-      mathml:
-       - "<math><msub intent='f-distribution($a1)'><mi>F</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/F-Distribution.html"
-       - "https://www.encyclopediaofmath.org/index.php/F-distribution"
-    
-    - concept: faber-polynomial
-      arity: 1
-      en: $1<i>th</i> faber polynomial
-      property: function
-      area: "polynomials"
-      mathml:
-       - "<math><msub intent='faber-polynomial($a1)'><mi mathvariant='normal'>P</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FaberPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Faber_polynomials"
-       - "https://www.encyclopediaofmath.org/index.php/Faber_polynomials"
-    
-    - concept: falling-factorial
-      arity: 2
-      en: falling factorial $1 $2
-      property: mixfix
-      area: "combinatorics"
-      mathml:
-        - "<math><msub intent='falling-factorial($a1,$a2)'><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow><mi arg='a2'>n</mi></msub></math>"
-        - "<math><msup intent='falling-factorial($a1,$a2)'><mi arg='a1'>x</mi><munder><mi arg='a2'>n</mi><mo>_</mo></munder></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Falling_and_rising_factorials"
-       - "https://mathworld.wolfram.com/FallingFactorial.html"
-       - "https://dlmf.nist.gov/26.1#P1.p1"
-      alias:
-       - descending-factorial
-       - falling-sequential-product
-       - lower-factorial
-       - pochhammer-symbol
-    
-    - concept: fatou-set
-      arity: 1
-      en: fatou set of $1
-      property: function
-      area: "complex dynamics"
-      mathml:
-       - "<math><mrow intent='fatou-set($a1)'><mi>F</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Julia_set"
-    
-    - concept: farey-sequence
-      arity: 0
+    property: constant
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='euler-mascheroni-constant'>γ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Euler-MascheroniConstant.html"
+     - "https://en.wikipedia.org/wiki/%CE%93%27(1)"
+     - "https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant"
+  
+  - concept: eulerian-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: eulerian number of $a1
+    property: function
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='eulerian-number($a1)'><mi>A</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EulerianNumber.html"
+     - "https://en.wikipedia.org/wiki/Eulerian_number"
+     - "https://dlmf.nist.gov/26.14#SS1.p3"
+  
+  - concept: exclusive-or
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 exclusive or $a2
+    property: infix
+    subject-area: "logic"
+    mathml:
+     - "<math><mrow intent='exclusive-or($a1,$a2)'><mi arg='a1'>X</mi><mo>⊻</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='exclusive-or($a1,$a2)'><mi arg='a1'>X</mi><mo>⊕</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='exclusive-or($a1,$a2)'><mi arg='a1'>X</mi><mo>↮</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='exclusive-or($a1,$a2)'><mi arg='a1'>X</mi><mo>≢</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='exclusive-or($a1,$a2)'><mi arg='a1'>X</mi><mi>XOR</mi><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ExclusiveDisjunction.html"
+     - "https://ncatlab.org/nlab/show/exclusive+disjunction"
+     - "https://www.encyclopediaofmath.org/index.php/Exclusive_disjunction"
+     - "https://en.wikipedia.org/wiki/Exclusive_or"
+    alias:
+     - exclusive-disjunction
+     - xor
+  
+  - concept: expectation-value
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: expectation value of $a1
+    property: fenced
+    subject-area: "quantum physics"
+    mathml:
+     - "<math><mrow intent='expectation-value($a1)'><mo>⟨</mo><mi arg='a1'>X</mi><mo>⟩</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ExpectationValue.html"
+     - "https://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics)"
+     - "https://ncatlab.org/nlab/show/expectation+value"
+  
+  - concept: expected-value
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: expected value of $a1
+    property: function
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mrow intent='expected-value($a1)'><mi>E</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='expected-value($a1)'><mi>M</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><msub intent='expected-value($a1)'><mi>μ</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Expected_value#Notations"
+    alias:
+     - mathematical-expectation
+     - expectation
+     - mean
+     - average
+     - first-moment
+  
+  - concept: exponential-factorial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: exponential factorial of $a1
+    property: postfix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='exponential-factorial($a1)'><mi arg='a1'>x</mi><mo>$</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ExponentialFactorial.html"
+     - "https://en.wikipedia.org/wiki/Exponential_factorial"
+  
+  - concept: exponential-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: exponential integral of $a1
+    property: 
+    subject-area: 
+    mathml:
+     - "<math><mrow intent='exponential-integral($a1)'><mi>Ei</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ExponentialIntegral.html"
+     - "https://en.wikipedia.org/wiki/Exponential_integral"
+     - "https://dlmf.nist.gov/6.2#i"
+     - "https://dlmf.nist.gov/6.2#E1"
+     - "https://dlmf.nist.gov/6.2#SS1.p3"
+    alias:
+     - ei
+  
+  - concept: exterior
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: exterior of $a1
+    property: "function, msup"
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='exterior($a1)'><mi>ext</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><msup intent='exterior($a1)'><mi arg='a1'>X</mi><mi>e</mi></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Exterior.html"
+     - "https://en.wikipedia.org/wiki/Exterior_(topology)"
+  
+  - concept: exterior-derivative
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: exterior derivative of $a1
+    property: operator
+    subject-area: "differential forms"
+    mathml:
+     - "<math><mrow intent='exterior-derivative($a1)'><mi>d</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ExteriorDerivative.html"
+     - "https://en.wikipedia.org/wiki/Exterior_derivative"
+  
+  - concept: exterior-algebra
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: exterior algebra of $a1
+    property: function
+    subject-area: "multilinear algebra"
+    mathml:
+     - "<math><mrow intent='exterior-algebra($a1)'><mi>Λ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Exterior_algebra"
+  
+  - concept: exterior-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 exterior product $a2
+    property: infix
+    subject-area: "multilinear algebra"
+    mathml:
+     - "<math><mrow intent='exterior-product($a1,$a2)'><mi arg='a1'>X</mi><mo>∧</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ExteriorProduct.html"
+     - "https://www.encyclopediaofmath.org/index.php/Exterior_product"
+    alias:
+     - wedge-product
+  
+  - concept: f-distribution
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: f distribution of $a1
+    property: "indexed symbol"
+    subject-area: "probability theory"
+    mathml:
+     - "<math><msub intent='f-distribution($a1)'><mi>F</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/F-Distribution.html"
+     - "https://www.encyclopediaofmath.org/index.php/F-distribution"
+  
+  - concept: faber-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> faber polynomial
+    property: function
+    subject-area: "polynomials"
+    mathml:
+     - "<math><msub intent='faber-polynomial($a1)'><mi mathvariant='normal'>P</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FaberPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Faber_polynomials"
+     - "https://www.encyclopediaofmath.org/index.php/Faber_polynomials"
+  
+  - concept: falling-factorial
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: falling factorial $a1 $a2
+    property: mixfix
+    subject-area: "combinatorics"
+    mathml:
+      - "<math><msub intent='falling-factorial($a1,$a2)'><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow><mi arg='a2'>n</mi></msub></math>"
+      - "<math><msup intent='falling-factorial($a1,$a2)'><mi arg='a1'>x</mi><munder><mi arg='a2'>n</mi><mo>_</mo></munder></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Falling_and_rising_factorials"
+     - "https://mathworld.wolfram.com/FallingFactorial.html"
+     - "https://dlmf.nist.gov/26.1#P1.p1"
+    alias:
+     - descending-factorial
+     - falling-sequential-product
+     - lower-factorial
+     - pochhammer-symbol
+  
+  - concept: fatou-set
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fatou set of $a1
+    property: function
+    subject-area: "complex dynamics"
+    mathml:
+     - "<math><mrow intent='fatou-set($a1)'><mi>F</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Julia_set"
+  
+  - concept: farey-sequence
+    arity: 0
+    arguments: []
+    speech:
       en: farey sequence
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='farey-sequence'>F</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FareySequence.html"
-       - "https://en.wikipedia.org/wiki/Farey_sequence"
-    
-    - concept: feferman-schutte-ordinal
-      arity: 0
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='farey-sequence'>F</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FareySequence.html"
+     - "https://en.wikipedia.org/wiki/Farey_sequence"
+  
+  - concept: feferman-schutte-ordinal
+    arity: 0
+    arguments: []
+    speech:
       en: feferman schutte ordinal
-      property: symbol
-      area: "ordinal numbers"
-      mathml:
-       - "<math><msub intent='feferman-schutte-ordinal'><mi>Γ</mi><mn>0</mn></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Feferman%E2%80%93Sch%C3%BCtte_ordinal"
-    
-    - concept: feigenbaum-constant
-      arity: 0
+    property: symbol
+    subject-area: "ordinal numbers"
+    mathml:
+     - "<math><msub intent='feferman-schutte-ordinal'><mi>Γ</mi><mn>0</mn></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Feferman%E2%80%93Sch%C3%BCtte_ordinal"
+  
+  - concept: feigenbaum-constant
+    arity: 0
+    arguments: []
+    speech:
       en: feigenbaum constant
-      property: symbol
-      area: "chaos theory"
-      mathml:
-       - "<math><mi intent='feigenbaum-constant'>δ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FeigenbaumConstant.html"
-       - "https://en.wikipedia.org/wiki/Feigenbaum_constants"
-    
-    - concept: fermat-number
-      arity: 1
-      en: $1<i>th</i> fermat number
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='fermat-number($a1)'><mi>F</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FermatNumber.html"
-       - "https://en.wikipedia.org/wiki/Fermat_number"
-    
-    - concept: fermat-quotient
-      arity: 1
-      en: fermat quotient of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='fermat-quotient($a1)'><mi>q</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FermatQuotient.html"
-       - "https://en.wikipedia.org/wiki/Fermat_quotient"
-    
-    - concept: fermi-dirac-distribution
-      arity: 1
-      en: fermi dirac distribution of $1
-      property: function
-      area: "quantum statistics"
-      mathml:
-       - "<math><msub intent='fermi-dirac-distribution($a1)'><mover><mi>n</mi><mo>¯</mo></mover><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_distribution"
-      alias:
-       - f-d-distribution
-    
-    - concept: feynman-slash
-      arity: 1
-      en: feynman slash of $1
-      property: menclose
-      area: "quantum field theory"
-      mathml:
-       - "<math><menclose  notation='updiagonalstrike' intent='feynman-slash($a1)'><mi arg='a1'>A</mi></menclose></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Feynman_slash_notation"
-    
-    - concept: fibonacci-number
-      arity: 1
-      en: $1<i>th</i> fibonacci number
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='fibonacci-number($a1)'><mi>F</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FibonacciNumber.html"
-       - "https://en.wikipedia.org/wiki/Fibonacci_number"
-       - "https://en.wikipedia.org/wiki/Fibonacci_numbers_in_popular_culture"
-       - "https://dlmf.nist.gov/26.11#p4"
-       - "https://www.encyclopediaofmath.org/index.php/Fibonacci_numbers"
-    
-    - concept: fibonacci-polynomial
-      arity: 1
-      en: fibonacci polynomial of $1
-      property: "indexed function"
-      area: "polynomials"
-      mathml:
-       - "<math><msub intent='fibonacci-polynomial($a1)'><mi>F</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FibonacciPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Fibonacci_polynomials"
-       - "https://www.encyclopediaofmath.org/index.php/Fibonacci_polynomials"
-    
-    - concept: fibre-product
-      arity: 1
-      en: fibre product of $1
-      property: indexed infix
-      area: "category theory"
-      mathml:
-       - "<math><msub intent='fibre-product($a1)'><mi>×</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Pullback_(category_theory)"
-       - "https://www.encyclopediaofmath.org/index.php/Fibre_product"
-      alias:
-       - pullback
-       - fiber-product
-       - cartesian-square
-    
-    - concept: field-extension
-      arity: 2
-      en: $1 field extension $2
-      property: infix
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='field-extension($a1,$a2)'><mi arg='a1'>X</mi><mo>/</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FieldExtension.html"
-       - "https://en.wikipedia.org/wiki/Field_extension"
-       - "https://ncatlab.org/nlab/show/field+extension"
-       - "https://www.encyclopediaofmath.org/index.php/Field_extension"
-    
-    - concept: field-of-sets
-      arity: 2
+    property: symbol
+    subject-area: "chaos theory"
+    mathml:
+     - "<math><mi intent='feigenbaum-constant'>δ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FeigenbaumConstant.html"
+     - "https://en.wikipedia.org/wiki/Feigenbaum_constants"
+  
+  - concept: fermat-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> fermat number
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='fermat-number($a1)'><mi>F</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FermatNumber.html"
+     - "https://en.wikipedia.org/wiki/Fermat_number"
+  
+  - concept: fermat-quotient
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fermat quotient of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='fermat-quotient($a1)'><mi>q</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FermatQuotient.html"
+     - "https://en.wikipedia.org/wiki/Fermat_quotient"
+  
+  - concept: fermi-dirac-distribution
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fermi dirac distribution of $a1
+    property: function
+    subject-area: "quantum statistics"
+    mathml:
+     - "<math><msub intent='fermi-dirac-distribution($a1)'><mover><mi>n</mi><mo>¯</mo></mover><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_distribution"
+    alias:
+     - f-d-distribution
+  
+  - concept: feynman-slash
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: feynman slash of $a1
+    property: menclose
+    subject-area: "quantum field theory"
+    mathml:
+     - "<math><menclose  notation='updiagonalstrike' intent='feynman-slash($a1)'><mi arg='a1'>A</mi></menclose></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Feynman_slash_notation"
+  
+  - concept: fibonacci-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> fibonacci number
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='fibonacci-number($a1)'><mi>F</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FibonacciNumber.html"
+     - "https://en.wikipedia.org/wiki/Fibonacci_number"
+     - "https://en.wikipedia.org/wiki/Fibonacci_numbers_in_popular_culture"
+     - "https://dlmf.nist.gov/26.11#p4"
+     - "https://www.encyclopediaofmath.org/index.php/Fibonacci_numbers"
+  
+  - concept: fibonacci-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fibonacci polynomial of $a1
+    property: "indexed function"
+    subject-area: "polynomials"
+    mathml:
+     - "<math><msub intent='fibonacci-polynomial($a1)'><mi>F</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FibonacciPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Fibonacci_polynomials"
+     - "https://www.encyclopediaofmath.org/index.php/Fibonacci_polynomials"
+  
+  - concept: fibre-product
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fibre product of $a1
+    property: indexed infix
+    subject-area: "category theory"
+    mathml:
+     - "<math><msub intent='fibre-product($a1)'><mi>×</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Pullback_(category_theory)"
+     - "https://www.encyclopediaofmath.org/index.php/Fibre_product"
+    alias:
+     - pullback
+     - fiber-product
+     - cartesian-square
+  
+  - concept: field-extension
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 field extension $a2
+    property: infix
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='field-extension($a1,$a2)'><mi arg='a1'>X</mi><mo>/</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FieldExtension.html"
+     - "https://en.wikipedia.org/wiki/Field_extension"
+     - "https://ncatlab.org/nlab/show/field+extension"
+     - "https://www.encyclopediaofmath.org/index.php/Field_extension"
+  
+  - concept: field-of-sets
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: field of sets
-      property: fenced
-      area: "boolean algebra"
-      mathml:
-       - "<math><mrow intent='field-of-sets($a1,$a2)'><mo>(</mo><mi arg='a1'>X</mi><mo>,</mo><mi arg='a2'>F</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Field_of_sets"
-       - "https://www.encyclopediaofmath.org/index.php/Field_of_sets"
-    
-    - concept: first-isogonic-center
-      arity: 0
+    property: fenced
+    subject-area: "boolean algebra"
+    mathml:
+     - "<math><mrow intent='field-of-sets($a1,$a2)'><mo>(</mo><mi arg='a1'>X</mi><mo>,</mo><mi arg='a2'>F</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Field_of_sets"
+     - "https://www.encyclopediaofmath.org/index.php/Field_of_sets"
+  
+  - concept: first-isogonic-center
+    arity: 0
+    arguments: []
+    speech:
       en: first isogonic center
-      property: symbol
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='first-isogonic-center'><mi mathvariant='normal'>X</mi><mo>(</mo><mn>13</mn><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Fermat_point"
-    
-    - concept: fisher-information
-      arity: 1
-      en: fisher information of $1
-      property: function
-      area: "statistics"
-      mathml:
-       - "<math><mrow intent='fisher-information($a1)'><mi>I</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FisherInformation.html"
-       - "https://en.wikipedia.org/wiki/Fisher_information"
-      alias:
-       - information
-    
-    - concept: flattening
-      arity: 0
+    property: symbol
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='first-isogonic-center'><mi mathvariant='normal'>X</mi><mo>(</mo><mn>13</mn><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Fermat_point"
+  
+  - concept: fisher-information
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fisher information of $a1
+    property: function
+    subject-area: "statistics"
+    mathml:
+     - "<math><mrow intent='fisher-information($a1)'><mi>I</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FisherInformation.html"
+     - "https://en.wikipedia.org/wiki/Fisher_information"
+    alias:
+     - information
+  
+  - concept: flattening
+    arity: 0
+    arguments: []
+    speech:
       en: flattening
-      property: symbol
-      area: "celestial mechanics"
-      mathml:
-       - "<math><mi intent='flattening'>f</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Flattening.html"
-       - "https://en.wikipedia.org/wiki/Flattening"
-      alias:
-       - ellipticity
-       - oblateness
-    
-    - concept: floor
-      arity: 1
-      en: floor of $1
-      property: fenced, function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='floor($a1)'><mo>⌊</mo><mi arg='a1'>X</mi><mo>⌋</mo></mrow></math>"
-       - "<math><mrow intent='floor($a1)'><mo>&#x27e6;</mo><mi arg='a1'>X</mi><mo>&#x27e7;</mo></mrow></math>"
-       - "<math><mrow intent='floor($a1)'><mo>[</mo><mi arg='a1'>X</mi><mo>]</mo></mrow></math>"
-       - "<math><mrow intent='floor($a1)'><mi>floor</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://youtu.be/RxNs4SwP6lk"
-       - "https://youtu.be/RxNs4SwP6lk"
-       - "https://drive.google.com/file/d/1T3zc--Fbz0tFHaJq527Y_ZUyAvpOdSuM/view"
-    
-    - concept: fock-space
-      arity: 1
-      en: fock space of $1
-      property: function
-      area: "quantum mechanics"
-      mathml:
-       - "<math><mrow intent='fock-space($a1)'><mi>F</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Fock_space"
-       - "https://ncatlab.org/nlab/show/Fock+space"
-       - "https://www.encyclopediaofmath.org/index.php/Fock_space"
-    
-    - concept: forward-difference
-      arity: 3
-      en: $1<i>th</i> forward difference of $3 over $2
-      property: operator
-      area: "numerical analysis"
-      mathml:
-       - "<math><mrow intent='forward-difference($a1,$a2,$a3)'><msubsup><mi>&#x0394;</mi><mi arg='a2'>x</mi><mi arg='a1'>n</mi></msubsup><mrow><mi arg='a3'>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ForwardDifference.html)"
-       - "https://dlmf.nist.gov/18.1#EGx1"
-    
-    - concept: fourier-cosine-transform
-      arity: 1
-      en: fourier cosine transform of $1
-      property: operator
-      area: "functional analysis"
-      mathml:
-       - "<math><mrow intent='fourier-cosine-transform($a1)'><msub><mi>ℱ</mi><mi arg='a3'>c</mi></msub><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FourierCosineTransform.html"
-       - "https://dlmf.nist.gov/1.14#E9"
-       - "https://www.encyclopediaofmath.org/index.php/Fourier_cosine_transform"
-    
-    - concept: fourier-sine-transform
-      arity: 1
-      en: fourier sine transform of $1
-      property: operator
-      area: "functional analysis"
-      mathml:
-       - "<math><mrow intent='fourier-sine-transform($a1)'><msub><mi>ℱ</mi><mi>s</mi></msub><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FourierSineTransform.html"
-       - "https://dlmf.nist.gov/1.14#E10"
-       - "https://www.encyclopediaofmath.org/index.php/Fourier_sine_transform"
-    
-    - concept: fourier-transform
-      arity: 1
-      en: fourier transform of $1
-      property: mover
-      area: "fourier analysis"
-      mathml:
-       - "<math><mover intent='fourier-transform($a1)'><mi arg='a1'>f</mi><mo>^</mo></mover></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FourierTransform.html"
-       - "https://en.wikipedia.org/wiki/%E2%84%B1"
-       - "https://en.wikipedia.org/wiki/Fourier_transform"
-       - "https://dlmf.nist.gov/1.14#E1"
-       - "https://ncatlab.org/nlab/show/Fourier+transform"
-       - "https://www.encyclopediaofmath.org/index.php/Fourier_transform"
-    
-    - concept: fox-derivative
-      arity: 1
-      en: fox derivative of $1
-      property: mfrac
-      area: "geometric topology"
-      mathml:
-      - "<math><mfrac intent='fox-derivative(($a1)'><mi>∂</mi><mrow><mi>∂</mi><msub arg='a1'><mi>g</mi><mi>i</mi></msub></mrow></mfrac></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FoxDerivative.html"
-       - "https://en.wikipedia.org/wiki/Fox_derivative"
-       - "https://ncatlab.org/nlab/show/Fox+derivative"
-    
-    - concept: fox-wright-function
-      arity: 2
-      en: fox wright function  $1 $2
-      property: mmultiscripts
-      area: "special functions"
-      mathml:
-       - "<math><mmultiscripts intent='fox-wright-function($a1,$a2)'><mi>Ψ</mi><mi arg='a2'>q</mi><mrow/><mprescripts/><mi arg='a1'>p</mi><mrow/></mmultiscripts></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Fox%E2%80%93Wright_function"
-      alias:
-       - wright-function
-    
-    - concept: fractional-derivative
-      arity: 1
-      en: fractional derivative of $1
-      property: operator
-      area: "fractional caclulus"
-      mathml:
-       - "<math><msup intent='fractional-derivative($a1)'><mi>D</mi><mi arg='a1'>f</mi></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FractionalDerivative.html"
-       - "https://dlmf.nist.gov/1.15#E51"
-    
-    - concept: fractional-integral
-      arity: 1
-      en: fractional integral of $1
-      property: operator
-      area: "fractional caclulus"
-      mathml:
-       - "<math><msup intent='fractional-integral($a1)'><mi>I</mi><mi arg='a1'>f</mi></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FractionalIntegral.html"
-       - "https://dlmf.nist.gov/1.15#E47"
-       - "https://dlmf.nist.gov/2.6#E33"
-    
-    - concept: fractional-part
-      arity: 1
-      en: fractional part of $1
-      property: "function, fenced"
-      area: "arithmetic"
-      mathml:
-       - "<math><mrow intent='fractional-part($a1)'><mi>frac</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='fractional-part($a1)'><mo>&#x27e6;</mo><mi arg='a1'>x</mi><mo>&#x27e7;</mo></mrow></math>"
-       - "<math><mrow intent='fractional-part($a1)'><mo>{</mo><mi arg='a1'>x</mi><mo>}</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FractionalPart.html"
-       - "https://en.wikipedia.org/wiki/Fractional_part"
-       - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions"
-       - "https://en.wikipedia.org/wiki/Phase_(waves)"
-      alias:
-       - decimal-part
-    
-    - concept: franel-number
-      arity: 1
-      en: $1<i>th</i> franel number
-      property: "indexed symbol"
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='franel-number($a1)'><mi>Fr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FranelNumber.html"
-    
-    - concept: frattini-subgroup
-      arity: 1
-      en: frattini subgroup of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='frattini-subgroup($a1)'><mi>φ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='frattini-subgroup($a1)'><mi>ϕ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FrattiniSubgroup.html"
-       - "https://en.wikipedia.org/wiki/Frattini_subgroup"
-       - "https://www.encyclopediaofmath.org/index.php/Frattini_subgroup"
-    
-    - concept: frechet-derivative
-      arity: 1
-      en: frechet derivative of $1
-      property: operator
-      area: "banach spaces"
-      mathml:
-       - "<math><mrow intent='frechet-derivative($a1)'><mi>D</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FrechetDerivative.html"
-       - "https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative"
-       - "https://www.encyclopediaofmath.org/index.php/Frechet_derivative"
-       - "https://www.encyclopediaofmath.org/index.php/Fréchet_derivative"
-    
-    - concept: frechet-topology
-      arity: 0
+    property: symbol
+    subject-area: "celestial mechanics"
+    mathml:
+     - "<math><mi intent='flattening'>f</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Flattening.html"
+     - "https://en.wikipedia.org/wiki/Flattening"
+    alias:
+     - ellipticity
+     - oblateness
+  
+  - concept: floor
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: floor of $a1
+    property: fenced, function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='floor($a1)'><mo>⌊</mo><mi arg='a1'>X</mi><mo>⌋</mo></mrow></math>"
+     - "<math><mrow intent='floor($a1)'><mo>&#x27e6;</mo><mi arg='a1'>X</mi><mo>&#x27e7;</mo></mrow></math>"
+     - "<math><mrow intent='floor($a1)'><mo>[</mo><mi arg='a1'>X</mi><mo>]</mo></mrow></math>"
+     - "<math><mrow intent='floor($a1)'><mi>floor</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://youtu.be/RxNs4SwP6lk"
+     - "https://youtu.be/RxNs4SwP6lk"
+     - "https://drive.google.com/file/d/1T3zc--Fbz0tFHaJq527Y_ZUyAvpOdSuM/view"
+  
+  - concept: fock-space
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fock space of $a1
+    property: function
+    subject-area: "quantum mechanics"
+    mathml:
+     - "<math><mrow intent='fock-space($a1)'><mi>F</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Fock_space"
+     - "https://ncatlab.org/nlab/show/Fock+space"
+     - "https://www.encyclopediaofmath.org/index.php/Fock_space"
+  
+  - concept: forward-difference
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: $a1<i>th</i> forward difference of $a3 over $a2
+    property: operator
+    subject-area: "numerical analysis"
+    mathml:
+     - "<math><mrow intent='forward-difference($a1,$a2,$a3)'><msubsup><mi>&#x0394;</mi><mi arg='a2'>x</mi><mi arg='a1'>n</mi></msubsup><mrow><mi arg='a3'>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ForwardDifference.html)"
+     - "https://dlmf.nist.gov/18.1#EGx1"
+  
+  - concept: fourier-cosine-transform
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fourier cosine transform of $a1
+    property: operator
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><mrow intent='fourier-cosine-transform($a1)'><msub><mi>ℱ</mi><mi arg='a3'>c</mi></msub><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FourierCosineTransform.html"
+     - "https://dlmf.nist.gov/1.14#E9"
+     - "https://www.encyclopediaofmath.org/index.php/Fourier_cosine_transform"
+  
+  - concept: fourier-sine-transform
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fourier sine transform of $a1
+    property: operator
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><mrow intent='fourier-sine-transform($a1)'><msub><mi>ℱ</mi><mi>s</mi></msub><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FourierSineTransform.html"
+     - "https://dlmf.nist.gov/1.14#E10"
+     - "https://www.encyclopediaofmath.org/index.php/Fourier_sine_transform"
+  
+  - concept: fourier-transform
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fourier transform of $a1
+    property: mover
+    subject-area: "fourier analysis"
+    mathml:
+     - "<math><mover intent='fourier-transform($a1)'><mi arg='a1'>f</mi><mo>^</mo></mover></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FourierTransform.html"
+     - "https://en.wikipedia.org/wiki/%E2%84%B1"
+     - "https://en.wikipedia.org/wiki/Fourier_transform"
+     - "https://dlmf.nist.gov/1.14#E1"
+     - "https://ncatlab.org/nlab/show/Fourier+transform"
+     - "https://www.encyclopediaofmath.org/index.php/Fourier_transform"
+  
+  - concept: fox-derivative
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fox derivative of $a1
+    property: mfrac
+    subject-area: "geometric topology"
+    mathml:
+    - "<math><mfrac intent='fox-derivative(($a1)'><mi>∂</mi><mrow><mi>∂</mi><msub arg='a1'><mi>g</mi><mi>i</mi></msub></mrow></mfrac></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FoxDerivative.html"
+     - "https://en.wikipedia.org/wiki/Fox_derivative"
+     - "https://ncatlab.org/nlab/show/Fox+derivative"
+  
+  - concept: fox-wright-function
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: fox wright function  $a1 $a2
+    property: mmultiscripts
+    subject-area: "special functions"
+    mathml:
+     - "<math><mmultiscripts intent='fox-wright-function($a1,$a2)'><mi>Ψ</mi><mi arg='a2'>q</mi><mrow/><mprescripts/><mi arg='a1'>p</mi><mrow/></mmultiscripts></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Fox%E2%80%93Wright_function"
+    alias:
+     - wright-function
+  
+  - concept: fractional-derivative
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fractional derivative of $a1
+    property: operator
+    subject-area: "fractional caclulus"
+    mathml:
+     - "<math><msup intent='fractional-derivative($a1)'><mi>D</mi><mi arg='a1'>f</mi></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FractionalDerivative.html"
+     - "https://dlmf.nist.gov/1.15#E51"
+  
+  - concept: fractional-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fractional integral of $a1
+    property: operator
+    subject-area: "fractional caclulus"
+    mathml:
+     - "<math><msup intent='fractional-integral($a1)'><mi>I</mi><mi arg='a1'>f</mi></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FractionalIntegral.html"
+     - "https://dlmf.nist.gov/1.15#E47"
+     - "https://dlmf.nist.gov/2.6#E33"
+  
+  - concept: fractional-part
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fractional part of $a1
+    property: "function, fenced"
+    subject-area: "arithmetic"
+    mathml:
+     - "<math><mrow intent='fractional-part($a1)'><mi>frac</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='fractional-part($a1)'><mo>&#x27e6;</mo><mi arg='a1'>x</mi><mo>&#x27e7;</mo></mrow></math>"
+     - "<math><mrow intent='fractional-part($a1)'><mo>{</mo><mi arg='a1'>x</mi><mo>}</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FractionalPart.html"
+     - "https://en.wikipedia.org/wiki/Fractional_part"
+     - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions"
+     - "https://en.wikipedia.org/wiki/Phase_(waves)"
+    alias:
+     - decimal-part
+  
+  - concept: franel-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> franel number
+    property: "indexed symbol"
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='franel-number($a1)'><mi>Fr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FranelNumber.html"
+  
+  - concept: frattini-subgroup
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: frattini subgroup of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='frattini-subgroup($a1)'><mi>φ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='frattini-subgroup($a1)'><mi>ϕ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FrattiniSubgroup.html"
+     - "https://en.wikipedia.org/wiki/Frattini_subgroup"
+     - "https://www.encyclopediaofmath.org/index.php/Frattini_subgroup"
+  
+  - concept: frechet-derivative
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: frechet derivative of $a1
+    property: operator
+    subject-area: "banach spaces"
+    mathml:
+     - "<math><mrow intent='frechet-derivative($a1)'><mi>D</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FrechetDerivative.html"
+     - "https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative"
+     - "https://www.encyclopediaofmath.org/index.php/Frechet_derivative"
+     - "https://www.encyclopediaofmath.org/index.php/Fréchet_derivative"
+  
+  - concept: frechet-topology
+    arity: 0
+    arguments: []
+    speech:
       en: frechet topology
-      property: constant
-      area: "topology"
-      mathml:
-       - "<math><msub intent='frechet-topology'><mi>T</mi><mn>1</mn></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions"
-      alias:
-       - tikhonov-space
-       - accessible-space
-    
-    - concept: fredholm-determinant
-      arity: 1
-      en: fredholm determinant of $1
-      property: function
-      area: "mathematical physics"
-      mathml:
-       - "<math><mrow intent='fredholm-determinant($a1)'><mi>det</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Fredholm_determinant"
-       - "https://ncatlab.org/nlab/show/Fredholm+determinant"
-       - "https://ncatlab.org/nlab/show/Fredholm+determinant"
-    
-    - concept: free-algebra
-      arity: 2
-      en: free algebra $1 $2
-      property: mixfix
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='free-algebra($a1,$a2)'><mi arg='a1'>R</mi><mo>⟨</mo><mi arg='a2'>X</mi><mo>⟩</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FreeAlgebra.html"
-       - "https://en.wikipedia.org/wiki/Free_algebra"
-       - "https://www.encyclopediaofmath.org/index.php/Free_algebra"
-    
-    - concept: free-module
-      arity: 2
-      en: $1 free module on $2
-      property: mixfix, msup
-      area: "module theory"
-      mathml:
-       - "<math><mrow intent='free-module($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>{</mo><mi arg='a2'>E</mi><mo>}</mo></mrow></mrow></math>"
-       - "<math><msup intent='free-module($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>(</mo><mi arg='a2'>E</mi><mo>)</mo></mrow></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FreeModule.html"
-       - "https://en.wikipedia.org/wiki/Free_module"
-       - "https://ncatlab.org/nlab/show/free+module"
-       - "https://www.encyclopediaofmath.org/index.php/Free_module"
-    
-    - concept: free-monoid
-      arity: 1
-      en: free monoid of $1
-      property: msup
-      area: "abstract algebra"
-      mathml:
-       - "<math><msup intent='free-monoid($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Free_monoid"
-       - "https://en.wikipedia.org/wiki/Monoid_factorisation"
-       - "https://ncatlab.org/nlab/show/free+monoid"
-    
-    - concept: free-product
-      arity: 2
-      en: $1 free product $2
-      property: infix
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='free-product($a1,$a2)'><mi arg='a1'>X</mi><mo>*</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FreeProduct.html"
-       - "https://en.wikipedia.org/wiki/Free_product"
-       - "https://www.encyclopediaofmath.org/index.php/Free_product"
-    
-    - concept: fresnel-integral
-      arity: 1
-      en: fresnel integral of $1
-      property: operator
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='fresnel-integral($a1)'><mi>ℱ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='fresnel-integral($a1)'><mi>C</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='fresnel-integral($a1)'><mi>S</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FresnelIntegrals.html"
-       - "https://en.wikipedia.org/wiki/Fresnel_integral"
-       - "https://dlmf.nist.gov/7.2#iii"
-       - "https://dlmf.nist.gov/7.2#E7"
-       - "https://dlmf.nist.gov/7.2#E6"
-       - "https://dlmf.nist.gov/7.2#E8"
-       - "https://www.encyclopediaofmath.org/index.php/Fresnel_integrals"
-    
-    - concept: frobenius-norm
-      arity: 1
-      en: frobenius norm of $1
-      property: indexed fenced
-      area: "linear algebra"
-      mathml:
-       - "<math><msub intent='frobenius-norm($a1)'><mrow><mo>‖</mo><mi arg='a1'>A</mi><mo>‖</mo></mrow><mi>F</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FrobeniusNorm.html"
-       - "https://www.encyclopediaofmath.org/index.php/Frobenius_matrix_norm"
-      alias:
-       - euclidean-norm
-       - frobenius-matrix-norm
-    
-    - concept: frolicher-nijenhuis-bracket
-      arity: 2
+    property: constant
+    subject-area: "topology"
+    mathml:
+     - "<math><msub intent='frechet-topology'><mi>T</mi><mn>1</mn></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions"
+    alias:
+     - tikhonov-space
+     - accessible-space
+  
+  - concept: fredholm-determinant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fredholm determinant of $a1
+    property: function
+    subject-area: "mathematical physics"
+    mathml:
+     - "<math><mrow intent='fredholm-determinant($a1)'><mi>det</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Fredholm_determinant"
+     - "https://ncatlab.org/nlab/show/Fredholm+determinant"
+     - "https://ncatlab.org/nlab/show/Fredholm+determinant"
+  
+  - concept: free-algebra
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: free algebra $a1 $a2
+    property: mixfix
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='free-algebra($a1,$a2)'><mi arg='a1'>R</mi><mo>⟨</mo><mi arg='a2'>X</mi><mo>⟩</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FreeAlgebra.html"
+     - "https://en.wikipedia.org/wiki/Free_algebra"
+     - "https://www.encyclopediaofmath.org/index.php/Free_algebra"
+  
+  - concept: free-module
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 free module on $a2
+    property: mixfix, msup
+    subject-area: "module theory"
+    mathml:
+     - "<math><mrow intent='free-module($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>{</mo><mi arg='a2'>E</mi><mo>}</mo></mrow></mrow></math>"
+     - "<math><msup intent='free-module($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>(</mo><mi arg='a2'>E</mi><mo>)</mo></mrow></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FreeModule.html"
+     - "https://en.wikipedia.org/wiki/Free_module"
+     - "https://ncatlab.org/nlab/show/free+module"
+     - "https://www.encyclopediaofmath.org/index.php/Free_module"
+  
+  - concept: free-monoid
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: free monoid of $a1
+    property: msup
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><msup intent='free-monoid($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Free_monoid"
+     - "https://en.wikipedia.org/wiki/Monoid_factorisation"
+     - "https://ncatlab.org/nlab/show/free+monoid"
+  
+  - concept: free-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 free product $a2
+    property: infix
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='free-product($a1,$a2)'><mi arg='a1'>X</mi><mo>*</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FreeProduct.html"
+     - "https://en.wikipedia.org/wiki/Free_product"
+     - "https://www.encyclopediaofmath.org/index.php/Free_product"
+  
+  - concept: fresnel-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: fresnel integral of $a1
+    property: operator
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='fresnel-integral($a1)'><mi>ℱ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='fresnel-integral($a1)'><mi>C</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='fresnel-integral($a1)'><mi>S</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FresnelIntegrals.html"
+     - "https://en.wikipedia.org/wiki/Fresnel_integral"
+     - "https://dlmf.nist.gov/7.2#iii"
+     - "https://dlmf.nist.gov/7.2#E7"
+     - "https://dlmf.nist.gov/7.2#E6"
+     - "https://dlmf.nist.gov/7.2#E8"
+     - "https://www.encyclopediaofmath.org/index.php/Fresnel_integrals"
+  
+  - concept: frobenius-norm
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: frobenius norm of $a1
+    property: indexed fenced
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><msub intent='frobenius-norm($a1)'><mrow><mo>‖</mo><mi arg='a1'>A</mi><mo>‖</mo></mrow><mi>F</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FrobeniusNorm.html"
+     - "https://www.encyclopediaofmath.org/index.php/Frobenius_matrix_norm"
+    alias:
+     - euclidean-norm
+     - frobenius-matrix-norm
+  
+  - concept: frolicher-nijenhuis-bracket
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: frolicher nijenhuis bracket
-      property: fenced
-      area: "differntial geometry"
-      mathml:
-       - "<math><mrow intent='frolicher-nijenhuis-bracket($a1,$a2)'><mo>[</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Fr%C3%B6licher%E2%80%93Nijenhuis_bracket"
-       - "https://encyclopediaofmath.org/wiki/Fr%C3%B6licher-Nijenhuis_bracket"
-    
-    - concept: functional-congruence
-      arity: 3
-      en: functional congruence of $1 and $2 mod $3
-      property: mixfix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='functional-congruence($a1,$a2,$a3)'><mi arg='a1'>f</mi><mo>≡</mo><mi arg='a2'>g</mi></mrow><mrow><mo>(</mo><mi>mod</mi><mi arg='a3'>n</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FunctionalCongruence.html"
-      alias:
-       - identical-congruence
-    
-    - concept: functor-category
-      arity: 2
+    property: fenced
+    subject-area: "differntial geometry"
+    mathml:
+     - "<math><mrow intent='frolicher-nijenhuis-bracket($a1,$a2)'><mo>[</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Fr%C3%B6licher%E2%80%93Nijenhuis_bracket"
+     - "https://encyclopediaofmath.org/wiki/Fr%C3%B6licher-Nijenhuis_bracket"
+  
+  - concept: functional-congruence
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: functional congruence of $a1 and $a2 mod $a3
+    property: mixfix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='functional-congruence($a1,$a2,$a3)'><mi arg='a1'>f</mi><mo>≡</mo><mi arg='a2'>g</mi></mrow><mrow><mo>(</mo><mi>mod</mi><mi arg='a3'>n</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FunctionalCongruence.html"
+    alias:
+     - identical-congruence
+  
+  - concept: functor-category
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: functor category
-      property: msup, fenced
-      area: "category theory"
-      mathml:
-       - "<math><msup intent='functor-category($a1,$a2)'><mi arg='a1'>f</mi><mi arg='a2'>g</mi></msup></math>"
-       - "<math><mrow intent='functor-category($a1,$a2)'><mo>[</mo><mi arg='a1'>f</mi><mo>,</mo><mi arg='a2'>g</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Functor_category"
-       - "https://ncatlab.org/nlab/show/functor+category"
-    
-    - concept: fundamental-matrix
-      arity: 0
+    property: msup, fenced
+    subject-area: "category theory"
+    mathml:
+     - "<math><msup intent='functor-category($a1,$a2)'><mi arg='a1'>f</mi><mi arg='a2'>g</mi></msup></math>"
+     - "<math><mrow intent='functor-category($a1,$a2)'><mo>[</mo><mi arg='a1'>f</mi><mo>,</mo><mi arg='a2'>g</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Functor_category"
+     - "https://ncatlab.org/nlab/show/functor+category"
+  
+  - concept: fundamental-matrix
+    arity: 0
+    arguments: []
+    speech:
       en: fundamental matrix
-      property: symbol
-      area: "computer vision"
-      mathml:
-       - "<math><mi intent='fundamental-matrix'>F</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Fundamental_matrix_(computer_vision)"
-    
-    - concept: g-function
-      arity: 1
-      en: g function of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='g-function($a1)'><mi>G</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/G-Function.html"
-       - "https://en.wikipedia.org/wiki/Meijer_G-function"
-      alias:
-       - meijer-g-function
-    
-    - concept: gabor-transform
-      arity: 1
-      en: gabor transform of $1
-      property: operator
-      area: "integral transforms"
-      mathml:
-       - "<math><mrow intent='gabor-transform($a1)'><mi>G</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Gabor_transform"
-       - "https://en.wikipedia.org/wiki/Gabor%E2%80%93Wigner_transform"
-       - "https://www.encyclopediaofmath.org/index.php/Gabor_transform"
-    
-    - concept: gain-function
-      arity: 1
-      en: gain function of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='gain-function($a1)'><mi>φ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Gain_graph"
-       - "https://en.wikipedia.org/wiki/Gain_group"
-       - "https://www.encyclopediaofmath.org/index.php/Gain_function"
-    
-    - concept: galilean-transformation
-      arity: 1
-      en: galilean transformation of $1
-      property: function
-      area: "physics"
-      mathml:
-       - "<math><mrow intent='galilean-transformation($a1)'><mi>G</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GalileanTransformation.html"
-       - "https://en.wikipedia.org/wiki/Galilean_transformation"
-       - "https://www.encyclopediaofmath.org/index.php/Galilean_transformation"
-    
-    - concept: galois-field
-      arity: 1
-      en: galois field of $1
-      property: function
-      area: "finite fields"
-      mathml:
-       - "<math><mrow intent='galois-field($a1)'><mi>GF</mi><mrow><mo>(</mo><mi arg='a1'>p</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><msub intent='galois-field($a1)'><mi>F</mi><mi arg='a1'>p</mi></msub></math>"
-       - "<math><msub intent='galois-field($a1)'><mi>𝔽</mi><mi arg='a1'>p</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GaloisField.html"
-       - "https://en.wikipedia.org/wiki/Finite_field"
-       - "https://www.encyclopediaofmath.org/index.php/Galois_field"
-      alias:
-       - finite-field
-    
-    - concept: galois-group
-      arity: 1
-      en: galois group of $1
-      property: function
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='galois-group($a1)'><mi>Gal</mi><mi arg='a1'>G</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GaloisGroup.html"
-       - "https://en.wikipedia.org/wiki/Galois_group"
-       - "https://ncatlab.org/nlab/show/Galois+group"
-       - "https://www.encyclopediaofmath.org/index.php/Galois_group"
-    
-    - concept: gamma-distribution
-      arity: 0
+    property: symbol
+    subject-area: "computer vision"
+    mathml:
+     - "<math><mi intent='fundamental-matrix'>F</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Fundamental_matrix_(computer_vision)"
+  
+  - concept: g-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: g function of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='g-function($a1)'><mi>G</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/G-Function.html"
+     - "https://en.wikipedia.org/wiki/Meijer_G-function"
+    alias:
+     - meijer-g-function
+  
+  - concept: gabor-transform
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: gabor transform of $a1
+    property: operator
+    subject-area: "integral transforms"
+    mathml:
+     - "<math><mrow intent='gabor-transform($a1)'><mi>G</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Gabor_transform"
+     - "https://en.wikipedia.org/wiki/Gabor%E2%80%93Wigner_transform"
+     - "https://www.encyclopediaofmath.org/index.php/Gabor_transform"
+  
+  - concept: gain-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: gain function of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='gain-function($a1)'><mi>φ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Gain_graph"
+     - "https://en.wikipedia.org/wiki/Gain_group"
+     - "https://www.encyclopediaofmath.org/index.php/Gain_function"
+  
+  - concept: galilean-transformation
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: galilean transformation of $a1
+    property: function
+    subject-area: "physics"
+    mathml:
+     - "<math><mrow intent='galilean-transformation($a1)'><mi>G</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GalileanTransformation.html"
+     - "https://en.wikipedia.org/wiki/Galilean_transformation"
+     - "https://www.encyclopediaofmath.org/index.php/Galilean_transformation"
+  
+  - concept: galois-field
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: galois field of $a1
+    property: function
+    subject-area: "finite fields"
+    mathml:
+     - "<math><mrow intent='galois-field($a1)'><mi>GF</mi><mrow><mo>(</mo><mi arg='a1'>p</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><msub intent='galois-field($a1)'><mi>F</mi><mi arg='a1'>p</mi></msub></math>"
+     - "<math><msub intent='galois-field($a1)'><mi>𝔽</mi><mi arg='a1'>p</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GaloisField.html"
+     - "https://en.wikipedia.org/wiki/Finite_field"
+     - "https://www.encyclopediaofmath.org/index.php/Galois_field"
+    alias:
+     - finite-field
+  
+  - concept: galois-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: galois group of $a1
+    property: function
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='galois-group($a1)'><mi>Gal</mi><mi arg='a1'>G</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GaloisGroup.html"
+     - "https://en.wikipedia.org/wiki/Galois_group"
+     - "https://ncatlab.org/nlab/show/Galois+group"
+     - "https://www.encyclopediaofmath.org/index.php/Galois_group"
+  
+  - concept: gamma-distribution
+    arity: 0
+    arguments: []
+    speech:
       en: gamma distribution
-      property: symbol
-      area: "probability theory"
-      mathml:
-       - "<math><mi intent='gamma-distribution'>Γ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GammaDistribution.html"
-       - "https://en.wikipedia.org/wiki/Gamma_distribution"
-    
-    - concept: gamma-function
-      arity: 1
-      en: gamma function of $1
-      property: operator
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='gamma-function($a1)'><mi>Γ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GammaFunction.html"
-       - "https://en.wikipedia.org/wiki/%CE%93(x)"
-       - "https://en.wikipedia.org/wiki/Gamma_function"
-       - "https://dlmf.nist.gov/5#PT2"
-       - "https://dlmf.nist.gov/5.2#E1"
-       - "https://ncatlab.org/nlab/show/Gamma+function"
-      alias:
-       - euler-integral-of-the-second-kind
-    
-    - concept: gateaux-derivative
-      arity: 3
-      en: gateaux derivative of $1 at $2 ; £3
-      property: mixfix
-      area: "differential calculus"
-      mathml:
-      - "<math><mrow intent='gateaux-derivative($a1,$a2,$a3)'><mi>d</mi><mi arg='a1'>F</mi><mrow><mo>(</mo><mi arg='a2'>u</mi><mo>;</mo><mi arg='a3'>ψ)</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GateauxDerivative.html"
-       - "https://en.wikipedia.org/wiki/G%C3%A2teaux_derivative"
-       - "https://www.encyclopediaofmath.org/index.php/Gateaux_derivative"
-      alias:
-       - gateaux-differential
-    
-    - concept: gauss
-      arity: 1
-      en: gauss of $1
-      property: unit
-      area: "physics"
-      mathml:
-       - "<math><mrow intent='gauss($a1)'><mi>G</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Gauss_(unit)"
-    
-    - concept: gaussian-distribution
-      arity: 0
+    property: symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mi intent='gamma-distribution'>Γ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GammaDistribution.html"
+     - "https://en.wikipedia.org/wiki/Gamma_distribution"
+  
+  - concept: gamma-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: gamma function of $a1
+    property: operator
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='gamma-function($a1)'><mi>Γ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GammaFunction.html"
+     - "https://en.wikipedia.org/wiki/%CE%93(x)"
+     - "https://en.wikipedia.org/wiki/Gamma_function"
+     - "https://dlmf.nist.gov/5#PT2"
+     - "https://dlmf.nist.gov/5.2#E1"
+     - "https://ncatlab.org/nlab/show/Gamma+function"
+    alias:
+     - euler-integral-of-the-second-kind
+  
+  - concept: gateaux-derivative
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: gateaux derivative of $a1 at $a2 ; £3
+    property: mixfix
+    subject-area: "differential calculus"
+    mathml:
+    - "<math><mrow intent='gateaux-derivative($a1,$a2,$a3)'><mi>d</mi><mi arg='a1'>F</mi><mrow><mo>(</mo><mi arg='a2'>u</mi><mo>;</mo><mi arg='a3'>ψ)</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GateauxDerivative.html"
+     - "https://en.wikipedia.org/wiki/G%C3%A2teaux_derivative"
+     - "https://www.encyclopediaofmath.org/index.php/Gateaux_derivative"
+    alias:
+     - gateaux-differential
+  
+  - concept: gauss
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: gauss of $a1
+    property: unit
+    subject-area: "physics"
+    mathml:
+     - "<math><mrow intent='gauss($a1)'><mi>G</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Gauss_(unit)"
+  
+  - concept: gaussian-distribution
+    arity: 0
+    arguments: []
+    speech:
       en: gaussian distribution
-      property: symbol
-      area: "probability theory"
-      mathml:
-       - "<math><mi intent='gaussian-distribution'>𝒩</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Normal_distribution"
-      alias:
-       - normal-distribution
-       - gauss-distribution
-       - laplace-gauss-distribution
-    
-    - concept: gaussian-curvature
-      arity: 1
-      en: gaussian curvature of $1
-      property: function
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='gaussian-curvature($a1)'><mi>Κ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GaussianCurvature.html"
-       - "https://en.wikipedia.org/wiki/Gaussian_curvature"
-       - "https://www.encyclopediaofmath.org/index.php/Gaussian_curvature"
-    
-    - concept: gaussian-integers
-      arity: 0
+    property: symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mi intent='gaussian-distribution'>𝒩</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Normal_distribution"
+    alias:
+     - normal-distribution
+     - gauss-distribution
+     - laplace-gauss-distribution
+  
+  - concept: gaussian-curvature
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: gaussian curvature of $a1
+    property: function
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='gaussian-curvature($a1)'><mi>Κ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GaussianCurvature.html"
+     - "https://en.wikipedia.org/wiki/Gaussian_curvature"
+     - "https://www.encyclopediaofmath.org/index.php/Gaussian_curvature"
+  
+  - concept: gaussian-integers
+    arity: 0
+    arguments: []
+    speech:
       en: gaussian integers
-      property: constant
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='gaussian-integers'><mi>ℤ</mi><mo>[</mo><mi>i</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GaussianInteger.html"
-       - "https://en.wikipedia.org/wiki/Gaussian_integer"
-       - "https://en.wikipedia.org/wiki/Gaussian_prime"
-    
-    - concept: gegenbauer-polynomial
-      arity: 2
+    property: constant
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='gaussian-integers'><mi>ℤ</mi><mo>[</mo><mi>i</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GaussianInteger.html"
+     - "https://en.wikipedia.org/wiki/Gaussian_integer"
+     - "https://en.wikipedia.org/wiki/Gaussian_prime"
+  
+  - concept: gegenbauer-polynomial
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: gegenbauer polynomial
-      property: "indexed function"
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><mrow intent='gegenbauer-polynomial($a1,$a2)'><msubsup><mi>C</mi><mi arg='a1'>n</mi><mrow><mo>(</mo><mi arg='a2'>α</mi><mo>)</mo></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
-      notation: "msubsup C $1 ($2"
-      urls: 
-       - "https://mathworld.wolfram.com/GegenbauerPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Gegenbauer_polynomials"
-       - "https://www.encyclopediaofmath.org/index.php/Gegenbauer_polynomials"
-       - "https://dlmf.nist.gov/18.3#T1.t1.r3"
-    
-    - concept: gelfand-triple
-      arity: 3
-      en: gelfand triple of $1, $2 and $3
-      property: fenced
-      area: "functional analysis"
-      mathml:
-       - "<math><mrow intent='gelfand-triple($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Rigged_Hilbert_space#Formal_definition_(Gelfand_triple)"
-    
-    - concept: gelfond-constant
-      arity: 0
+    property: "indexed function"
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><mrow intent='gegenbauer-polynomial($a1,$a2)'><msubsup><mi>C</mi><mi arg='a1'>n</mi><mrow><mo>(</mo><mi arg='a2'>α</mi><mo>)</mo></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
+    notation: "msubsup C $a1 ($a2"
+    urls: 
+     - "https://mathworld.wolfram.com/GegenbauerPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Gegenbauer_polynomials"
+     - "https://www.encyclopediaofmath.org/index.php/Gegenbauer_polynomials"
+     - "https://dlmf.nist.gov/18.3#T1.t1.r3"
+  
+  - concept: gelfand-triple
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: gelfand triple of $a1, $a2 and $a3
+    property: fenced
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><mrow intent='gelfand-triple($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Rigged_Hilbert_space#Formal_definition_(Gelfand_triple)"
+  
+  - concept: gelfond-constant
+    arity: 0
+    arguments: []
+    speech:
       en: gelfond constant
-      property: constant
-      area: "transcendental constants"
-      mathml:
-       - "<math><msup intent='gelfond-constant'><mi>e</mi><mi>π</mi></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GelfondsConstant.html"
-       - "https://en.wikipedia.org/wiki/Gelfond%27s_constant"
-    
-    - concept: gelfond-schneider-constant
-      arity: 0
+    property: constant
+    subject-area: "transcendental constants"
+    mathml:
+     - "<math><msup intent='gelfond-constant'><mi>e</mi><mi>π</mi></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GelfondsConstant.html"
+     - "https://en.wikipedia.org/wiki/Gelfond%27s_constant"
+  
+  - concept: gelfond-schneider-constant
+    arity: 0
+    arguments: []
+    speech:
       en: gelfond schneider constant
-      property: constant
-      area: "transcendental constants"
-      mathml:
-       - "<math><msup intent='gelfond-schneider-constant'><mn>2</mn><msqrt><mn>2</mn></msqrt></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Gelfond-SchneiderConstant.html"
-       - "https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constant"
-    
-    - concept: gell-mann-matrix
-      arity: 0
+    property: constant
+    subject-area: "transcendental constants"
+    mathml:
+     - "<math><msup intent='gelfond-schneider-constant'><mn>2</mn><msqrt><mn>2</mn></msqrt></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Gelfond-SchneiderConstant.html"
+     - "https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constant"
+  
+  - concept: gell-mann-matrix
+    arity: 0
+    arguments: []
+    speech:
       en: gell mann matrix
-      property: symbol
-      area: "particle physics"
-      mathml:
-       - "<math><mi intent='gell-mann-matrix'>λ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Gell-MannMatrix.html"
-       - "https://en.wikipedia.org/wiki/Gell-Mann_matrices"
-       - "https://www.encyclopediaofmath.org/index.php/Gell-Mann_matrices"
-    
-    - concept: general-linear-group
-      arity: 1
-      en: general linear group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='general-linear-group($a1)'><mi>GL</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='general-linear-group($a1)'><mi>Aut</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GeneralLinearGroup.html"
-       - "https://en.wikipedia.org/wiki/General_linear_group"
-       - "https://en.wikipedia.org/wiki/GL(n,C)"
-       - "https://ncatlab.org/nlab/show/general+linear+group"
-       - "https://www.encyclopediaofmath.org/index.php/General_linear_group"
-    
-    - concept: generalized-hypergeometric-function
-      arity: 2
-      en: generalized hypergeometric function $1 $2
-      property: mmultiscripts
-      area: "special functions"
-      mathml:
-       - "<math><mmultiscripts intent='fox-wright-function($a1,$a2)'><mi>F</mi><mi arg='a2'>q</mi><mrow/><mprescripts/><mi arg='a1'>p</mi><mrow/></mmultiscripts></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GeneralizedHypergeometricFunction.html"
-       - "https://en.wikipedia.org/wiki/Generalized_hypergeometric_function"
-       - "https://dlmf.nist.gov/16.2#i"
-       - "https://dlmf.nist.gov/16.2#E1"
-       - "https://dlmf.nist.gov/16.5#p4"
-       - "https://dlmf.nist.gov/16.2#E1"
-       - "https://dlmf.nist.gov/16.5#p4"
-       - "https://dlmf.nist.gov/16.2#E1"
-       - "https://dlmf.nist.gov/16.5#p4"
-       - "https://dlmf.nist.gov/16.2#E1"
-       - "https://dlmf.nist.gov/16.5#p4"
-    
-    - concept: generalized-mean
-      arity: 1
-      en: generalized mean of $1
-      property: function
-      area: "means"
-      mathml:
-       - "<math><msub intent='generalized-mean($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GeneralizedMean.html"
-       - "https://en.wikipedia.org/wiki/Generalized_mean"
-       - "https://en.wikipedia.org/wiki/Power_mean"
-      alias:
-       - hoelder-mean
-       - power-mean
-    
-    - concept: genocchi-number
-      arity: 1
+    property: symbol
+    subject-area: "particle physics"
+    mathml:
+     - "<math><mi intent='gell-mann-matrix'>λ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Gell-MannMatrix.html"
+     - "https://en.wikipedia.org/wiki/Gell-Mann_matrices"
+     - "https://www.encyclopediaofmath.org/index.php/Gell-Mann_matrices"
+  
+  - concept: general-linear-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: general linear group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='general-linear-group($a1)'><mi>GL</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='general-linear-group($a1)'><mi>Aut</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GeneralLinearGroup.html"
+     - "https://en.wikipedia.org/wiki/General_linear_group"
+     - "https://en.wikipedia.org/wiki/GL(n,C)"
+     - "https://ncatlab.org/nlab/show/general+linear+group"
+     - "https://www.encyclopediaofmath.org/index.php/General_linear_group"
+  
+  - concept: generalized-hypergeometric-function
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: generalized hypergeometric function $a1 $a2
+    property: mmultiscripts
+    subject-area: "special functions"
+    mathml:
+     - "<math><mmultiscripts intent='fox-wright-function($a1,$a2)'><mi>F</mi><mi arg='a2'>q</mi><mrow/><mprescripts/><mi arg='a1'>p</mi><mrow/></mmultiscripts></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GeneralizedHypergeometricFunction.html"
+     - "https://en.wikipedia.org/wiki/Generalized_hypergeometric_function"
+     - "https://dlmf.nist.gov/16.2#i"
+     - "https://dlmf.nist.gov/16.2#E1"
+     - "https://dlmf.nist.gov/16.5#p4"
+     - "https://dlmf.nist.gov/16.2#E1"
+     - "https://dlmf.nist.gov/16.5#p4"
+     - "https://dlmf.nist.gov/16.2#E1"
+     - "https://dlmf.nist.gov/16.5#p4"
+     - "https://dlmf.nist.gov/16.2#E1"
+     - "https://dlmf.nist.gov/16.5#p4"
+  
+  - concept: generalized-mean
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: generalized mean of $a1
+    property: function
+    subject-area: "means"
+    mathml:
+     - "<math><msub intent='generalized-mean($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GeneralizedMean.html"
+     - "https://en.wikipedia.org/wiki/Generalized_mean"
+     - "https://en.wikipedia.org/wiki/Power_mean"
+    alias:
+     - hoelder-mean
+     - power-mean
+  
+  - concept: genocchi-number
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: genocchi number
-      property: symbol
-      area: "integer sequences"
-      mathml:
-       - "<math><msub intent='genocchi-number($a1)'><mi>G</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GenocchiNumber.html"
-       - "https://en.wikipedia.org/wiki/Genocchi_number"
-       - "https://en.wikipedia.org/wiki/Genocchi_prime"
-       - "https://dlmf.nist.gov/24.15#i"
-    
-    - concept: geodesic-curvature
-      arity: 0
+    property: symbol
+    subject-area: "integer sequences"
+    mathml:
+     - "<math><msub intent='genocchi-number($a1)'><mi>G</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GenocchiNumber.html"
+     - "https://en.wikipedia.org/wiki/Genocchi_number"
+     - "https://en.wikipedia.org/wiki/Genocchi_prime"
+     - "https://dlmf.nist.gov/24.15#i"
+  
+  - concept: geodesic-curvature
+    arity: 0
+    arguments: []
+    speech:
       en: geodesic curvature
-      property: symbol
-      area: "riemannian geometry"
-      mathml:
-       - "<math><msub intent='geodesic-curvature'><mi>k</mi><mi>g</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GeodesicCurvature.html"
-       - "https://en.wikipedia.org/wiki/Geodesic_curvature"
-       - "https://www.encyclopediaofmath.org/index.php/Geodesic_curvature"
-    
-    - concept: geodesic-distance
-      arity: 1
-      en: geodesic distance of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='geodesic-distance($a1)'><mi>d</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Distance_(graph_theory)"
-       - "https://en.wikipedia.org/wiki/Diameter_(graph_theory)"
-       - "https://en.wikipedia.org/wiki/Radius_(graph_theory)"
-       - "https://www.encyclopediaofmath.org/index.php/Geodesic_distance"
-      alias:
-       - distance
-    
-    - concept: geometric-genus
-      arity: 1
-      en: geometric genus of $1
-      property: function
-      area: "algebraic geometry"
-      mathml:
-       - "<math><msub intent='geometric-genus($a1)'><mi arg='a1'>p</mi><mi>g</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GeometricGenus.html"
-       - "https://en.wikipedia.org/wiki/Geometric_genus"
-       - "https://www.encyclopediaofmath.org/index.php/Geometric_genus"
-    
-    - concept: geometric-integral
-      arity: 2
-      en: geometric integral over $1 $2
-      property: indexed
-      area: "calculus"
-      mathml:
-       - "<math><mrow intent='geometric-integral($a1,$2)'><munderover><mo>Π</mo><mi arg='a1'>a</mi><mi arg='a2'>b</mi></munderover></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Product_integral"
-    
-    - concept: geometric-mean
-      arity: 1
-      en: geometric mean of $1
-      property: function
-      area: "means"
-      mathml:
-       - "<math><mrow intent='geometric-mean($a1)'><mi>GM</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GeometricMean.html"
-       - "https://en.wikipedia.org/wiki/Geometric_mean"
-       - "https://www.encyclopediaofmath.org/index.php/Geometric_mean"
-    
-    - concept: geometric-product
-      arity: 2
-      en: $1 geometric product $2
-      property: infix
-      area: "geometric algebra"
-      mathml:
-       - "<math><mrow intent='geometric-product($a1,$a2)'><mi arg='a1'>X</mi><mo>&#x2062;</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Geometric_algebra"
-    
-    - concept: germ
-      arity: 2
-      en: germ of $1 at $2
-      property: mixfix
-      area: "topology"
-      mathml:
-       - "<math><msub intent='germ($a1,$a2)'><mrow><mo>[</mo><mi arg='a1'>S</mi><mo>]</mo></mrow><mi arg='a2'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Germ_(mathematics)"
-       - "https://ncatlab.org/nlab/show/germ"
-       - "https://www.encyclopediaofmath.org/index.php/Germ"
-    
-    - concept: glaisher-constant
-      arity: 0
+    property: symbol
+    subject-area: "riemannian geometry"
+    mathml:
+     - "<math><msub intent='geodesic-curvature'><mi>k</mi><mi>g</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GeodesicCurvature.html"
+     - "https://en.wikipedia.org/wiki/Geodesic_curvature"
+     - "https://www.encyclopediaofmath.org/index.php/Geodesic_curvature"
+  
+  - concept: geodesic-distance
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: geodesic distance of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='geodesic-distance($a1)'><mi>d</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Distance_(graph_theory)"
+     - "https://en.wikipedia.org/wiki/Diameter_(graph_theory)"
+     - "https://en.wikipedia.org/wiki/Radius_(graph_theory)"
+     - "https://www.encyclopediaofmath.org/index.php/Geodesic_distance"
+    alias:
+     - distance
+  
+  - concept: geometric-genus
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: geometric genus of $a1
+    property: function
+    subject-area: "algebraic geometry"
+    mathml:
+     - "<math><msub intent='geometric-genus($a1)'><mi arg='a1'>p</mi><mi>g</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GeometricGenus.html"
+     - "https://en.wikipedia.org/wiki/Geometric_genus"
+     - "https://www.encyclopediaofmath.org/index.php/Geometric_genus"
+  
+  - concept: geometric-integral
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: geometric integral over $a1 $a2
+    property: indexed
+    subject-area: "calculus"
+    mathml:
+     - "<math><mrow intent='geometric-integral($a1,$a2)'><munderover><mo>Π</mo><mi arg='a1'>a</mi><mi arg='a2'>b</mi></munderover></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Product_integral"
+  
+  - concept: geometric-mean
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: geometric mean of $a1
+    property: function
+    subject-area: "means"
+    mathml:
+     - "<math><mrow intent='geometric-mean($a1)'><mi>GM</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GeometricMean.html"
+     - "https://en.wikipedia.org/wiki/Geometric_mean"
+     - "https://www.encyclopediaofmath.org/index.php/Geometric_mean"
+  
+  - concept: geometric-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 geometric product $a2
+    property: infix
+    subject-area: "geometric algebra"
+    mathml:
+     - "<math><mrow intent='geometric-product($a1,$a2)'><mi arg='a1'>X</mi><mo>&#x2062;</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Geometric_algebra"
+  
+  - concept: germ
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: germ of $a1 at $a2
+    property: mixfix
+    subject-area: "topology"
+    mathml:
+     - "<math><msub intent='germ($a1,$a2)'><mrow><mo>[</mo><mi arg='a1'>S</mi><mo>]</mo></mrow><mi arg='a2'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Germ_(mathematics)"
+     - "https://ncatlab.org/nlab/show/germ"
+     - "https://www.encyclopediaofmath.org/index.php/Germ"
+  
+  - concept: glaisher-constant
+    arity: 0
+    arguments: []
+    speech:
       en: glaisher constant
-      property: constant
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='glaisher-constant'>A</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GlaisherConstant.html"
-       - "https://en.wikipedia.org/wiki/Glaisher%E2%80%93Kinkelin_constant"
-       - "https://dlmf.nist.gov/5.17#E6"
-      alias:
-       - glaisher-kinkelin-constant
-    
-    - concept: global-dimension
-      arity: 1
-      en: global dimension of $1
-      property: function
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='global-dimension($a1)'><mi>gl dim</mi><mrow><mo>(</mo><mi arg='a1'>A</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Global_dimension"
-      alias:
-       - global-homological-dimension
-       - homological-dimension
-    
-    - concept: golden-ratio
-      arity: 0
+    property: constant
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='glaisher-constant'>A</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GlaisherConstant.html"
+     - "https://en.wikipedia.org/wiki/Glaisher%E2%80%93Kinkelin_constant"
+     - "https://dlmf.nist.gov/5.17#E6"
+    alias:
+     - glaisher-kinkelin-constant
+  
+  - concept: global-dimension
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: global dimension of $a1
+    property: function
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='global-dimension($a1)'><mi>gl dim</mi><mrow><mo>(</mo><mi arg='a1'>A</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Global_dimension"
+    alias:
+     - global-homological-dimension
+     - homological-dimension
+  
+  - concept: golden-ratio
+    arity: 0
+    arguments: []
+    speech:
       en: golden ratio
-      property: constant
-      area: "geometry"
-      mathml:
-       - "<math><mi intent='golden-ratio'>φ</mi></math>"
-       - "<math><mi intent='golden-ratio'>ϕ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GoldenRatio.html"
-       - "https://en.wikipedia.org/wiki/Golden_ratio"
-       - "https://en.wikipedia.org/wiki/List_of_works_designed_with_the_golden_ratio"
-       - "https://www.encyclopediaofmath.org/index.php/Golden_ratio"
-      alias:
-       - golden-number
-       - golden-mean
-       - golden-section
-       - medial-section
-       - divine-proportion
-       - divine-section
-       - golden-proportion
-       - golden-cut
-    
-    - concept: graham-number
-      arity: 0
+    property: constant
+    subject-area: "geometry"
+    mathml:
+     - "<math><mi intent='golden-ratio'>φ</mi></math>"
+     - "<math><mi intent='golden-ratio'>ϕ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GoldenRatio.html"
+     - "https://en.wikipedia.org/wiki/Golden_ratio"
+     - "https://en.wikipedia.org/wiki/List_of_works_designed_with_the_golden_ratio"
+     - "https://www.encyclopediaofmath.org/index.php/Golden_ratio"
+    alias:
+     - golden-number
+     - golden-mean
+     - golden-section
+     - medial-section
+     - divine-proportion
+     - divine-section
+     - golden-proportion
+     - golden-cut
+  
+  - concept: graham-number
+    arity: 0
+    arguments: []
+    speech:
       en: graham number
-      property: constant
-      area: "ramsey theory"
-      mathml:
-       - "<math><msub intent='graham-number'><mi>G</mi><mn>64</mn></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GrahamsNumber.html"
-       - "https://en.wikipedia.org/wiki/Graham%27s_number"
-    
-    - concept: gram-determinant
-      arity: 1
-      en: gram determinant of $1
-      property: function
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='gram-determinant($a1)'><mi>G</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='gram-determinant($a1)'><mi>Γ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GramDeterminant.html"
-       - "https://www.encyclopediaofmath.org/index.php/Gram_determinant"
-    
-    - concept: gram-matrix
-      arity: 0
+    property: constant
+    subject-area: "ramsey theory"
+    mathml:
+     - "<math><msub intent='graham-number'><mi>G</mi><mn>64</mn></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GrahamsNumber.html"
+     - "https://en.wikipedia.org/wiki/Graham%27s_number"
+  
+  - concept: gram-determinant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: gram determinant of $a1
+    property: function
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='gram-determinant($a1)'><mi>G</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='gram-determinant($a1)'><mi>Γ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GramDeterminant.html"
+     - "https://www.encyclopediaofmath.org/index.php/Gram_determinant"
+  
+  - concept: gram-matrix
+    arity: 0
+    arguments: []
+    speech:
       en: gram matrix
-      property: symbol
-      area: "linear algebra"
-      mathml:
-       - "<math><mi intent='gram-matrix'>G</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GramMatrix.html"
-       - "https://en.wikipedia.org/wiki/Gramian_matrix"
-       - "https://www.encyclopediaofmath.org/index.php/Gram_matrix"
-      alias:
-       - gramian-matrix
-       - gramian
-    
-    - concept: grassmannian
-      arity: 1
-      en: grassmannian of $1
-      property: function
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='grassmannian($a1)'><mi>Gr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Grassmannian.html"
-       - "https://en.wikipedia.org/wiki/Grassmannian"
-       - "https://ncatlab.org/nlab/show/Grassmannian"
-    
-    - concept: green-function
-      arity: 1
-      en: green function of $1
-      property: function
-      area: "mathematical physics"
-      mathml:
-       - "<math><mrow intent='green-function($a1)'><mi>G</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GreensFunction.html"
-       - "https://en.wikipedia.org/wiki/Green%27s_function_(many-body_theory)"
-       - "https://en.wikipedia.org/wiki/Green%27s_function"
-       - "https://en.wikipedia.org/wiki/Propagator"
-       - "https://www.encyclopediaofmath.org/index.php/Green_function"
-    
-    - concept: grobner-basis
-      arity: 0
+    property: symbol
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mi intent='gram-matrix'>G</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GramMatrix.html"
+     - "https://en.wikipedia.org/wiki/Gramian_matrix"
+     - "https://www.encyclopediaofmath.org/index.php/Gram_matrix"
+    alias:
+     - gramian-matrix
+     - gramian
+  
+  - concept: grassmannian
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: grassmannian of $a1
+    property: function
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='grassmannian($a1)'><mi>Gr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Grassmannian.html"
+     - "https://en.wikipedia.org/wiki/Grassmannian"
+     - "https://ncatlab.org/nlab/show/Grassmannian"
+  
+  - concept: green-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: green function of $a1
+    property: function
+    subject-area: "mathematical physics"
+    mathml:
+     - "<math><mrow intent='green-function($a1)'><mi>G</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GreensFunction.html"
+     - "https://en.wikipedia.org/wiki/Green%27s_function_(many-body_theory)"
+     - "https://en.wikipedia.org/wiki/Green%27s_function"
+     - "https://en.wikipedia.org/wiki/Propagator"
+     - "https://www.encyclopediaofmath.org/index.php/Green_function"
+  
+  - concept: grobner-basis
+    arity: 0
+    arguments: []
+    speech:
       en: grobner basis
-      property: symbol
-      area: "computer algebra"
-      mathml:
-       - "<math><mi intent='grobner-basis'>G</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GroebnerBasis.html"
-       - "https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis"
-       - "https://www.encyclopediaofmath.org/index.php/Gröbner_basis"
-    
-    - concept: group-algebra
-      arity: 2
-      en: group algebra $2 over $1
-      property: mixfix
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='group-algebra($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>[</mo><mi arg='a2'>G</mi><mo>]</mo></mrow></mrow></math>"
-       - "<math><mrow intent='group-algebra($a1,$a2)'><mi arg='a1'>R</mi><mi arg='a2'>G</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GroupAlgebra.html"
-       - "https://en.wikipedia.org/wiki/Group_algebra"
-       - "https://ncatlab.org/nlab/show/group+algebra"
-       - "https://www.encyclopediaofmath.org/index.php/Group_algebra"
-    
-    - concept: group-of-units
-      arity: 1
-      en: group of units of $1
-      property: msup, function
-      area: "ring theory"
-      mathml:
-       - "<math><msup intent='group-of-units($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
-       - "<math><msup intent='group-of-units($a1)'><mi arg='a1'>X</mi><mo>×</mo></msup></math>"
-       - "<math><mrow intent='group-of-units($a1)'><mi>U</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/group+of+units"
-       - "https://ncatlab.org/nlab/show/group+of+units"
-    
-    - concept: group-ring
-      arity: 2
-      en: group ring $2 over $1
-      property: mixfix, infix
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='group-ring($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>[</mo><mi arg='a2'>G</mi><mo>]</mo></mrow></mrow></math>"
-       - "<math><mrow intent='group-ring($a1,$a2)'><mi arg='a1'>R</mi><mi arg='a2'>G</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GroupRing.html"
-       - "https://en.wikipedia.org/wiki/Group_ring"
-    
-    - concept: gudermannian-function
-      arity: 1
-      en: gudermannian function of $1
-      property: function
-      area: "trigonometry"
-      mathml:
-       - "<math><mrow intent='gudermannian-function($a1)'><mi>gd</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/GudermannianFunction.html"
-       - "https://en.wikipedia.org/wiki/Gudermannian_function"
-       - "https://dlmf.nist.gov/4.23#E39"
-      alias:
-       - gudermannian
-    
-    - concept: hadamard-product
-      arity: 2
-      en: $1 hadamard product $2
-      property: infix
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='hadamard-product($a1,$a2)'><mi arg='a1'>X</mi><mo>∘</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='hadamard-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⊙</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HadamardProduct.html"
-       - "https://en.wikipedia.org/wiki/Hadamard_product_(matrices)"
-      alias:
-       - elementwise-product
-       - entrywise-product
-       - schur-product
-    
-    - concept: hahn-polynomial
-      arity: 1
-      en: hahn polynomial of $1
-      property: function
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><msub intent='hahn-polynomial($a1)'><mi>q</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HahnPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Hahn_polynomials"
-       - "https://dlmf.nist.gov/18.19#T1.t1.r3"
-    
-    - concept: hamiltonian
-      arity: 1
-      en: hamiltonian of $1
-      property: operator
-      area: "quantum mechanics"
-      mathml:
-       - "<math><mrow intent='hamiltonian($a1)'><mi>H</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      notationc: "mover H ˇ"
-      notationb: "mover H ^"
-      notationa: "mrow &lt; H &gt;"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)"
-       - "https://en.wikipedia.org/wiki/Hamiltonian_vector_field"
-       - "https://en.wikipedia.org/wiki/Hamiltonian_(control_theory)"
-       - "https://ncatlab.org/nlab/show/Hamiltonian"
-       - "https://www.encyclopediaofmath.org/index.php/Hamiltonian"
-    
-    - concept: hankel-function
-      arity: 1
-      en: hankel function of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='hankel-function($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HankelFunction.html"
-       - "https://dlmf.nist.gov/10.1"
-       - "https://www.encyclopediaofmath.org/index.php/Hankel_functions"
-    
-    - concept: hardy-class
-      arity: 1
-      en: hardy class of $1
-      property: "indexed symbol"
-      area: "complex analysis"
-      mathml:
-       - "<math><msup intent='hardy-class($a1)'><mi>H</mi><mi arg='a1'>x</mi></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Hardy_space"
-       - "https://www.encyclopediaofmath.org/index.php/Hardy_classes"
-      alias:
-       - hardy-space
-    
-    - concept: hardy-space
-      arity: 1
-      en: hardy space of $1
-      property: mixfix
-      area: "complex analysis"
-      mathml:
-       - "<math><msup intent='hardy-space($a1)'><mi>H</mi><mi arg='a1'>p</mi></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HardySpace.html"
-       - "https://en.wikipedia.org/wiki/Hardy_space"
-       - "https://www.encyclopediaofmath.org/index.php/Hardy_spaces"
-    
-    - concept: hardy-littlewood-maximal-operator
-      arity: 1
-      en: hardy littlewood maximal operator of $1
-      property: operator
-      area: "real analysis"
-      mathml:
-       - "<math><mrow intent='hardy-littlewood-maximal-operator($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Hardy%E2%80%93Littlewood_maximal_function"
-      alias:
-       - hardy-littlewood-maximal-function
-    
-    - concept: harmonic-mean
-      arity: 1
-      en: harmonic mean of $1
-      property: function
-      area: "means"
-      mathml:
-       - "<math><mrow intent='harmonic-mean($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HarmonicMean.html"
-       - "https://en.wikipedia.org/wiki/Harmonic_mean"
-       - "https://en.wikipedia.org/wiki/Subcontrary_mean"
-      alias:
-       - subcontrary-mean
-    
-    - concept: hausdorff-measure
-      arity: 1
-      en: hausdorff measure of $1
-      property: "indexed function"
-      area: "metric geometry"
-      mathml:
-       - "<math><msup intent='hausdorff-measure($a1)'><mi>H</mi><mi arg='a1'>d</mi></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HausdorffMeasure.html"
-       - "https://en.wikipedia.org/wiki/Hausdorff_measure"
-    
-    - concept: hausdorff-metric
-      arity: 2
-      en: hausdorff distance $1 $2
-      property: function
-      area: "metric geometry"
-      mathml:
-       - "<math><mrow intent='hausdorff-metric($a1)'><msub><mi>d</mi><mi>H</mi></msub><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>,</mo><mi arg='a2'>Y</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Hausdorff_distance"
-       - "https://ncatlab.org/nlab/show/Hausdorff+metric"
-    
-    - concept: hausdorff-space
-      arity: 0
+    property: symbol
+    subject-area: "computer algebra"
+    mathml:
+     - "<math><mi intent='grobner-basis'>G</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GroebnerBasis.html"
+     - "https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis"
+     - "https://www.encyclopediaofmath.org/index.php/Gröbner_basis"
+  
+  - concept: group-algebra
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: group algebra $a2 over $a1
+    property: mixfix
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='group-algebra($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>[</mo><mi arg='a2'>G</mi><mo>]</mo></mrow></mrow></math>"
+     - "<math><mrow intent='group-algebra($a1,$a2)'><mi arg='a1'>R</mi><mi arg='a2'>G</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GroupAlgebra.html"
+     - "https://en.wikipedia.org/wiki/Group_algebra"
+     - "https://ncatlab.org/nlab/show/group+algebra"
+     - "https://www.encyclopediaofmath.org/index.php/Group_algebra"
+  
+  - concept: group-of-units
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: group of units of $a1
+    property: msup, function
+    subject-area: "ring theory"
+    mathml:
+     - "<math><msup intent='group-of-units($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
+     - "<math><msup intent='group-of-units($a1)'><mi arg='a1'>X</mi><mo>×</mo></msup></math>"
+     - "<math><mrow intent='group-of-units($a1)'><mi>U</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/group+of+units"
+     - "https://ncatlab.org/nlab/show/group+of+units"
+  
+  - concept: group-ring
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: group ring $a2 over $a1
+    property: mixfix, infix
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='group-ring($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>[</mo><mi arg='a2'>G</mi><mo>]</mo></mrow></mrow></math>"
+     - "<math><mrow intent='group-ring($a1,$a2)'><mi arg='a1'>R</mi><mi arg='a2'>G</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GroupRing.html"
+     - "https://en.wikipedia.org/wiki/Group_ring"
+  
+  - concept: gudermannian-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: gudermannian function of $a1
+    property: function
+    subject-area: "trigonometry"
+    mathml:
+     - "<math><mrow intent='gudermannian-function($a1)'><mi>gd</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/GudermannianFunction.html"
+     - "https://en.wikipedia.org/wiki/Gudermannian_function"
+     - "https://dlmf.nist.gov/4.23#E39"
+    alias:
+     - gudermannian
+  
+  - concept: hadamard-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 hadamard product $a2
+    property: infix
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='hadamard-product($a1,$a2)'><mi arg='a1'>X</mi><mo>∘</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='hadamard-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⊙</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HadamardProduct.html"
+     - "https://en.wikipedia.org/wiki/Hadamard_product_(matrices)"
+    alias:
+     - elementwise-product
+     - entrywise-product
+     - schur-product
+  
+  - concept: hahn-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hahn polynomial of $a1
+    property: function
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><msub intent='hahn-polynomial($a1)'><mi>q</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HahnPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Hahn_polynomials"
+     - "https://dlmf.nist.gov/18.19#T1.t1.r3"
+  
+  - concept: hamiltonian
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hamiltonian of $a1
+    property: operator
+    subject-area: "quantum mechanics"
+    mathml:
+     - "<math><mrow intent='hamiltonian($a1)'><mi>H</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    notationc: "mover H ˇ"
+    notationb: "mover H ^"
+    notationa: "mrow &lt; H &gt;"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)"
+     - "https://en.wikipedia.org/wiki/Hamiltonian_vector_field"
+     - "https://en.wikipedia.org/wiki/Hamiltonian_(control_theory)"
+     - "https://ncatlab.org/nlab/show/Hamiltonian"
+     - "https://www.encyclopediaofmath.org/index.php/Hamiltonian"
+  
+  - concept: hankel-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hankel function of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='hankel-function($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HankelFunction.html"
+     - "https://dlmf.nist.gov/10.1"
+     - "https://www.encyclopediaofmath.org/index.php/Hankel_functions"
+  
+  - concept: hardy-class
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hardy class of $a1
+    property: "indexed symbol"
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><msup intent='hardy-class($a1)'><mi>H</mi><mi arg='a1'>x</mi></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Hardy_space"
+     - "https://www.encyclopediaofmath.org/index.php/Hardy_classes"
+    alias:
+     - hardy-space
+  
+  - concept: hardy-space
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hardy space of $a1
+    property: mixfix
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><msup intent='hardy-space($a1)'><mi>H</mi><mi arg='a1'>p</mi></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HardySpace.html"
+     - "https://en.wikipedia.org/wiki/Hardy_space"
+     - "https://www.encyclopediaofmath.org/index.php/Hardy_spaces"
+  
+  - concept: hardy-littlewood-maximal-operator
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hardy littlewood maximal operator of $a1
+    property: operator
+    subject-area: "real analysis"
+    mathml:
+     - "<math><mrow intent='hardy-littlewood-maximal-operator($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Hardy%E2%80%93Littlewood_maximal_function"
+    alias:
+     - hardy-littlewood-maximal-function
+  
+  - concept: harmonic-mean
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: harmonic mean of $a1
+    property: function
+    subject-area: "means"
+    mathml:
+     - "<math><mrow intent='harmonic-mean($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HarmonicMean.html"
+     - "https://en.wikipedia.org/wiki/Harmonic_mean"
+     - "https://en.wikipedia.org/wiki/Subcontrary_mean"
+    alias:
+     - subcontrary-mean
+  
+  - concept: hausdorff-measure
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hausdorff measure of $a1
+    property: "indexed function"
+    subject-area: "metric geometry"
+    mathml:
+     - "<math><msup intent='hausdorff-measure($a1)'><mi>H</mi><mi arg='a1'>d</mi></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HausdorffMeasure.html"
+     - "https://en.wikipedia.org/wiki/Hausdorff_measure"
+  
+  - concept: hausdorff-metric
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: hausdorff distance $a1 $a2
+    property: function
+    subject-area: "metric geometry"
+    mathml:
+     - "<math><mrow intent='hausdorff-metric($a1)'><msub><mi>d</mi><mi>H</mi></msub><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>,</mo><mi arg='a2'>Y</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Hausdorff_distance"
+     - "https://ncatlab.org/nlab/show/Hausdorff+metric"
+  
+  - concept: hausdorff-space
+    arity: 0
+    arguments: []
+    speech:
       en: hausdorff space
-      property: constant
-      area: "topology"
-      mathml:
-       - "<math><msub intent='hausdorff-space'><mi>T</mi><mn>2</mn></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions"
-      alias:
-       - separated-space
-    
-    - concept: hazard-function
-      arity: 1
-      en: hazard function of $1
-      property: function
-      area: "engineering"
-      mathml:
-       - "<math><mrow intent='hazard-function($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HazardFunction.html"
-      alias:
-       - failure-rate
-    
-    - concept: heaviside-function
-      arity: 1
-      en: heaviside function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='heaviside-function($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://dlmf.nist.gov/1.16#E13)[https://en.wikipedia.org/wiki/Heaviside_step_function"
-       - "https://en.wikipedia.org/wiki/Heaviside_step_function"
-      alias:
-       - heaviside-step-function
-       - unit-step-function
-    
-    - concept: heawood-number
-      arity: 1
-      en: heawood number of $1
-      property: function
-      area: "topological graph theory"
-      mathml:
-       - "<math><mrow intent='heawood-number($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Heawood_number"
-    
-    - concept: hecke-operator
-      arity: 1
-      en: hecke operator of $1
-      property: operator
-      area: "modular forms"
-      mathml:
-       - "<math><msub intent='hecke-operator($a1)'><mi>T</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HeckeOperator.html"
-       - "https://en.wikipedia.org/wiki/Hecke_operator"
-    
-    - concept: height-function
-      arity: 1
-      en: height function of $1
-      property: function
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='height-function($a1)'><mi>H</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='height-function($a1)'><mi>h</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Height_of_a_polynomial"
-    
-    - concept: height-of-abelian-group
-      arity: 1
-      en: height of abelian group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='height-of-abelian-group($a1)'><mi>h</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Height_(abelian_group)"
-    
-    - concept: height-of-prime-ideal
-      arity: 1
-      en: height of prime ideal of $1
-      property: function
-      area: "commutative algebra"
-      mathml:
-       - "<math><mrow intent='height-of-prime-ideal($a1)'><mi>ht</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Krull_dimension#height"
-      alias:
-       - codimension-of-prime-ideal
-       - rank-of-prime-ideal
-       - altitude-of-prime-ideal
-    
-    - concept: heisenberg-group
-      arity: 1
+    property: constant
+    subject-area: "topology"
+    mathml:
+     - "<math><msub intent='hausdorff-space'><mi>T</mi><mn>2</mn></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions"
+    alias:
+     - separated-space
+  
+  - concept: hazard-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hazard function of $a1
+    property: function
+    subject-area: "engineering"
+    mathml:
+     - "<math><mrow intent='hazard-function($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HazardFunction.html"
+    alias:
+     - failure-rate
+  
+  - concept: heaviside-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: heaviside function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='heaviside-function($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://dlmf.nist.gov/1.16#E13)[https://en.wikipedia.org/wiki/Heaviside_step_function"
+     - "https://en.wikipedia.org/wiki/Heaviside_step_function"
+    alias:
+     - heaviside-step-function
+     - unit-step-function
+  
+  - concept: heawood-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: heawood number of $a1
+    property: function
+    subject-area: "topological graph theory"
+    mathml:
+     - "<math><mrow intent='heawood-number($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Heawood_number"
+  
+  - concept: hecke-operator
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hecke operator of $a1
+    property: operator
+    subject-area: "modular forms"
+    mathml:
+     - "<math><msub intent='hecke-operator($a1)'><mi>T</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HeckeOperator.html"
+     - "https://en.wikipedia.org/wiki/Hecke_operator"
+  
+  - concept: height-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: height function of $a1
+    property: function
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='height-function($a1)'><mi>H</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='height-function($a1)'><mi>h</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Height_of_a_polynomial"
+  
+  - concept: height-of-abelian-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: height of abelian group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='height-of-abelian-group($a1)'><mi>h</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Height_(abelian_group)"
+  
+  - concept: height-of-prime-ideal
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: height of prime ideal of $a1
+    property: function
+    subject-area: "commutative algebra"
+    mathml:
+     - "<math><mrow intent='height-of-prime-ideal($a1)'><mi>ht</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Krull_dimension#height"
+    alias:
+     - codimension-of-prime-ideal
+     - rank-of-prime-ideal
+     - altitude-of-prime-ideal
+  
+  - concept: heisenberg-group
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: heisenberg group
-      property: symbol
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='heisenberg-group($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HeisenbergGroup.html"
-       - "https://en.wikipedia.org/wiki/Heisenberg_group"
-       - "https://ncatlab.org/nlab/show/Heisenberg+group"
-    
-    - concept: hermite-polynomial
-      arity: 1
-      en: hermite polynomial of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='hermite-polynomial($a1)'><mi>H</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='hermite-polynomial($a1)'><mi>He</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HermitePolynomial.html"
-       - "https://en.wikipedia.org/wiki/Hermite_polynomials"
-       - "https://dlmf.nist.gov/18.3"
-       - "https://dlmf.nist.gov/18.3#T1.t1.r28"
-       - "https://dlmf.nist.gov/18.3#T1.t1.r29"
-    
-    - concept: hermitian-adjoint
-      arity: 1
-      en: hermitian adjoint of $1
-      property: msup
-      area: "functional analysis"
-      mathml:
-       - "<math><msup intent='hermitian-adjoint($a1)'><mi arg='a1'>A</mi><mo>†</mo></msup></math>"
-       - "<math><msup intent='hermitian-adjoint($a1)'><mi arg='a1'>A</mi><mo>*</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Hermitian_adjoint"
-      alias:
-       - adjoint-operator
-    
-    - concept: hermitian-conjugate
-      arity: 1
-      en: hermitian conjugate of $1
-      property: msup
-      area: "linear algebra"
-      mathml:
-       - "<math><msup intent='hermitian-conjugate($a1)'><mi arg='a1'>A</mi><mi>H</mi></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HermitianConjugate.html"
-       - "https://en.wikipedia.org/wiki/Conjugate_transpose"
-      alias:
-       - adjoint-matrix
-    
-    - concept: heronian-mean
-      arity: 1
-      en: heronian mean of $1
-      property: function
-      area: "means"
-      mathml:
-       - "<math><mrow intent='heronian-mean($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HeronianMean.html"
-       - "https://en.wikipedia.org/wiki/Heronian_mean"
-    
-    - concept: hessian
-      arity: 1
-      en: hessian of $1
-      property: operator
-      area: "differential operators"
-      mathml:
-       - "<math><mrow intent='hessian($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Hessian.html"
-       - "https://en.wikipedia.org/wiki/Hessian_matrix"
-       - "https://ncatlab.org/nlab/show/Hessian"
-      alias:
-       - hessian-matrix
-    
-    - concept: heun-function
-      arity: 1
-      en: heun function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='heun-function($a1)'><mi>Hf</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='heun-function($a1)'><mi>H⁢ℓ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Heun_function"
-       - "https://dlmf.nist.gov/31.1"
-       - "https://dlmf.nist.gov/31.4#p1"
-       - "https://dlmf.nist.gov/31.3#E1"
-    
-    - concept: heun-polynomial
-      arity: 1
-      en: heun polynomial of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='heun-polynomial($a1)'><mi>Hp</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Heun_function"
-       - "https://dlmf.nist.gov/31.5#p1"
-       - "https://dlmf.nist.gov/31.5#E2"
-    
-    - concept: hexadecimal
-      arity: 1
-      en: hexadecimal of $1
-      property: unit
-      area: "arithmetic"
-      mathml:
-       - "<math><mrow intent='hexadecimal($a1)'><mi>hex</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      notationb: "msub $1 hex"
-      notationa: "msub $1 16"
-      urls: 
-       - "https://mathworld.wolfram.com/Hexadecimal.html"
-       - "https://en.wikipedia.org/wiki/Hexadecimal"
-    
-    - concept: hilbert-symbol
-      arity: 2
+    property: symbol
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='heisenberg-group($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HeisenbergGroup.html"
+     - "https://en.wikipedia.org/wiki/Heisenberg_group"
+     - "https://ncatlab.org/nlab/show/Heisenberg+group"
+  
+  - concept: hermite-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hermite polynomial of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='hermite-polynomial($a1)'><mi>H</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='hermite-polynomial($a1)'><mi>He</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HermitePolynomial.html"
+     - "https://en.wikipedia.org/wiki/Hermite_polynomials"
+     - "https://dlmf.nist.gov/18.3"
+     - "https://dlmf.nist.gov/18.3#T1.t1.r28"
+     - "https://dlmf.nist.gov/18.3#T1.t1.r29"
+  
+  - concept: hermitian-adjoint
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hermitian adjoint of $a1
+    property: msup
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><msup intent='hermitian-adjoint($a1)'><mi arg='a1'>A</mi><mo>†</mo></msup></math>"
+     - "<math><msup intent='hermitian-adjoint($a1)'><mi arg='a1'>A</mi><mo>*</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Hermitian_adjoint"
+    alias:
+     - adjoint-operator
+  
+  - concept: hermitian-conjugate
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hermitian conjugate of $a1
+    property: msup
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><msup intent='hermitian-conjugate($a1)'><mi arg='a1'>A</mi><mi>H</mi></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HermitianConjugate.html"
+     - "https://en.wikipedia.org/wiki/Conjugate_transpose"
+    alias:
+     - adjoint-matrix
+  
+  - concept: heronian-mean
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: heronian mean of $a1
+    property: function
+    subject-area: "means"
+    mathml:
+     - "<math><mrow intent='heronian-mean($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HeronianMean.html"
+     - "https://en.wikipedia.org/wiki/Heronian_mean"
+  
+  - concept: hessian
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hessian of $a1
+    property: operator
+    subject-area: "differential operators"
+    mathml:
+     - "<math><mrow intent='hessian($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Hessian.html"
+     - "https://en.wikipedia.org/wiki/Hessian_matrix"
+     - "https://ncatlab.org/nlab/show/Hessian"
+    alias:
+     - hessian-matrix
+  
+  - concept: heun-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: heun function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='heun-function($a1)'><mi>Hf</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='heun-function($a1)'><mi>H⁢ℓ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Heun_function"
+     - "https://dlmf.nist.gov/31.1"
+     - "https://dlmf.nist.gov/31.4#p1"
+     - "https://dlmf.nist.gov/31.3#E1"
+  
+  - concept: heun-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: heun polynomial of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='heun-polynomial($a1)'><mi>Hp</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Heun_function"
+     - "https://dlmf.nist.gov/31.5#p1"
+     - "https://dlmf.nist.gov/31.5#E2"
+  
+  - concept: hexadecimal
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hexadecimal of $a1
+    property: unit
+    subject-area: "arithmetic"
+    mathml:
+     - "<math><mrow intent='hexadecimal($a1)'><mi>hex</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    notationb: "msub $a1 hex"
+    notationa: "msub $a1 16"
+    urls: 
+     - "https://mathworld.wolfram.com/Hexadecimal.html"
+     - "https://en.wikipedia.org/wiki/Hexadecimal"
+  
+  - concept: hilbert-symbol
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: hilbert symbol
-      property: fenced
-      area: "quadratic forms"
-      mathml:
-       - "<math><mrow intent='hilbert-symbol($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HilbertSymbol.html"
-       - "https://en.wikipedia.org/wiki/Hilbert_symbol"
-    
-    - concept: hilbert-schmidt-norm
-      arity: 1
-      en: hilbert schmidt norm of $1
-      property: fenced
-      area: "matrix norms"
-      mathml:
-       - "<math><msub intent='hilbert-schmidt-norm($a1)'><mrow><mo>|</mo><mi arg='a1'>X</mi><mo>|</mo></mrow><mi>HS</mi></msub></math>"
-      notation: "msub mrow | $1 | HS"
-      urls: 
-       - "https://mathworld.wolfram.com/Hilbert-SchmidtNorm.html"
-       - "https://en.wikipedia.org/wiki/Hilbert%E2%80%93Schmidt_operator"
-      alias:
-    
-    - concept: hit-or-miss-transform
-      arity: 2
-      en: $1 hit or miss transform $2
-      property: infix
-      area: "mathematical morphology"
-      mathml:
-       - "<math><mrow intent='hit-or-miss-transform($a1,$a2)'><mi arg='a1'>X</mi><mo>⊙</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Hit-or-miss_transform"
-    
-    - concept: hodge-star-operator
-      arity: 1
-      en: hodge star operator of $1
-      property: prefix
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='hodge-star-operator($a1)'><mo>⋆</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Hodge_dual"
-       - "https://ncatlab.org/nlab/show/Hodge+star+operator"
-    
-    - concept: holomorph
-      arity: 1
-      en: holomorph of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='holomorph($a1)'><mi>Hol</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Holomorph_(mathematics)"
-       - "https://ncatlab.org/nlab/show/holomorph"
-    
-    - concept: holonomy-group
-      arity: 1
-      en: holonomy group of $1
-      property: "indexed symbol"
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='holonomy-group($a1)'><mi>Hol</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Holonomy.html"
-       - "https://en.wikipedia.org/wiki/Holonomy"
-       - "https://ncatlab.org/nlab/show/holonomy"
-    
-    - concept: home-prime
-      arity: 1
-      en: home prime of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='home-prime($a1)'><mi>HP</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HomePrime.html"
-       - "https://en.wikipedia.org/wiki/Home_prime"
-    
-    - concept: homology-group
-      arity: 1
-      en: homology group of $1
-      property: function
-      area: "homology theory"
-      mathml:
-       - "<math><msub intent='homology-group($a1)'><mi>H</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HomologyGroup.html"
-       - "https://en.wikipedia.org/wiki/Singular_homology"
-    
-    - concept: homomorphic-product
-      arity: 2
-      en: $1 homomorphic product $2
-      property: infix
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='homomorphic-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⋉</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Graph_product"
-    
-    
-    - concept: homotopy-category
-      arity: 1
-      en: homotopy category of $1
-      property: function
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='homotopy-category($a1)'><mi>Ho</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/homotopy+category"
-    
-    - concept: horsepower-mechanical
-      arity: 1
-      en: $1 horsepower
-      property: unit
-      area: "imperial unit"
-      mathml:
-       - "<math><mrow intent='horsepower-mechanical($a1)'><mi arg='a1'>x</mi><mo>&#x2009;</mo><mi>hp</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Horsepower"
-      alias:
-       - horsepower
-    
-    - concept: horsepower-metric
-      arity: 1
-      en: horsepower metric of $1
-      property: unit
-      area: "metric unit"
-      mathml:
-       - "<math><mrow intent='horsepower-metric($a1)'><mi>PS</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='horsepower-metric($a1)'><mi>cv</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='horsepower-metric($a1)'><mi>hk</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='horsepower-metric($a1)'><mi>pk</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='horsepower-metric($a1)'><mi>ks</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='horsepower-metric($a1)'><mi>ch</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Metric_horsepower"
-      alias:
-       - horsepower
-    
-    - concept: hurwitz-zeta-function
-      arity: 1
-      en: hurwitz zeta function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='hurwitz-zeta-function($a1)'><mi>ζ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HurwitzZetaFunction.html"
-       - "https://en.wikipedia.org/wiki/Hurwitz_zeta_function"
-       - "https://dlmf.nist.gov/25.11"
-       - "https://dlmf.nist.gov/25.11#E1"
-    
-    - concept: hvat
-      arity: 1
-      en: hvat of $1
-      property: unit
-      area: "customary units"
-      mathml:
-       - "<math><mrow intent='hvat($a1)'><mi>hvat</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Kubni_hvat"
-       - "https://en.wikipedia.org/wiki/%C4%8Cetvorni_hvat"
-       - "https://en.wikipedia.org/wiki/Hvat"
-       - "https://en.wikipedia.org/wiki/Kvadratni_hvat"
-    
-    - concept: hydrated-compound
-      arity: 2
-      en: $1 hydrated compound $2
-      property: infix
-      area: "chemistry"
-      mathml:
-       - "<math><mrow intent='hydrated-compound($a1,$a2)'><mi arg='a1'>X</mi><mo>⋅</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='hydrated-compound($a1,$a2)'><mi arg='a1'>X</mi><mo>•</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Hydrate"
-       - "https://en.wikipedia.org/wiki/Cobalt(II)_chloride"
-       - "https://www.youtube.com/watch?v=PV_3WBTDyJc"
-    
-    - concept: hyperbolic-cosine-integral
-      arity: 1
-      en: hyperbolic cosine integral of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='hyperbolic-cosine-integral($a1)'><mi>Chi</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HyperbolicCosineIntegral.html"
-       - "https://dlmf.nist.gov/6.2#E16"
-    
-    - concept: hyperbolic-plane
-      arity: 0
+    property: fenced
+    subject-area: "quadratic forms"
+    mathml:
+     - "<math><mrow intent='hilbert-symbol($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HilbertSymbol.html"
+     - "https://en.wikipedia.org/wiki/Hilbert_symbol"
+  
+  - concept: hilbert-schmidt-norm
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hilbert schmidt norm of $a1
+    property: fenced
+    subject-area: "matrix norms"
+    mathml:
+     - "<math><msub intent='hilbert-schmidt-norm($a1)'><mrow><mo>|</mo><mi arg='a1'>X</mi><mo>|</mo></mrow><mi>HS</mi></msub></math>"
+    notation: "msub mrow | $a1 | HS"
+    urls: 
+     - "https://mathworld.wolfram.com/Hilbert-SchmidtNorm.html"
+     - "https://en.wikipedia.org/wiki/Hilbert%E2%80%93Schmidt_operator"
+    alias:
+  
+  - concept: hit-or-miss-transform
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 hit or miss transform $a2
+    property: infix
+    subject-area: "mathematical morphology"
+    mathml:
+     - "<math><mrow intent='hit-or-miss-transform($a1,$a2)'><mi arg='a1'>X</mi><mo>⊙</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Hit-or-miss_transform"
+  
+  - concept: hodge-star-operator
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hodge star operator of $a1
+    property: prefix
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='hodge-star-operator($a1)'><mo>⋆</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Hodge_dual"
+     - "https://ncatlab.org/nlab/show/Hodge+star+operator"
+  
+  - concept: holomorph
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: holomorph of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='holomorph($a1)'><mi>Hol</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Holomorph_(mathematics)"
+     - "https://ncatlab.org/nlab/show/holomorph"
+  
+  - concept: holonomy-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: holonomy group of $a1
+    property: "indexed symbol"
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='holonomy-group($a1)'><mi>Hol</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Holonomy.html"
+     - "https://en.wikipedia.org/wiki/Holonomy"
+     - "https://ncatlab.org/nlab/show/holonomy"
+  
+  - concept: home-prime
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: home prime of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='home-prime($a1)'><mi>HP</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HomePrime.html"
+     - "https://en.wikipedia.org/wiki/Home_prime"
+  
+  - concept: homology-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: homology group of $a1
+    property: function
+    subject-area: "homology theory"
+    mathml:
+     - "<math><msub intent='homology-group($a1)'><mi>H</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HomologyGroup.html"
+     - "https://en.wikipedia.org/wiki/Singular_homology"
+  
+  - concept: homomorphic-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 homomorphic product $a2
+    property: infix
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='homomorphic-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⋉</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Graph_product"
+  
+  
+  - concept: homotopy-category
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: homotopy category of $a1
+    property: function
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='homotopy-category($a1)'><mi>Ho</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/homotopy+category"
+  
+  - concept: horsepower-mechanical
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1 horsepower
+    property: unit
+    subject-area: "imperial unit"
+    mathml:
+     - "<math><mrow intent='horsepower-mechanical($a1)'><mi arg='a1'>x</mi><mo>&#x2009;</mo><mi>hp</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Horsepower"
+    alias:
+     - horsepower
+  
+  - concept: horsepower-metric
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: horsepower metric of $a1
+    property: unit
+    subject-area: "metric unit"
+    mathml:
+     - "<math><mrow intent='horsepower-metric($a1)'><mi>PS</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='horsepower-metric($a1)'><mi>cv</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='horsepower-metric($a1)'><mi>hk</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='horsepower-metric($a1)'><mi>pk</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='horsepower-metric($a1)'><mi>ks</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='horsepower-metric($a1)'><mi>ch</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Metric_horsepower"
+    alias:
+     - horsepower
+  
+  - concept: hurwitz-zeta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hurwitz zeta function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='hurwitz-zeta-function($a1)'><mi>ζ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HurwitzZetaFunction.html"
+     - "https://en.wikipedia.org/wiki/Hurwitz_zeta_function"
+     - "https://dlmf.nist.gov/25.11"
+     - "https://dlmf.nist.gov/25.11#E1"
+  
+  - concept: hvat
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hvat of $a1
+    property: unit
+    subject-area: "customary units"
+    mathml:
+     - "<math><mrow intent='hvat($a1)'><mi>hvat</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Kubni_hvat"
+     - "https://en.wikipedia.org/wiki/%C4%8Cetvorni_hvat"
+     - "https://en.wikipedia.org/wiki/Hvat"
+     - "https://en.wikipedia.org/wiki/Kvadratni_hvat"
+  
+  - concept: hydrated-compound
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 hydrated compound $a2
+    property: infix
+    subject-area: "chemistry"
+    mathml:
+     - "<math><mrow intent='hydrated-compound($a1,$a2)'><mi arg='a1'>X</mi><mo>⋅</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='hydrated-compound($a1,$a2)'><mi arg='a1'>X</mi><mo>•</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Hydrate"
+     - "https://en.wikipedia.org/wiki/Cobalt(II)_chloride"
+     - "https://www.youtube.com/watch?v=PV_3WBTDyJc"
+  
+  - concept: hyperbolic-cosine-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hyperbolic cosine integral of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='hyperbolic-cosine-integral($a1)'><mi>Chi</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HyperbolicCosineIntegral.html"
+     - "https://dlmf.nist.gov/6.2#E16"
+  
+  - concept: hyperbolic-plane
+    arity: 0
+    arguments: []
+    speech:
       en: hyperbolic plane
-      property: symbol
-      area: "non-euclidean geometry"
-      mathml:
-       - "<math><msup intent='hyperbolic-plane'><mi>ℍ</mi><mn>2</mn></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HyperbolicPlane.html"
-       - "https://ncatlab.org/nlab/show/hyperbolic+plane"
-    
-    - concept: hyperbolic-sine-integral
-      arity: 1
-      en: hyperbolic sine integral of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='hyperbolic-sine-integral($a1)'><mi>Shi</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HyperbolicSineIntegral.html"
-       - "https://dlmf.nist.gov/6.2#E15"
-    
-    - concept: hyperbolic-space
-      arity: 1
+    property: symbol
+    subject-area: "non-euclidean geometry"
+    mathml:
+     - "<math><msup intent='hyperbolic-plane'><mi>ℍ</mi><mn>2</mn></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HyperbolicPlane.html"
+     - "https://ncatlab.org/nlab/show/hyperbolic+plane"
+  
+  - concept: hyperbolic-sine-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hyperbolic sine integral of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='hyperbolic-sine-integral($a1)'><mi>Shi</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HyperbolicSineIntegral.html"
+     - "https://dlmf.nist.gov/6.2#E15"
+  
+  - concept: hyperbolic-space
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: hyperbolic space
-      property: symbol
-      area: "non-euclidean geometry"
-      mathml:
-       - "<math><msup intent='hyperbolic-space($1)'><mi mathvariant='normal'>H</mi><mi arg='a1'>n</mi></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/HyperbolicSpace.html"
-       - "https://en.wikipedia.org/wiki/Hyperbolic_space"
-    
-    - concept: hyperbolic-umbilic-canonical-integral-function
-      arity: 1
-      en: hyperbolic umbilic canonical integral function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='hyperbolic-umbilic-canonical-integral-function($a1)'><msup><mo>Ψ</mo><mrow><mo>(</mo><mi mathvariant='normal'>E</mi><mo>)</mo></mrow></msup><mi arg='a1'>z</mi></mrow></math>"
-      urls: 
-       - "https://dlmf.nist.gov/36.2#E11"
-       - "https://dlmf.nist.gov/36.3#i"
-       - "https://dlmf.nist.gov/36.3#ii"
-    
-    - concept: hyperdeterminant
-      arity: 1
-      en: hyperdeterminant of $1
-      property: "function, fenced"
-      area: "multilinear algebra"
-      mathml:
-       - "<math><mrow intent='hyperdeterminant($a1)'><mi>det</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='hyperdeterminant($a1)'><mo>|</mo><mi arg='a1'>x</mi><mo>|</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Hyperdeterminant.html"
-       - "https://en.wikipedia.org/wiki/Hyperdeterminant"
-       - "https://ncatlab.org/nlab/show/hyperdeterminant"
-    
-    - concept: hypertorus
-      arity: 1
-      en: $1<i>th</i> hypertorus
-      property: "indexed symbol"
-      area: "topology"
-      mathml:
-       - "<math><msup intent='hypertorus($a1)'><mi>T</mi><mi arg='a1'>n</mi></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Torus#n-dimensional_torus"
-      alias:
-       - n-torus
-       - n-dimensional-torus
-    
-    - concept: identity-element
-      arity: 0
+    property: symbol
+    subject-area: "non-euclidean geometry"
+    mathml:
+     - "<math><msup intent='hyperbolic-space($a1)'><mi mathvariant='normal'>H</mi><mi arg='a1'>n</mi></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/HyperbolicSpace.html"
+     - "https://en.wikipedia.org/wiki/Hyperbolic_space"
+  
+  - concept: hyperbolic-umbilic-canonical-integral-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hyperbolic umbilic canonical integral function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='hyperbolic-umbilic-canonical-integral-function($a1)'><msup><mo>Ψ</mo><mrow><mo>(</mo><mi mathvariant='normal'>E</mi><mo>)</mo></mrow></msup><mi arg='a1'>z</mi></mrow></math>"
+    urls: 
+     - "https://dlmf.nist.gov/36.2#E11"
+     - "https://dlmf.nist.gov/36.3#i"
+     - "https://dlmf.nist.gov/36.3#ii"
+  
+  - concept: hyperdeterminant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: hyperdeterminant of $a1
+    property: "function, fenced"
+    subject-area: "multilinear algebra"
+    mathml:
+     - "<math><mrow intent='hyperdeterminant($a1)'><mi>det</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='hyperdeterminant($a1)'><mo>|</mo><mi arg='a1'>x</mi><mo>|</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Hyperdeterminant.html"
+     - "https://en.wikipedia.org/wiki/Hyperdeterminant"
+     - "https://ncatlab.org/nlab/show/hyperdeterminant"
+  
+  - concept: hypertorus
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> hypertorus
+    property: "indexed symbol"
+    subject-area: "topology"
+    mathml:
+     - "<math><msup intent='hypertorus($a1)'><mi>T</mi><mi arg='a1'>n</mi></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Torus#n-dimensional_torus"
+    alias:
+     - n-torus
+     - n-dimensional-torus
+  
+  - concept: identity-element
+    arity: 0
+    arguments: []
+    speech:
       en: identity element
-      property: symbol
-      area: "group theory"
-      mathml:
-       - "<math><mi intent='identity-element'>e</mi></math>"
-       - "<math><mi intent='identity-element'>I</mi></math>"
-       - "<math><mi intent='identity-element'>E</mi></math>"
-      notationa: "mn 1"
-      urls: 
-       - "https://mathworld.wolfram.com/IdentityElement.html"
-       - "https://en.wikipedia.org/wiki/Identity_element"
-       - "https://ncatlab.org/nlab/show/identity+element"
-      alias:
-       - identity
-       - two-sided-identity
-    
-    - concept: identity-function
-      arity: 1
-      en: identity function of $1
-      property: function
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='identity-function($a1)'><mi>id</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><msub intent='identity-function($a1)'><mi>id</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='identity-function($a1)'><mi>I</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/IdentityFunction.html"
-       - "https://en.wikipedia.org/wiki/Identity_function"
-       - "https://ncatlab.org/nlab/show/identity+function"
-      alias:
-       - identity-map
-       - identity-relation
-       - identity-transformation
-    
-    - concept: identity-functor
-      arity: 1
-      en: identity functor of $1
-      property: function
-      area: "category theory"
-      mathml:
-       - "<math><msub intent='identity-functor($a1)'><mi>1</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='identity-functor($a1)'><mi>I</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='identity-functor($a1)'><mi>Id</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/identity+functor"
-       - "https://en.wikipedia.org/wiki/Functor"
-    
-    - concept: identity-matrix
-      arity: 0
+    property: symbol
+    subject-area: "group theory"
+    mathml:
+     - "<math><mi intent='identity-element'>e</mi></math>"
+     - "<math><mi intent='identity-element'>I</mi></math>"
+     - "<math><mi intent='identity-element'>E</mi></math>"
+    notationa: "mn 1"
+    urls: 
+     - "https://mathworld.wolfram.com/IdentityElement.html"
+     - "https://en.wikipedia.org/wiki/Identity_element"
+     - "https://ncatlab.org/nlab/show/identity+element"
+    alias:
+     - identity
+     - two-sided-identity
+  
+  - concept: identity-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: identity function of $a1
+    property: function
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='identity-function($a1)'><mi>id</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><msub intent='identity-function($a1)'><mi>id</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='identity-function($a1)'><mi>I</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/IdentityFunction.html"
+     - "https://en.wikipedia.org/wiki/Identity_function"
+     - "https://ncatlab.org/nlab/show/identity+function"
+    alias:
+     - identity-map
+     - identity-relation
+     - identity-transformation
+  
+  - concept: identity-functor
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: identity functor of $a1
+    property: function
+    subject-area: "category theory"
+    mathml:
+     - "<math><msub intent='identity-functor($a1)'><mi>1</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='identity-functor($a1)'><mi>I</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='identity-functor($a1)'><mi>Id</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/identity+functor"
+     - "https://en.wikipedia.org/wiki/Functor"
+  
+  - concept: identity-matrix
+    arity: 0
+    arguments: []
+    speech:
       en: identity matrix
-      property: symbol
-      area: "linear algebra"
-      mathml:
-       - "<math><mi intent='identity-matrix'>I</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/IdentityMatrix.html"
-       - "https://en.wikipedia.org/wiki/Identity_matrix"
-      alias:
-       - unit-matrix
-    
-    - concept: image
-      arity: 1
-      en: image $1
-      property: mixfix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='image($a1)'><mi>Image</mi><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='image($a1)'><mi arg='a1'>f</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><msup intent='image($a1)'><mi>X</mi><mo>→</mo></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Image.html"
-       - "https://en.wikipedia.org/wiki/Image_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Range_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Image_(category_theory)"
-       - "https://en.wikipedia.org/wiki/Image"
-       - "https://ncatlab.org/nlab/show/image"
-    
-    - concept: incenter
-      arity: 0
+    property: symbol
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mi intent='identity-matrix'>I</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/IdentityMatrix.html"
+     - "https://en.wikipedia.org/wiki/Identity_matrix"
+    alias:
+     - unit-matrix
+  
+  - concept: image
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: image $a1
+    property: mixfix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='image($a1)'><mi>Image</mi><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='image($a1)'><mi arg='a1'>f</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><msup intent='image($a1)'><mi>X</mi><mo>→</mo></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Image.html"
+     - "https://en.wikipedia.org/wiki/Image_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Range_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Image_(category_theory)"
+     - "https://en.wikipedia.org/wiki/Image"
+     - "https://ncatlab.org/nlab/show/image"
+  
+  - concept: incenter
+    arity: 0
+    arguments: []
+    speech:
       en: incenter
-      property: symbol
-      area: "geometry"
-      mathml:
-       - "<math><mi intent='incenter'>I</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Incenter.html"
-       - "https://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle"
-       - "https://en.wikipedia.org/wiki/Gergonne_point"
-       - "https://en.wikipedia.org/wiki/Incentre"
-    
-    - concept: incidence-relation
-      arity: 2
-      en: $1 incidence relation $2
-      property: infix
-      area: "projective geometry"
-      mathml:
-       - "<math><mrow intent='incidence-relation($a1,$a2)'><mi arg='a1'>X</mi><mi>I</mi><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Incidence_(geometry)"
-       - "https://en.wikipedia.org/wiki/Incidence_(epidemiology)"
-       - "https://www.encyclopediaofmath.org/index.php/Incidence"
-    
-    - concept: incidence-structure
-      arity: 3
-      en: incidence structure of $1, $2 and $3
-      property: fenced
-      area: "incidence geometry"
-      mathml:
-       - "<math><mrow intent='incidence-structure($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>P</mi><mo>,</mo><mi arg='a2'>L</mi><mo>,</mo><mi arg='a3'>I</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Incidence_structure"
-    
-    - concept: inclusion-map
-      arity: 1
-      en: inclusion map of $1
-      property: function
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='inclusion-map($a1)'><mi>ι</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Inclusion_map"
-      alias:
-       - inclusion-function
-       - insertion
-       - canonical-injection
-    
-    - concept: incomparability
-      arity: 2
-      en: $1 incomparable to $2
-      property: infix
-      area: "order theory"
-      mathml:
-       - "<math><mrow intent='incomparability($a1,$a2)'><mi arg='a1'>X</mi><mo>⪋̸</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Comparability"
-      alias:
-       - incomparable
-    
-    - concept: incomplete-beta-function
-      arity: 1
-      en: incomplete beta function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='incomplete-beta-function($a1)'><mi>B</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/IncompleteBetaFunction.html"
-       - "https://dlmf.nist.gov/8.17"
-       - "https://dlmf.nist.gov/8.17#E1"
-       - "https://dlmf.nist.gov/8.17#E2"
-    
-    - concept: incomplete-elliptic-integral-of-the-first-kind
-      arity: 1
-      en: incomplete elliptic integral of the first kind of $1
-      property: function
-      area: "elliptic functions"
-      mathml:
-       - "<math><mrow intent='incomplete-elliptic-integral-of-the-first-kind($a1)'><mi>F</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EllipticIntegral.html"
-       - "https://en.wikipedia.org/wiki/Elliptic_integral"
-       - "https://www.encyclopediaofmath.org/index.php/Elliptic_integral"
-    
-    - concept: incomplete-elliptic-integral-of-the-second-kind
-      arity: 1
-      en: incomplete elliptic integral of the second kind of $1
-      property: function
-      area: "elliptic functions"
-      mathml:
-       - "<math><mrow intent='incomplete-elliptic-integral-of-the-second-kind($a1)'><mi>E</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/EllipticIntegral.html"
-       - "https://en.wikipedia.org/wiki/Elliptic_integral"
-       - "https://www.encyclopediaofmath.org/index.php/Elliptic_integral"
-    
-    - concept: incomplete-gamma-function
-      arity: 1
-      en: incomplete gamma function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='incomplete-gamma-function($a1)'><mi>Γ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/IncompleteGammaFunction.html"
-       - "https://en.wikipedia.org/wiki/Incomplete_gamma_function"
-       - "https://en.wikipedia.org/wiki/Regularized_Gamma_function"
-       - "https://dlmf.nist.gov/8#PT2"
-       - "https://dlmf.nist.gov/8.2#E2"
-       - "https://dlmf.nist.gov/8.2#E1"
-       - "https://dlmf.nist.gov/8.2#E6"
-    
-    - concept: increase
-      arity: 1
-      en: increase of $1
-      property: postfix
-      area: "physics"
-      mathml:
-       - "<math><mrow intent='increase($a1)'><mi arg='a1'>x</mi><mo>↑</mo></mrow></math>"
-      urls: 
-       - "https://youtu.be/HZ7a9YkF204?t=4606"
-    
-    - concept: increase-tends-to
-      arity: 2
-      en: $1 increase tends to $2
-      property: infix
-      area: "calculus"
-      mathml:
-       - "<math><mrow intent='increase-tends-to($a1,$a2)'><mi arg='a1'>X</mi><mo>↗</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://math.stackexchange.com/questions/1886232/what-does-this-notation-mean-limes-from-left-right"
-       - "http://pi.math.cornell.edu/~web6720/MATH%206710%20notes.pdf"
-    
-    - concept: independent
-      arity: 2
-      en: $1 independent $2
-      property: infix
-      area: "probability theory"
-      mathml:
-       - "<math><mrow intent='independent($a1,$a2)'><mi arg='a1'>X</mi><mo>⟂</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='independent($a1,$a2)'><mi arg='a1'>X</mi><mo>⫫</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Independence_(probability_theory)"
-       - "https://en.wikipedia.org/wiki/Independence_(mathematical_logic)"
-       - "https://www.encyclopediaofmath.org/index.php/Independence"
-    
-    - concept: index-of-subgroup
-      arity: 2
+    property: symbol
+    subject-area: "geometry"
+    mathml:
+     - "<math><mi intent='incenter'>I</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Incenter.html"
+     - "https://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle"
+     - "https://en.wikipedia.org/wiki/Gergonne_point"
+     - "https://en.wikipedia.org/wiki/Incentre"
+  
+  - concept: incidence-relation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 incidence relation $a2
+    property: infix
+    subject-area: "projective geometry"
+    mathml:
+     - "<math><mrow intent='incidence-relation($a1,$a2)'><mi arg='a1'>X</mi><mi>I</mi><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Incidence_(geometry)"
+     - "https://en.wikipedia.org/wiki/Incidence_(epidemiology)"
+     - "https://www.encyclopediaofmath.org/index.php/Incidence"
+  
+  - concept: incidence-structure
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: incidence structure of $a1, $a2 and $a3
+    property: fenced
+    subject-area: "incidence geometry"
+    mathml:
+     - "<math><mrow intent='incidence-structure($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>P</mi><mo>,</mo><mi arg='a2'>L</mi><mo>,</mo><mi arg='a3'>I</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Incidence_structure"
+  
+  - concept: inclusion-map
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: inclusion map of $a1
+    property: function
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='inclusion-map($a1)'><mi>ι</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Inclusion_map"
+    alias:
+     - inclusion-function
+     - insertion
+     - canonical-injection
+  
+  - concept: incomparability
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 incomparable to $a2
+    property: infix
+    subject-area: "order theory"
+    mathml:
+     - "<math><mrow intent='incomparability($a1,$a2)'><mi arg='a1'>X</mi><mo>⪋̸</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Comparability"
+    alias:
+     - incomparable
+  
+  - concept: incomplete-beta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: incomplete beta function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='incomplete-beta-function($a1)'><mi>B</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/IncompleteBetaFunction.html"
+     - "https://dlmf.nist.gov/8.17"
+     - "https://dlmf.nist.gov/8.17#E1"
+     - "https://dlmf.nist.gov/8.17#E2"
+  
+  - concept: incomplete-elliptic-integral-of-the-first-kind
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: incomplete elliptic integral of the first kind of $a1
+    property: function
+    subject-area: "elliptic functions"
+    mathml:
+     - "<math><mrow intent='incomplete-elliptic-integral-of-the-first-kind($a1)'><mi>F</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EllipticIntegral.html"
+     - "https://en.wikipedia.org/wiki/Elliptic_integral"
+     - "https://www.encyclopediaofmath.org/index.php/Elliptic_integral"
+  
+  - concept: incomplete-elliptic-integral-of-the-second-kind
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: incomplete elliptic integral of the second kind of $a1
+    property: function
+    subject-area: "elliptic functions"
+    mathml:
+     - "<math><mrow intent='incomplete-elliptic-integral-of-the-second-kind($a1)'><mi>E</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/EllipticIntegral.html"
+     - "https://en.wikipedia.org/wiki/Elliptic_integral"
+     - "https://www.encyclopediaofmath.org/index.php/Elliptic_integral"
+  
+  - concept: incomplete-gamma-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: incomplete gamma function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='incomplete-gamma-function($a1)'><mi>Γ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/IncompleteGammaFunction.html"
+     - "https://en.wikipedia.org/wiki/Incomplete_gamma_function"
+     - "https://en.wikipedia.org/wiki/Regularized_Gamma_function"
+     - "https://dlmf.nist.gov/8#PT2"
+     - "https://dlmf.nist.gov/8.2#E2"
+     - "https://dlmf.nist.gov/8.2#E1"
+     - "https://dlmf.nist.gov/8.2#E6"
+  
+  - concept: increase
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: increase of $a1
+    property: postfix
+    subject-area: "physics"
+    mathml:
+     - "<math><mrow intent='increase($a1)'><mi arg='a1'>x</mi><mo>↑</mo></mrow></math>"
+    urls: 
+     - "https://youtu.be/HZ7a9YkF204?t=4606"
+  
+  - concept: increase-tends-to
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 increase tends to $a2
+    property: infix
+    subject-area: "calculus"
+    mathml:
+     - "<math><mrow intent='increase-tends-to($a1,$a2)'><mi arg='a1'>X</mi><mo>↗</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://math.stackexchange.com/questions/1886232/what-does-this-notation-mean-limes-from-left-right"
+     - "http://pi.math.cornell.edu/~web6720/MATH%206710%20notes.pdf"
+  
+  - concept: independent
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 independent $a2
+    property: infix
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mrow intent='independent($a1,$a2)'><mi arg='a1'>X</mi><mo>⟂</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='independent($a1,$a2)'><mi arg='a1'>X</mi><mo>⫫</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Independence_(probability_theory)"
+     - "https://en.wikipedia.org/wiki/Independence_(mathematical_logic)"
+     - "https://www.encyclopediaofmath.org/index.php/Independence"
+  
+  - concept: index-of-subgroup
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: index of subgroup
-      property: fenced
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='index-of-subgroup($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>:</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
-       - "<math><mrow intent='index-of-subgroup($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>:</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
-       - "<math><mrow intent='index-of-subgroup($a1,$a2)'><mo>|</mo><mi arg='a1'>x</mi><mo>:</mo><mi arg='a2'>y</mi><mo>|</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Index_of_a_subgroup"
-    
-    - concept: index-of-lie-algebra
-      arity: 1
-      en: index of lie algebra of $1
-      property: function
-      area: "lie algebra"
-      mathml:
-       - "<math><mrow intent='index-of-lie-algebra($a1)'><mi>ind</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Index_of_a_Lie_algebra"
-    
-    - concept: infimum
-      arity: 1
-      en: infimum of $1
-      property: "function, largeop"
-      area: "order theory"
-      mathml:
-       - "<math><mrow intent='infimum($a1)'><mi>inf</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='infimum($a1)'><mo>⋀</mo><mi arg='a1'>X</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Infimum.html"
-       - "https://en.wikipedia.org/wiki/Infimum_and_supremum"
-      alias:
-       - meet
-       - greatest-lower-bound
-    
-    - concept: infimum-limit
-      arity: 1
-      en: infimum limit of $1
-      property: indexed
-      area: "limits"
-      mathml:
-       - "<math><mrow intent='infimum-limit($a1)'><mi>lim inf</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='infimum-limit($a1)'><munder><mi>lim</mi><mo>_</mo></munder><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/InfimumLimit.html"
-       - "https://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior"
-      alias:
-       - limit-inferior
-       - limit-infimum
-       - liminf
-       - inferior-limit
-       - lower-limit
-       - inner-limit
-    
-    - concept: infinite-product
-      arity: 1
-      en: infinite product of $1
-      property: indexed
-      area: "mathematical analysis"
-      mathml:
-       - "<math><mrow intent='infinite-product($a1)'><munderover><mo>Π</mo><mn>1</mn><mo>∞</mo></munderover><msub arg='a1'><mi>a</mi><mi>n</mi></msub></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/InfiniteProduct.html"
-       - "https://en.wikipedia.org/wiki/Infinite_product"
-       - "https://www.encyclopediaofmath.org/index.php/Infinite_product"
-    
-    - concept: infinitely-many-concurrently-active-copies
-      arity: 1
-      en: infinitely many concurrently active copies of $1
-      property: prefix
-      area: "formal languages"
-      mathml:
-       - "<math><mrow intent='infinitely-many-concurrently-active-copies($a1)'><mo>!</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://arxiv.org/pdf/0903.3513.pdf"
-    
-    - concept: injection
-      arity: 3
-      en: injection $1, from $2 to $3
-      property: mixfix, 
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='injection($a1,$a2,$a3)'><mi arg='a1'>f</mi><mo>:</mo><mi arg='a2'>X</mi><mo>↣</mo><mi arg='a3'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Bijection#Definition"
-    
-    - concept: inner-automorphism-group
-      arity: 1
-      en: inner automorphism group of $1
-      property: function
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='inner-automorphism-group($a1)'><mi>Inn</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/InnerAutomorphism.html"
-       - "https://en.wikipedia.org/wiki/Inner_automorphism"
-       - "https://ncatlab.org/nlab/show/inner+automorphism"
-       - "https://www.encyclopediaofmath.org/index.php/Inner_automorphism"
-      alias:
-       - inner-automorphism
-    
-    - concept: inner-jordan-measure
-      arity: 1
-      en: inner jordan measure of $1
-      property: function
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='inner-jordan-measure($a1)'><msub><mi>m</mi><mo>*</mo></msub><mrow><mo>(</mo><mi arg='a1'>N</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JordanMeasure.html"
-       - "https://en.wikipedia.org/wiki/Jordan_measure"
-       - "https://www.encyclopediaofmath.org/index.php/Jordan_measure"
-    
-    - concept: inner-product
-      arity: 2
-      en: $1 inner product $2
-      property: infix, fenced
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='inner-product($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>⋅</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
-       - "<math><mrow intent='inner-product($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/InnerProduct.html"
-       - "https://en.wikipedia.org/wiki/Dot_product"
-       - "https://en.wikipedia.org/wiki/Inner_product_space"
-       - "https://www.encyclopediaofmath.org/index.php/Inner_product"
-       - "https://mathoverflow.net/a/366118"
-    
-    - concept: instantaneous-activity
-      arity: 2
-      en: instantaneous activity of $1 at $2
-      property: mixfix
-      area: "chemistry"
-      mathml:
-       - "<math><msub intent='instantaneous-activity($a1,$a2)'><mrow><mo>{</mo><mi arg='a1'>X</mi><mo>}</mo></mrow><mi arg='a2'>t</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Reaction_quotient"
-    
-    - concept: integer-part
-      arity: 1
-      en: integer part of $1
-      property: "function, fenced"
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='integer-part($a1)'><mi>int</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      notationa: "[ $1 ]"
-      urls: 
-       - "https://mathworld.wolfram.com/IntegerPart.html"
-       - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions"
-    
-    - concept: interior
-      arity: 1
-      en: interior of $1
-      property: msup
-      area: "topology"
-      mathml:
-       - "<math><msup intent='interior($a1)'><mi arg='a1'>X</mi><mo>o</mo></msup></math>"
-       - "<math><msup intent='interior($a1)'><mi arg='a1'>X</mi><mo>∘</mo></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Interior.html"
-       - "https://en.wikipedia.org/wiki/Interior_(topology)"
-       - "https://ncatlab.org/nlab/show/interior"
-       - "https://www.encyclopediaofmath.org/index.php/Interior"
-    
-    - concept: interior-product
-      arity: 2
-      en: interior product of $1 $2
-      property: "infix, indexed function"
-      area: "differential forms"
-      mathml:
-       - "<math><mrow intent='interior-product($a1)'><mi arg='a1'>X</mi><mo>⨼</mo><mi arg='a2'>ω</mi></mrow></math>"
-       - "<math><mrow intent='interior-product($a1)'><msub><mi>ι</mi><mi arg='a1'>X</mi></msub><mi arg='a2'>ω</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/InteriorProduct.html"
-       - "https://en.wikipedia.org/wiki/Interior_product"
-    
-    - concept: intersection-number
-      arity: 2
-      en: $1 intersection number $2
-      property: infix
-      area: "algebraic geometry"
-      mathml:
-       - "<math><mrow intent='intersection-number($a1,$a2)'><mi arg='a1'>X</mi><mo>⋅</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Intersection_number"
-    
-    - concept: inverse-image
-      arity: 2
-      en: inverse image $1 $2
-      property: mixfix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='inverse-image($a1,$a2)'><msup><mi arg='a1'>f</mi><mn>−1</mn></msup><mrow><mo>[</mo><mi arg='a2'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Image_(mathematics)"
-       - "https://ncatlab.org/nlab/show/inverse+image"
-      alias:
-       - preimage
-    
-    - concept: inverse-limit
-      arity: 1
-      en: inverse limit of $1
-      property: prefix
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='inverse-limit($a1)'><munder><mi>lim</mi><mo>←</mo></munder><mrow><mo>(</mo><msub arg='a1'><mi>A</mi><mi>i</mi></msub><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/InverseLimit.html"
-       - "https://en.wikipedia.org/wiki/Inverse_limit"
-       - "https://ncatlab.org/nlab/show/inverse+limit"
-      alias:
-       - projective limit
-    
-    - concept: inverse-moment-of-function
-      arity: 2
-      en: $2<i>th</i> inverse moment of function $1
-      property: "msub, mixfix"
-      area: "mathematics"
-      mathml:
-       - "<math><mrow intent='inverse-moment-of-function($a1,$a2)'><mi>E</mi><mrow><mo>[</mo><msup><mi arg='a1'>X</mi><mrow><mo>−</mo><mi arg='a2'>n</mi></mrow></msup><mo>]</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Moment_(mathematics)"
-      alias:
-       - inverse-moment
-    
-    - concept: inverse-tangent-integral
-      arity: 1
-      en: inverse tangent integral of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='inverse-tangent-integral($a1)'><mi>Ti</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Polylogarithm"
-    
-    - concept: inverse-wishart-distribution
-      arity: 0
+    property: fenced
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='index-of-subgroup($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>:</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
+     - "<math><mrow intent='index-of-subgroup($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>:</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
+     - "<math><mrow intent='index-of-subgroup($a1,$a2)'><mo>|</mo><mi arg='a1'>x</mi><mo>:</mo><mi arg='a2'>y</mi><mo>|</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Index_of_a_subgroup"
+  
+  - concept: index-of-lie-algebra
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: index of lie algebra of $a1
+    property: function
+    subject-area: "lie algebra"
+    mathml:
+     - "<math><mrow intent='index-of-lie-algebra($a1)'><mi>ind</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Index_of_a_Lie_algebra"
+  
+  - concept: infimum
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: infimum of $a1
+    property: "function, largeop"
+    subject-area: "order theory"
+    mathml:
+     - "<math><mrow intent='infimum($a1)'><mi>inf</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='infimum($a1)'><mo>⋀</mo><mi arg='a1'>X</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Infimum.html"
+     - "https://en.wikipedia.org/wiki/Infimum_and_supremum"
+    alias:
+     - meet
+     - greatest-lower-bound
+  
+  - concept: infimum-limit
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: infimum limit of $a1
+    property: indexed
+    subject-area: "limits"
+    mathml:
+     - "<math><mrow intent='infimum-limit($a1)'><mi>lim inf</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='infimum-limit($a1)'><munder><mi>lim</mi><mo>_</mo></munder><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/InfimumLimit.html"
+     - "https://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior"
+    alias:
+     - limit-inferior
+     - limit-infimum
+     - liminf
+     - inferior-limit
+     - lower-limit
+     - inner-limit
+  
+  - concept: infinite-product
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: infinite product of $a1
+    property: indexed
+    subject-area: "mathematical analysis"
+    mathml:
+     - "<math><mrow intent='infinite-product($a1)'><munderover><mo>Π</mo><mn>1</mn><mo>∞</mo></munderover><msub arg='a1'><mi>a</mi><mi>n</mi></msub></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/InfiniteProduct.html"
+     - "https://en.wikipedia.org/wiki/Infinite_product"
+     - "https://www.encyclopediaofmath.org/index.php/Infinite_product"
+  
+  - concept: infinitely-many-concurrently-active-copies
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: infinitely many concurrently active copies of $a1
+    property: prefix
+    subject-area: "formal languages"
+    mathml:
+     - "<math><mrow intent='infinitely-many-concurrently-active-copies($a1)'><mo>!</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://arxiv.org/pdf/0903.3513.pdf"
+  
+  - concept: injection
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: injection $a1, from $a2 to $a3
+    property: mixfix, 
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='injection($a1,$a2,$a3)'><mi arg='a1'>f</mi><mo>:</mo><mi arg='a2'>X</mi><mo>↣</mo><mi arg='a3'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Bijection#Definition"
+  
+  - concept: inner-automorphism-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: inner automorphism group of $a1
+    property: function
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='inner-automorphism-group($a1)'><mi>Inn</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/InnerAutomorphism.html"
+     - "https://en.wikipedia.org/wiki/Inner_automorphism"
+     - "https://ncatlab.org/nlab/show/inner+automorphism"
+     - "https://www.encyclopediaofmath.org/index.php/Inner_automorphism"
+    alias:
+     - inner-automorphism
+  
+  - concept: inner-jordan-measure
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: inner jordan measure of $a1
+    property: function
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='inner-jordan-measure($a1)'><msub><mi>m</mi><mo>*</mo></msub><mrow><mo>(</mo><mi arg='a1'>N</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JordanMeasure.html"
+     - "https://en.wikipedia.org/wiki/Jordan_measure"
+     - "https://www.encyclopediaofmath.org/index.php/Jordan_measure"
+  
+  - concept: inner-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 inner product $a2
+    property: infix, fenced
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='inner-product($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>⋅</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
+     - "<math><mrow intent='inner-product($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/InnerProduct.html"
+     - "https://en.wikipedia.org/wiki/Dot_product"
+     - "https://en.wikipedia.org/wiki/Inner_product_space"
+     - "https://www.encyclopediaofmath.org/index.php/Inner_product"
+     - "https://mathoverflow.net/a/366118"
+  
+  - concept: instantaneous-activity
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: instantaneous activity of $a1 at $a2
+    property: mixfix
+    subject-area: "chemistry"
+    mathml:
+     - "<math><msub intent='instantaneous-activity($a1,$a2)'><mrow><mo>{</mo><mi arg='a1'>X</mi><mo>}</mo></mrow><mi arg='a2'>t</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Reaction_quotient"
+  
+  - concept: integer-part
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: integer part of $a1
+    property: "function, fenced"
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='integer-part($a1)'><mi>int</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    notationa: "[ $a1 ]"
+    urls: 
+     - "https://mathworld.wolfram.com/IntegerPart.html"
+     - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions"
+  
+  - concept: interior
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: interior of $a1
+    property: msup
+    subject-area: "topology"
+    mathml:
+     - "<math><msup intent='interior($a1)'><mi arg='a1'>X</mi><mo>o</mo></msup></math>"
+     - "<math><msup intent='interior($a1)'><mi arg='a1'>X</mi><mo>∘</mo></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Interior.html"
+     - "https://en.wikipedia.org/wiki/Interior_(topology)"
+     - "https://ncatlab.org/nlab/show/interior"
+     - "https://www.encyclopediaofmath.org/index.php/Interior"
+  
+  - concept: interior-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: interior product of $a1 $a2
+    property: "infix, indexed function"
+    subject-area: "differential forms"
+    mathml:
+     - "<math><mrow intent='interior-product($a1)'><mi arg='a1'>X</mi><mo>⨼</mo><mi arg='a2'>ω</mi></mrow></math>"
+     - "<math><mrow intent='interior-product($a1)'><msub><mi>ι</mi><mi arg='a1'>X</mi></msub><mi arg='a2'>ω</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/InteriorProduct.html"
+     - "https://en.wikipedia.org/wiki/Interior_product"
+  
+  - concept: intersection-number
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 intersection number $a2
+    property: infix
+    subject-area: "algebraic geometry"
+    mathml:
+     - "<math><mrow intent='intersection-number($a1,$a2)'><mi arg='a1'>X</mi><mo>⋅</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Intersection_number"
+  
+  - concept: inverse-image
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: inverse image $a1 $a2
+    property: mixfix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='inverse-image($a1,$a2)'><msup><mi arg='a1'>f</mi><mn>−1</mn></msup><mrow><mo>[</mo><mi arg='a2'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Image_(mathematics)"
+     - "https://ncatlab.org/nlab/show/inverse+image"
+    alias:
+     - preimage
+  
+  - concept: inverse-limit
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: inverse limit of $a1
+    property: prefix
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='inverse-limit($a1)'><munder><mi>lim</mi><mo>←</mo></munder><mrow><mo>(</mo><msub arg='a1'><mi>A</mi><mi>i</mi></msub><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/InverseLimit.html"
+     - "https://en.wikipedia.org/wiki/Inverse_limit"
+     - "https://ncatlab.org/nlab/show/inverse+limit"
+    alias:
+     - projective limit
+  
+  - concept: inverse-moment-of-function
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a2<i>th</i> inverse moment of function $a1
+    property: "msub, mixfix"
+    subject-area: "mathematics"
+    mathml:
+     - "<math><mrow intent='inverse-moment-of-function($a1,$a2)'><mi>E</mi><mrow><mo>[</mo><msup><mi arg='a1'>X</mi><mrow><mo>−</mo><mi arg='a2'>n</mi></mrow></msup><mo>]</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Moment_(mathematics)"
+    alias:
+     - inverse-moment
+  
+  - concept: inverse-tangent-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: inverse tangent integral of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='inverse-tangent-integral($a1)'><mi>Ti</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Polylogarithm"
+  
+  - concept: inverse-wishart-distribution
+    arity: 0
+    arguments: []
+    speech:
       en: inverse wishart distribution
-      property: symbol
-      area: "probability theory"
-      mathml:
-       - "<math><msubsup intent='inverse-wishart-distribution'><mi>W</mi><mi>p</mi><mn>−1</mn></msubsup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WishartDistribution.html"
-       - "https://en.wikipedia.org/wiki/Wishart_distribution"
-       - "https://www.encyclopediaofmath.org/index.php/Wishart_distribution"
-    
-    - concept: ionic-charge
-      arity: 2
+    property: symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><msubsup intent='inverse-wishart-distribution'><mi>W</mi><mi>p</mi><mn>−1</mn></msubsup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WishartDistribution.html"
+     - "https://en.wikipedia.org/wiki/Wishart_distribution"
+     - "https://www.encyclopediaofmath.org/index.php/Wishart_distribution"
+  
+  - concept: ionic-charge
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: ionic charge
-      property: msup
-      area: "chemistry"
-      mathml:
-       - "<math><msup intent='ionic-charge($a1,$a2)'><mi arg='a1'>Fe</mi><mrow arg='a2'><mn>2</mn></mrow></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Ion#Chemistry"
-    
-    - concept: isogonal-conjugate
-      arity: 1
-      en: isogonal conjugate of $1
-      property: msup
-      area: "geometry"
-      mathml:
-       - "<math><msup intent='isogonal-conjugate($a1)'><mi arg='a1'>X</mi><mn>-1</mn></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/IsogonalConjugate.html"
-       - "https://en.wikipedia.org/wiki/Isogonal_conjugate"
-    
-    - concept: isomorphism
-      arity: 2
-      en: $1 isomorphism $2
-      property: infix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='isomorphism($a1,$a2)'><mi arg='a1'>X</mi><mover><mo>↦</mo><mo>∼</mo></mover><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='isomorphism($a1,$a2)'><mi arg='a1'>X</mi><mo>≅</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Isomorphism.html"
-       - "https://en.wikipedia.org/wiki/Isomorphism"
-       - "https://ncatlab.org/nlab/show/isomorphism"
-       - "https://www.encyclopediaofmath.org/index.php/Isomorphism"
-      alias:
-       - natural-isomorphism
-    
-    - concept: isotropy-group
-      arity: 2
+    property: msup
+    subject-area: "chemistry"
+    mathml:
+     - "<math><msup intent='ionic-charge($a1,$a2)'><mi arg='a1'>Fe</mi><mrow arg='a2'><mn>2</mn></mrow></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Ion#Chemistry"
+  
+  - concept: isogonal-conjugate
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: isogonal conjugate of $a1
+    property: msup
+    subject-area: "geometry"
+    mathml:
+     - "<math><msup intent='isogonal-conjugate($a1)'><mi arg='a1'>X</mi><mn>-1</mn></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/IsogonalConjugate.html"
+     - "https://en.wikipedia.org/wiki/Isogonal_conjugate"
+  
+  - concept: isomorphism
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 isomorphism $a2
+    property: infix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='isomorphism($a1,$a2)'><mi arg='a1'>X</mi><mover><mo>↦</mo><mo>∼</mo></mover><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='isomorphism($a1,$a2)'><mi arg='a1'>X</mi><mo>≅</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Isomorphism.html"
+     - "https://en.wikipedia.org/wiki/Isomorphism"
+     - "https://ncatlab.org/nlab/show/isomorphism"
+     - "https://www.encyclopediaofmath.org/index.php/Isomorphism"
+    alias:
+     - natural-isomorphism
+  
+  - concept: isotropy-group
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: isotropy group
-      property: msub
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='isotropy-group($a1,$a2)'><mi arg='a1'>G</mi><mi arg='a2'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/IsotropyGroup.html"
-       - "https://www.encyclopediaofmath.org/index.php/Isotropy_group"
-      alias:
-       - little-group
-       - stabilizer-subgroup
-    
-    - concept: iverson-bracket
-      arity: 1
-      en: iverson bracket of $1
-      property: fenced
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='iverson-bracket($a1)'><mo>[</mo><mi arg='a1'>P</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Iverson_bracket"
-    
-    - concept: j-invariant
-      arity: 1
-      en: j invariant of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='j-invariant($a1)'><mi>j</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/j-Invariant.html"
-       - "https://ncatlab.org/nlab/show/j-invariant"
-    
-    - concept: jacobi-matrix
-      arity: 1
-      en: jacobi matrix of $1
-      property: function
-      area: "operator theory"
-      mathml:
-       - "<math><mrow intent='jacobi-matrix($a1)'><mi>J</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JacobiMatrix.html"
-       - "https://en.wikipedia.org/wiki/Jacobi_operator"
-       - "https://www.encyclopediaofmath.org/index.php/Jacobi_matrix"
-      alias:
-       - jacobi-operator
-    
-    - concept: jacobi-polynomial
-      arity: 2
-      en: $1<i>th</i>jacobi polynomial of $2
-      property: function
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><mrow intent='jacobi-polynomial($a1,$2)'><msubsup><mi>P</mi><mi arg='a1'>n</mi><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow></msubsup><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      notation: "msubsup P"
-      urls: 
-       - "https://mathworld.wolfram.com/JacobiPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Heckman%E2%80%93Opdam_polynomials"
-       - "https://en.wikipedia.org/wiki/Jacobi_polynomials"
-       - "https://dlmf.nist.gov/18.3"
-       - "https://dlmf.nist.gov/18.3#T1.t1.r3"
-       - "https://www.encyclopediaofmath.org/index.php/Jacobi_polynomials"
-    
-    - concept: jacobi-symbol
-      arity: 2
+    property: msub
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='isotropy-group($a1,$a2)'><mi arg='a1'>G</mi><mi arg='a2'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/IsotropyGroup.html"
+     - "https://www.encyclopediaofmath.org/index.php/Isotropy_group"
+    alias:
+     - little-group
+     - stabilizer-subgroup
+  
+  - concept: iverson-bracket
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: iverson bracket of $a1
+    property: fenced
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='iverson-bracket($a1)'><mo>[</mo><mi arg='a1'>P</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Iverson_bracket"
+  
+  - concept: j-invariant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: j invariant of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='j-invariant($a1)'><mi>j</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/j-Invariant.html"
+     - "https://ncatlab.org/nlab/show/j-invariant"
+  
+  - concept: jacobi-matrix
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: jacobi matrix of $a1
+    property: function
+    subject-area: "operator theory"
+    mathml:
+     - "<math><mrow intent='jacobi-matrix($a1)'><mi>J</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JacobiMatrix.html"
+     - "https://en.wikipedia.org/wiki/Jacobi_operator"
+     - "https://www.encyclopediaofmath.org/index.php/Jacobi_matrix"
+    alias:
+     - jacobi-operator
+  
+  - concept: jacobi-polynomial
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1<i>th</i>jacobi polynomial of $a2
+    property: function
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><mrow intent='jacobi-polynomial($a1,$a2)'><msubsup><mi>P</mi><mi arg='a1'>n</mi><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow></msubsup><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    notation: "msubsup P"
+    urls: 
+     - "https://mathworld.wolfram.com/JacobiPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Heckman%E2%80%93Opdam_polynomials"
+     - "https://en.wikipedia.org/wiki/Jacobi_polynomials"
+     - "https://dlmf.nist.gov/18.3"
+     - "https://dlmf.nist.gov/18.3#T1.t1.r3"
+     - "https://www.encyclopediaofmath.org/index.php/Jacobi_polynomials"
+  
+  - concept: jacobi-symbol
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: jacobi symbol
-      property: mixfix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='jacobi-symbol($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JacobiSymbol.html"
-       - "https://en.wikipedia.org/wiki/Jacobi_symbol"
-       - "https://dlmf.nist.gov/27.9#p3"
-       - "https://www.encyclopediaofmath.org/index.php/Jacobi_symbol"
-    
-    - concept: jacobi-theta-function
-      arity: 1
-      en: jacobi theta function of $1
-      property: function
-      area: "special-functions"
-      mathml:
-       - "<math><mrow intent='jacobi-theta-function($a1)'><mi>ϑ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JacobiThetaFunctions.html"
-       - "https://en.wikipedia.org/wiki/Jacobi_theta_functions_(notational_variations)"
-    
-    - concept: jacobi-zeta-function
-      arity: 2
+    property: mixfix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='jacobi-symbol($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JacobiSymbol.html"
+     - "https://en.wikipedia.org/wiki/Jacobi_symbol"
+     - "https://dlmf.nist.gov/27.9#p3"
+     - "https://www.encyclopediaofmath.org/index.php/Jacobi_symbol"
+  
+  - concept: jacobi-theta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: jacobi theta function of $a1
+    property: function
+    subject-area: "special-functions"
+    mathml:
+     - "<math><mrow intent='jacobi-theta-function($a1)'><mi>ϑ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JacobiThetaFunctions.html"
+     - "https://en.wikipedia.org/wiki/Jacobi_theta_functions_(notational_variations)"
+  
+  - concept: jacobi-zeta-function
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: jacobi zeta function
-      property: function
-      area: "special-functions"
-      mathml:
-       - "<math><mrow intent='jacobi-zeta-function($a1,$a2)'><mi>Z</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>k</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JacobiZetaFunction.html"
-       - "https://en.wikipedia.org/wiki/Jacobi_zeta_function"
-       - "https://dlmf.nist.gov/22.16#iii"
-       - "https://dlmf.nist.gov/22.16#E32"
-    
-    - concept: jacobian-elliptic-function
-      arity: 1
-      en: jacobian elliptic function of $1
-      property: function
-      area: "special-functions"
-      mathml:
-       - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>sn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>cn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>dn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>sd</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>cd</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>sc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://dlmf.nist.gov/22.2"
-       - "https://dlmf.nist.gov/22.2#E5"
-       - "https://dlmf.nist.gov/22.2#E6"
-       - "https://dlmf.nist.gov/22.2#E7"
-       - "https://dlmf.nist.gov/22.2#E8"
-       - "https://dlmf.nist.gov/22.2#E4"
-       - "https://dlmf.nist.gov/22.2#E9"
-    
-    - concept: jacobson-radical
-      arity: 1
-      en: jacobson radical of $1
-      property: function
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='jacobson-radical($a1)'><mi>J</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='jacobson-radical($a1)'><mi>rad</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JacobsonRadical.html"
-       - "https://en.wikipedia.org/wiki/Jacobson_radical"
-       - "https://ncatlab.org/nlab/show/Jacobson+radical"
-       - "https://www.encyclopediaofmath.org/index.php/Jacobson_radical"
-    
-    - concept: jacobsthal-number
-      arity: 0
+    property: function
+    subject-area: "special-functions"
+    mathml:
+     - "<math><mrow intent='jacobi-zeta-function($a1,$a2)'><mi>Z</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>k</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JacobiZetaFunction.html"
+     - "https://en.wikipedia.org/wiki/Jacobi_zeta_function"
+     - "https://dlmf.nist.gov/22.16#iii"
+     - "https://dlmf.nist.gov/22.16#E32"
+  
+  - concept: jacobian-elliptic-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: jacobian elliptic function of $a1
+    property: function
+    subject-area: "special-functions"
+    mathml:
+     - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>sn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>cn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>dn</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>sd</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>cd</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='jacobian-elliptic-function($a1)'><mi>sc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://dlmf.nist.gov/22.2"
+     - "https://dlmf.nist.gov/22.2#E5"
+     - "https://dlmf.nist.gov/22.2#E6"
+     - "https://dlmf.nist.gov/22.2#E7"
+     - "https://dlmf.nist.gov/22.2#E8"
+     - "https://dlmf.nist.gov/22.2#E4"
+     - "https://dlmf.nist.gov/22.2#E9"
+  
+  - concept: jacobson-radical
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: jacobson radical of $a1
+    property: function
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='jacobson-radical($a1)'><mi>J</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='jacobson-radical($a1)'><mi>rad</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JacobsonRadical.html"
+     - "https://en.wikipedia.org/wiki/Jacobson_radical"
+     - "https://ncatlab.org/nlab/show/Jacobson+radical"
+     - "https://www.encyclopediaofmath.org/index.php/Jacobson_radical"
+  
+  - concept: jacobsthal-number
+    arity: 0
+    arguments: []
+    speech:
       en: jacobsthal number
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='jacobsthal-number'>J</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JacobsthalNumber.html"
-       - "https://en.wikipedia.org/wiki/Jacobsthal_number"
-    
-    - concept: janko-group
-      arity: 0
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='jacobsthal-number'>J</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JacobsthalNumber.html"
+     - "https://en.wikipedia.org/wiki/Jacobsthal_number"
+  
+  - concept: janko-group
+    arity: 0
+    arguments: []
+    speech:
       en: janko group
-      property: symbol
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='janko-group'><mi>J</mi><mn>1</mn></msub></math>"
-       - "<math><msub intent='janko-group'><mi>J</mi><mn>2</mn></msub></math>"
-       - "<math><msub intent='janko-group'><mi>J</mi><mn>3</mn></msub></math>"
-       - "<math><msub intent='janko-group'><mi>J</mi><mn>4</mn></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JankoGroups.html"
-       - "https://en.wikipedia.org/wiki/Janko_group"
-    
-    - concept: jet
-      arity: 3
-      en: $1 jet of $3 at $2
-      property: function
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='jet($a1,$a2,$a3)'><msubsup><mi>J</mi><mi arg='a3'>x</mi><mi arg='a1'>k</mi></msubsup><mi arg='a3'>f</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Jet_(mathematics)"
-       - "https://www.encyclopediaofmath.org/index.php/Jet"
-    
-    - concept: join
-      arity: 1
-      en: join of $1
-      property: indexed
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='join($a1)'><msub><mo>⋁</mo><mrow><mi>α</mi><mo>∈</mo><mi>𝒜</mi></mrow></msub><mrow arg='a1'><mi>Σ</mi><mi>α</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Join.html"
-       - "https://en.wikipedia.org/wiki/Join_(sigma_algebra)"
-       - "https://en.wikipedia.org/wiki/Join_(topology)"
-       - "https://ncatlab.org/nlab/show/join"
-       - "https://www.encyclopediaofmath.org/index.php/Join"
-    
-    - concept: jone-polynomial
-      arity: 1
-      en: jone polynomial of $1
-      property: function
-      area: "knot theory"
-      mathml:
-       - "<math><mrow intent='jone-polynomial($a1)'><mi>V</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JonesPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Jones_polynomial"
-       - "https://ncatlab.org/nlab/show/Jones+polynomial"
-    
-    - concept: jordan-block
-      arity: 2
+    property: symbol
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='janko-group'><mi>J</mi><mn>1</mn></msub></math>"
+     - "<math><msub intent='janko-group'><mi>J</mi><mn>2</mn></msub></math>"
+     - "<math><msub intent='janko-group'><mi>J</mi><mn>3</mn></msub></math>"
+     - "<math><msub intent='janko-group'><mi>J</mi><mn>4</mn></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JankoGroups.html"
+     - "https://en.wikipedia.org/wiki/Janko_group"
+  
+  - concept: jet
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: $a1 jet of $a3 at $a2
+    property: function
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='jet($a1,$a2,$a3)'><msubsup><mi>J</mi><mi arg='a3'>x</mi><mi arg='a1'>k</mi></msubsup><mi arg='a3'>f</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Jet_(mathematics)"
+     - "https://www.encyclopediaofmath.org/index.php/Jet"
+  
+  - concept: join
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: join of $a1
+    property: indexed
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='join($a1)'><msub><mo>⋁</mo><mrow><mi>α</mi><mo>∈</mo><mi>𝒜</mi></mrow></msub><mrow arg='a1'><mi>Σ</mi><mi>α</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Join.html"
+     - "https://en.wikipedia.org/wiki/Join_(sigma_algebra)"
+     - "https://en.wikipedia.org/wiki/Join_(topology)"
+     - "https://ncatlab.org/nlab/show/join"
+     - "https://www.encyclopediaofmath.org/index.php/Join"
+  
+  - concept: jone-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: jone polynomial of $a1
+    property: function
+    subject-area: "knot theory"
+    mathml:
+     - "<math><mrow intent='jone-polynomial($a1)'><mi>V</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JonesPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Jones_polynomial"
+     - "https://ncatlab.org/nlab/show/Jones+polynomial"
+  
+  - concept: jordan-block
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: jordan block
-      property: "indexed symbol"
-      area: "linear algebra"
-      mathml:
-       - "<math><msub intent='jordan-block($a1,$a2)'><mi>J</mi><mrow><mi arg='a1'>a</mi><mi arg='a2'>b</mi></mrow></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JordanBlock.html"
-       - "https://en.wikipedia.org/wiki/Jordan_matrix"
-      alias:
-       - jordan-matrix
-    
-    - concept: jordan-measure
-      arity: 1
-      en: jordan measure of $1
-      property: function
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='jordan-measure($a1)'><mi>m</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JordanMeasure.html"
-       - "https://en.wikipedia.org/wiki/Jordan_measure"
-       - "https://www.encyclopediaofmath.org/index.php/Jordan_measure"
-    
-    - concept: jordan-totient-function
-      arity: 1
-      en: jordan totient function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='jordan-totient-function($a1)'><mi>J</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Jordan%27s_totient_function"
-    
-    - concept: julia-set
-      arity: 1
-      en: julia set of $1
-      property: function
-      area: "complex dynamics"
-      mathml:
-       - "<math><mrow intent='julia-set($a1)'><mi>J</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JuliaSet.html"
-       - "https://en.wikipedia.org/wiki/Julia_set"
-       - "https://www.encyclopediaofmath.org/index.php/Julia_set"
-    
-    - concept: kaprekar-constant
-      arity: 0
+    property: "indexed symbol"
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><msub intent='jordan-block($a1,$a2)'><mi>J</mi><mrow><mi arg='a1'>a</mi><mi arg='a2'>b</mi></mrow></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JordanBlock.html"
+     - "https://en.wikipedia.org/wiki/Jordan_matrix"
+    alias:
+     - jordan-matrix
+  
+  - concept: jordan-measure
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: jordan measure of $a1
+    property: function
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='jordan-measure($a1)'><mi>m</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JordanMeasure.html"
+     - "https://en.wikipedia.org/wiki/Jordan_measure"
+     - "https://www.encyclopediaofmath.org/index.php/Jordan_measure"
+  
+  - concept: jordan-totient-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: jordan totient function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='jordan-totient-function($a1)'><mi>J</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Jordan%27s_totient_function"
+  
+  - concept: julia-set
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: julia set of $a1
+    property: function
+    subject-area: "complex dynamics"
+    mathml:
+     - "<math><mrow intent='julia-set($a1)'><mi>J</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JuliaSet.html"
+     - "https://en.wikipedia.org/wiki/Julia_set"
+     - "https://www.encyclopediaofmath.org/index.php/Julia_set"
+  
+  - concept: kaprekar-constant
+    arity: 0
+    arguments: []
+    speech:
       en: kaprekar constant
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><mn intent='kaprekar-constant'>6174</mn></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KaprekarConstant.html"
-       - "https://en.wikipedia.org/wiki/6174_(number)"
-      alias:
-       - kaprekar-number
-    
-    - concept: kauffman-bracket
-      arity: 1
-      en: kauffman bracket of $1
-      property: fenced
-      area: "knot theory"
-      mathml:
-       - "<math><mrow intent='kauffman-bracket($a1)'><mo>⟨</mo><mi arg='a1'>x</mi><mo>⟩</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Bracket_polynomial"
-      alias:
-       - bracket-polynomial
-    
-    - concept: kelvin-function
-      arity: 1
-      en: $1<i>th</i> order kelvin function 
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow><msub intent='kelvin-function($a1)'><mi>ber</mi><mi arg='a1'>v</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow><msub intent='kelvin-function($a1)'><mi>bei</mi><mi arg='a1'>v</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KelvinFunctions.html"
-       - "https://en.wikipedia.org/wiki/Kelvin_functions"
-       - "https://dlmf.nist.gov/10#PT5"
-       - "https://dlmf.nist.gov/10.61#E1"
-       - "https://dlmf.nist.gov/10.61#E1"
-       - "https://dlmf.nist.gov/10.61#E2"
-       - "https://dlmf.nist.gov/10.61#E2"
-       - "https://www.encyclopediaofmath.org/index.php/Kelvin_functions"
-    
-    - concept: kernel
-      arity: 1
-      en: kernel of $1
-      property: function
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='kernel($a1)'><mi>ker</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Kernel.html"
-       - "https://en.wikipedia.org/wiki/Kernel_(algebra)"
-       - "https://en.wikipedia.org/wiki/Kernel_(set_theory)"
-       - "https://en.wikipedia.org/wiki/Sunflower_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Kernel_(linear_algebra)"
-       - "https://en.wikipedia.org/wiki/Kernel_(category_theory)"
-       - "https://en.wikipedia.org/wiki/Kernel_(statistics)"
-       - "https://en.wikipedia.org/wiki/Covariance_function"
-       - "https://ncatlab.org/nlab/show/kernel"
-      alias:
-       - nullspace
-       - null-space
-    
-    - concept: khinchin-constant
-      arity: 0
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><mn intent='kaprekar-constant'>6174</mn></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KaprekarConstant.html"
+     - "https://en.wikipedia.org/wiki/6174_(number)"
+    alias:
+     - kaprekar-number
+  
+  - concept: kauffman-bracket
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: kauffman bracket of $a1
+    property: fenced
+    subject-area: "knot theory"
+    mathml:
+     - "<math><mrow intent='kauffman-bracket($a1)'><mo>⟨</mo><mi arg='a1'>x</mi><mo>⟩</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Bracket_polynomial"
+    alias:
+     - bracket-polynomial
+  
+  - concept: kelvin-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> order kelvin function 
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow><msub intent='kelvin-function($a1)'><mi>ber</mi><mi arg='a1'>v</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow><msub intent='kelvin-function($a1)'><mi>bei</mi><mi arg='a1'>v</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KelvinFunctions.html"
+     - "https://en.wikipedia.org/wiki/Kelvin_functions"
+     - "https://dlmf.nist.gov/10#PT5"
+     - "https://dlmf.nist.gov/10.61#E1"
+     - "https://dlmf.nist.gov/10.61#E1"
+     - "https://dlmf.nist.gov/10.61#E2"
+     - "https://dlmf.nist.gov/10.61#E2"
+     - "https://www.encyclopediaofmath.org/index.php/Kelvin_functions"
+  
+  - concept: kernel
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: kernel of $a1
+    property: function
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='kernel($a1)'><mi>ker</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Kernel.html"
+     - "https://en.wikipedia.org/wiki/Kernel_(algebra)"
+     - "https://en.wikipedia.org/wiki/Kernel_(set_theory)"
+     - "https://en.wikipedia.org/wiki/Sunflower_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Kernel_(linear_algebra)"
+     - "https://en.wikipedia.org/wiki/Kernel_(category_theory)"
+     - "https://en.wikipedia.org/wiki/Kernel_(statistics)"
+     - "https://en.wikipedia.org/wiki/Covariance_function"
+     - "https://ncatlab.org/nlab/show/kernel"
+    alias:
+     - nullspace
+     - null-space
+  
+  - concept: khinchin-constant
+    arity: 0
+    arguments: []
+    speech:
       en: khinchin constant
-      property: constant
-      area: "continued fractions"
-      mathml:
-       - "<math><mi intent='khinchin-constant'>K</mi></math>"
-      notationa: "msub K 0"
-      urls: 
-       - "https://mathworld.wolfram.com/KhinchinsConstant.html"
-       - "https://en.wikipedia.org/wiki/Khinchin%27s_constant"
-    
-    - concept: killing-form
-      arity: 1
-      en: killing form of $1
-      property: function
-      area: "lie algebra"
-      mathml:
-       - "<math><mrow intent='killing-form($a1)'><mi>B</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KillingForm.html"
-       - "https://en.wikipedia.org/wiki/Killing_form"
-       - "https://ncatlab.org/nlab/show/Killing+form"
-       - "https://www.encyclopediaofmath.org/index.php/Killing_form"
-    
-    - concept: kleene-star
-      arity: 1
-      en: kleene star of $1
-      property: msup
-      area: "formal languages"
-      mathml:
-       - "<math><msup intent='kleene-star($a1)'><mi arg='a1'>x</mi><mo>*</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Kleene_star"
-    
-    - concept: kleene-plus
-      arity: 1
-      en: kleene plus of $1
-      property: msup
-      area: "formal languages"
-      mathml:
-       - "<math><msup intent='kleene-plus($a1)'><mi arg='a1'>x</mi><mo>+</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Kleene_star"
-    
-    - concept: klein-four-group
-      arity: 0
+    property: constant
+    subject-area: "continued fractions"
+    mathml:
+     - "<math><mi intent='khinchin-constant'>K</mi></math>"
+    notationa: "msub K 0"
+    urls: 
+     - "https://mathworld.wolfram.com/KhinchinsConstant.html"
+     - "https://en.wikipedia.org/wiki/Khinchin%27s_constant"
+  
+  - concept: killing-form
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: killing form of $a1
+    property: function
+    subject-area: "lie algebra"
+    mathml:
+     - "<math><mrow intent='killing-form($a1)'><mi>B</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KillingForm.html"
+     - "https://en.wikipedia.org/wiki/Killing_form"
+     - "https://ncatlab.org/nlab/show/Killing+form"
+     - "https://www.encyclopediaofmath.org/index.php/Killing_form"
+  
+  - concept: kleene-star
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: kleene star of $a1
+    property: msup
+    subject-area: "formal languages"
+    mathml:
+     - "<math><msup intent='kleene-star($a1)'><mi arg='a1'>x</mi><mo>*</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Kleene_star"
+  
+  - concept: kleene-plus
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: kleene plus of $a1
+    property: msup
+    subject-area: "formal languages"
+    mathml:
+     - "<math><msup intent='kleene-plus($a1)'><mi arg='a1'>x</mi><mo>+</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Kleene_star"
+  
+  - concept: klein-four-group
+    arity: 0
+    arguments: []
+    speech:
       en: klein four group
-      property: symbol
-      area: "group theory"
-      mathml:
-       - "<math><mi intent='klein-four-group'>V</mi></math>"
-      notationa: "msub K 4"
-      urls: 
-       - "https://mathworld.wolfram.com/KleinFour-Group.html"
-       - "https://en.wikipedia.org/wiki/Klein_four-group"
-    
-    - concept: kloosterman-sum
-      arity: 1
-      en: kloosterman sum of $1
-      property: function
-      area: "analytic number theory"
-      mathml:
-       - "<math><mrow intent='kloosterman-sum($a1)'><mi>S</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='kloosterman-sum($a1)'><mi>K</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KloostermansSum.html"
-       - "https://en.wikipedia.org/wiki/Kloosterman_sum"
-    
-    - concept: kneser-graph
-      arity: 2
-      en: kneser graph $1 $2
-      property: "indexed symbol"
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='kneser-graph($a1,$a2)'><mi>K</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>,</mo><mi arg='a2'>k</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><msub intent='kneser-graph($a1,$a2)'><mi>KG</mi><mrow><mi arg='a1'>n</mi><mo>,</mo><mi arg='a2'>k</mi></mrow></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KneserGraph.html"
-       - "https://en.wikipedia.org/wiki/Kneser_graph"
-    
-    - concept: knodel-number
-      arity: 1
-      en: knodel number of $1
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='knodel-number($a1)'><mi>K</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KnoedelNumbers.html"
-       - "https://en.wikipedia.org/wiki/Kn%C3%B6del_number"
-    
-    - concept: kodaira-dimension
-      arity: 1
-      en: kodaira dimension of $1
-      property: function
-      area: "algebraic geometry"
-      mathml:
-       - "<math><mrow intent='kodaira-dimension($a1)'><mi>κ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Kodaira_dimension"
-       - "https://www.encyclopediaofmath.org/index.php/Kodaira_dimension"
-    
-    - concept: kolmogorov-complexity
-      arity: 1
-      en: kolmogorov complexity of $1
-      property: function
-      area: "information theory"
-      mathml:
-       - "<math><mrow intent='kolmogorov-complexity($a1)'><mi>K</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KolmogorovComplexity.html"
-       - "https://en.wikipedia.org/wiki/Kolmogorov_complexity"
-    
-    - concept: kolmogorov-space
-      arity: 0
+    property: symbol
+    subject-area: "group theory"
+    mathml:
+     - "<math><mi intent='klein-four-group'>V</mi></math>"
+    notationa: "msub K 4"
+    urls: 
+     - "https://mathworld.wolfram.com/KleinFour-Group.html"
+     - "https://en.wikipedia.org/wiki/Klein_four-group"
+  
+  - concept: kloosterman-sum
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: kloosterman sum of $a1
+    property: function
+    subject-area: "analytic number theory"
+    mathml:
+     - "<math><mrow intent='kloosterman-sum($a1)'><mi>S</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='kloosterman-sum($a1)'><mi>K</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KloostermansSum.html"
+     - "https://en.wikipedia.org/wiki/Kloosterman_sum"
+  
+  - concept: kneser-graph
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: kneser graph $a1 $a2
+    property: "indexed symbol"
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='kneser-graph($a1,$a2)'><mi>K</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>,</mo><mi arg='a2'>k</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><msub intent='kneser-graph($a1,$a2)'><mi>KG</mi><mrow><mi arg='a1'>n</mi><mo>,</mo><mi arg='a2'>k</mi></mrow></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KneserGraph.html"
+     - "https://en.wikipedia.org/wiki/Kneser_graph"
+  
+  - concept: knodel-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: knodel number of $a1
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='knodel-number($a1)'><mi>K</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KnoedelNumbers.html"
+     - "https://en.wikipedia.org/wiki/Kn%C3%B6del_number"
+  
+  - concept: kodaira-dimension
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: kodaira dimension of $a1
+    property: function
+    subject-area: "algebraic geometry"
+    mathml:
+     - "<math><mrow intent='kodaira-dimension($a1)'><mi>κ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Kodaira_dimension"
+     - "https://www.encyclopediaofmath.org/index.php/Kodaira_dimension"
+  
+  - concept: kolmogorov-complexity
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: kolmogorov complexity of $a1
+    property: function
+    subject-area: "information theory"
+    mathml:
+     - "<math><mrow intent='kolmogorov-complexity($a1)'><mi>K</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KolmogorovComplexity.html"
+     - "https://en.wikipedia.org/wiki/Kolmogorov_complexity"
+  
+  - concept: kolmogorov-space
+    arity: 0
+    arguments: []
+    speech:
       en: kolmogorov space
-      property: constant
-      area: "topology"
-      mathml:
-       - "<math><msub intent='kolmogorov-space'><mi>T</mi><mn>0</mn></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions"
-    
-    - concept: kontsevich-integral
-      arity: 1
-      en: kontsevich integral of $1
-      property: function
-      area: "knot theory"
-      mathml:
-       - "<math><mrow intent='kontsevich-integral($a1)'><mi>Z</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KontsevichIntegral.html"
-       - "https://en.wikipedia.org/wiki/Kontsevich_invariant"
-       - "https://ncatlab.org/nlab/show/Kontsevich+integral"
-       - "https://www.encyclopediaofmath.org/index.php/Kontsevich_integral"
-    
-    - concept: krawtchouk-polynomial
-      arity: 1
-      en: krawtchouk polynomial of $1
-      property: function
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><msub intent='krawtchouk-polynomial($a1)'><mi>K</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KrawtchoukPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Kravchuk_polynomials"
-       - "https://dlmf.nist.gov/18.19#T1.t1.r6"
-       - "https://www.encyclopediaofmath.org/index.php/Krawtchouk_polynomials"
-    
-    - concept: kripke-frame
-      arity: 2
+    property: constant
+    subject-area: "topology"
+    mathml:
+     - "<math><msub intent='kolmogorov-space'><mi>T</mi><mn>0</mn></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions"
+  
+  - concept: kontsevich-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: kontsevich integral of $a1
+    property: function
+    subject-area: "knot theory"
+    mathml:
+     - "<math><mrow intent='kontsevich-integral($a1)'><mi>Z</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KontsevichIntegral.html"
+     - "https://en.wikipedia.org/wiki/Kontsevich_invariant"
+     - "https://ncatlab.org/nlab/show/Kontsevich+integral"
+     - "https://www.encyclopediaofmath.org/index.php/Kontsevich_integral"
+  
+  - concept: krawtchouk-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: krawtchouk polynomial of $a1
+    property: function
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><msub intent='krawtchouk-polynomial($a1)'><mi>K</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KrawtchoukPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Kravchuk_polynomials"
+     - "https://dlmf.nist.gov/18.19#T1.t1.r6"
+     - "https://www.encyclopediaofmath.org/index.php/Krawtchouk_polynomials"
+  
+  - concept: kripke-frame
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: kripke frame
-      property: fenced
-      area: "modal logic"
-      mathml:
-       - "<math><mrow intent='kripke-frame($a1,$a2)'><mo>⟨</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>⟩</mo></mrow></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/Kripke+frame"
-    
-    - concept: kronecker-delta
-      arity: 2
+    property: fenced
+    subject-area: "modal logic"
+    mathml:
+     - "<math><mrow intent='kripke-frame($a1,$a2)'><mo>⟨</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>⟩</mo></mrow></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/Kripke+frame"
+  
+  - concept: kronecker-delta
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: kronecker delta
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='kronecker-delta($a1,$a2)'><mi>δ</mi><mrow><mi arg='a1'>i</mi><mi arg='a2'>j</mi></mrow></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KroneckerDelta.html"
-       - "https://en.wikipedia.org/wiki/Kronecker_delta"
-       - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4"
-       - "https://ncatlab.org/nlab/show/Kronecker+delta"
-    
-    - concept: kronecker-product
-      arity: 2
-      en: $1 kronecker product $2
-      property: infix
-      area: "matrix theory"
-      mathml:
-       - "<math><mrow intent='kronecker-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⊗</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KroneckerProduct.html"
-       - "https://en.wikipedia.org/wiki/Khatri-Rao_product"
-       - "https://en.wikipedia.org/wiki/Kronecker_product"
-       - "https://en.wikipedia.org/wiki/Tracy-Singh_product"
-       - "https://www.encyclopediaofmath.org/index.php/Kronecker_product"
-    
-    - concept: kronecker-symbol
-      arity: 2
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='kronecker-delta($a1,$a2)'><mi>δ</mi><mrow><mi arg='a1'>i</mi><mi arg='a2'>j</mi></mrow></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KroneckerDelta.html"
+     - "https://en.wikipedia.org/wiki/Kronecker_delta"
+     - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4"
+     - "https://ncatlab.org/nlab/show/Kronecker+delta"
+  
+  - concept: kronecker-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 kronecker product $a2
+    property: infix
+    subject-area: "matrix theory"
+    mathml:
+     - "<math><mrow intent='kronecker-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⊗</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KroneckerProduct.html"
+     - "https://en.wikipedia.org/wiki/Khatri-Rao_product"
+     - "https://en.wikipedia.org/wiki/Kronecker_product"
+     - "https://en.wikipedia.org/wiki/Tracy-Singh_product"
+     - "https://www.encyclopediaofmath.org/index.php/Kronecker_product"
+  
+  - concept: kronecker-symbol
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: kronecker symbol
-      property: fenced, fenced stacked
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='kronecker-symbol($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
-       - "<math><mrow intent='kronecker-symbol($a1,$a2)'><mo>(</mo><mfrac><mi arg='a1'>x</mi><mi arg='a2'>y</mi></mfrac><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KroneckerSymbol.html"
-       - "https://en.wikipedia.org/wiki/Kronecker_symbol"
-       - "https://www.encyclopediaofmath.org/index.php/Kronecker_symbol"
-    
-    - concept: krull-dimension
-      arity: 1
-      en: krull dimension of $1
-      property: function
-      area: "commutative algebra"
-      mathml:
-       - "<math><mrow intent='krull-dimension($a1)'><mi>dim</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/KrullDimension.html"
-       - "https://en.wikipedia.org/wiki/Krull_dimension"
-       - "https://en.wikipedia.org/wiki/Height_(ring_theory)"
-    
-    - concept: kulkarni-nomizu-product
-      arity: 2
-      en: kulkarni nomizu product of $1 and $2
-      property: embellished infix
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='kulkarni-nomizu-product($a1)'><mi arg='a1'>h</mi><menclose notation='circle'><mo>∧</mo></menclose><mi arg='a2'>k</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Kulkarni%E2%80%93Nomizu_product"
-    
-    - concept: kullback-leibler-distance
-      arity: 1
-      en: kullback leibler distance of $1
-      property: function
-      area: "mathematical statistics"
-      mathml:
-       - "<math><mrow intent='kullback-leibler-distance($a1)'><mi>KL</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      notationa: "msub D KL"
-      urls: 
-       - "http://users.monash.edu/~lloyd/tildeMML/KL/"
-       - "https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence"
-      alias:
-       - kl-distance
-       - kl-divergence
-       - kullback-leibler-divergence
-       - relative-entropy
-    
-    - concept: lagrange-bracket
-      arity: 4
-      en: "lagrange bracket of $1, $2, canonical coordinates $3, $4"
-      property: indexed fenced
-      area: "classical mechanics"
-      mathml:
-       - "<math><msub intent='lagrange-bracket($1,$2,$3,$4)'><mrow><mo>[</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>]</mo></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LagrangeBracket.html"
-       - "https://en.wikipedia.org/wiki/Lagrange_bracket"
-       - "https://www.encyclopediaofmath.org/index.php/Lagrange_bracket"
-    
-    - concept: lagrange-multiplier
-      arity: 0
+    property: fenced, fenced stacked
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='kronecker-symbol($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>|</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
+     - "<math><mrow intent='kronecker-symbol($a1,$a2)'><mo>(</mo><mfrac><mi arg='a1'>x</mi><mi arg='a2'>y</mi></mfrac><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KroneckerSymbol.html"
+     - "https://en.wikipedia.org/wiki/Kronecker_symbol"
+     - "https://www.encyclopediaofmath.org/index.php/Kronecker_symbol"
+  
+  - concept: krull-dimension
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: krull dimension of $a1
+    property: function
+    subject-area: "commutative algebra"
+    mathml:
+     - "<math><mrow intent='krull-dimension($a1)'><mi>dim</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/KrullDimension.html"
+     - "https://en.wikipedia.org/wiki/Krull_dimension"
+     - "https://en.wikipedia.org/wiki/Height_(ring_theory)"
+  
+  - concept: kulkarni-nomizu-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: kulkarni nomizu product of $a1 and $a2
+    property: embellished infix
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='kulkarni-nomizu-product($a1)'><mi arg='a1'>h</mi><menclose notation='circle'><mo>∧</mo></menclose><mi arg='a2'>k</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Kulkarni%E2%80%93Nomizu_product"
+  
+  - concept: kullback-leibler-distance
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: kullback leibler distance of $a1
+    property: function
+    subject-area: "mathematical statistics"
+    mathml:
+     - "<math><mrow intent='kullback-leibler-distance($a1)'><mi>KL</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    notationa: "msub D KL"
+    urls: 
+     - "http://users.monash.edu/~lloyd/tildeMML/KL/"
+     - "https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence"
+    alias:
+     - kl-distance
+     - kl-divergence
+     - kullback-leibler-divergence
+     - relative-entropy
+  
+  - concept: lagrange-bracket
+    arity: 4
+    arguments: [$a1, $a2, $a3, $a4]
+    speech:
+      en: "lagrange bracket of $a1, $a2, canonical coordinates $a3, $a4"
+    property: indexed fenced
+    subject-area: "classical mechanics"
+    mathml:
+     - "<math><msub intent='lagrange-bracket($a1,$a2,$a3,$a4)'><mrow><mo>[</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>]</mo></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LagrangeBracket.html"
+     - "https://en.wikipedia.org/wiki/Lagrange_bracket"
+     - "https://www.encyclopediaofmath.org/index.php/Lagrange_bracket"
+  
+  - concept: lagrange-multiplier
+    arity: 0
+    arguments: []
+    speech:
       en: lagrange multiplier
-      property: symbol
-      area: "mathematical optimization"
-      mathml:
-       - "<math><mi intent='lagrange-multiplier'>λ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LagrangeMultiplier.html"
-       - "https://en.wikipedia.org/wiki/Lagrange_multiplier"
-       - "https://ncatlab.org/nlab/show/Lagrange+multiplier"
-       - "https://www.encyclopediaofmath.org/index.php/Lagrange_multipliers"
-      alias:
-       - lagrangian
-    
-    - concept: lagrange-point
-      arity: 0
+    property: symbol
+    subject-area: "mathematical optimization"
+    mathml:
+     - "<math><mi intent='lagrange-multiplier'>λ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LagrangeMultiplier.html"
+     - "https://en.wikipedia.org/wiki/Lagrange_multiplier"
+     - "https://ncatlab.org/nlab/show/Lagrange+multiplier"
+     - "https://www.encyclopediaofmath.org/index.php/Lagrange_multipliers"
+    alias:
+     - lagrangian
+  
+  - concept: lagrange-point
+    arity: 0
+    arguments: []
+    speech:
       en: lagrange point
-      property: symbol
-      area: "celestial mechanics"
-      mathml:
-       - "<math><msub intent='lagrange-point'><mi>L</mi><mn>1</mn></msub></math>"
-       - "<math><msub intent='lagrange-point'><mi>L</mi><mn>2</mn></msub></math>"
-       - "<math><msub intent='lagrange-point'><mi>L</mi><mn>3</mn></msub></math>"
-       - "<math><msub intent='lagrange-point'><mi>L</mi><mn>4</mn></msub></math>"
-       - "<math><msub intent='lagrange-point'><mi>L</mi><mn>5</mn></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Lagrange_point"
-      alias:
-       - lagrangian-point
-       - l-point
-       - libration-point
-    
-    - concept: laguerre-polynomial
-      arity: 1
-      en: laguerre polynomial of $1
-      property: "indexed function"
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><mrow intent='laguerre-polynomial($a1)'><mi>L</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LaguerrePolynomial.html"
-       - "https://en.wikipedia.org/wiki/Laguerre_polynomials"
-       - "https://dlmf.nist.gov/18.3"
-       - "https://dlmf.nist.gov/18.1#I1.ix7.p1"
-       - "https://dlmf.nist.gov/18.3#T1.t1.r27"
-       - "https://www.encyclopediaofmath.org/index.php/Laguerre_polynomials"
-    
-    - concept: landau-constant
-      arity: 0
+    property: symbol
+    subject-area: "celestial mechanics"
+    mathml:
+     - "<math><msub intent='lagrange-point'><mi>L</mi><mn>1</mn></msub></math>"
+     - "<math><msub intent='lagrange-point'><mi>L</mi><mn>2</mn></msub></math>"
+     - "<math><msub intent='lagrange-point'><mi>L</mi><mn>3</mn></msub></math>"
+     - "<math><msub intent='lagrange-point'><mi>L</mi><mn>4</mn></msub></math>"
+     - "<math><msub intent='lagrange-point'><mi>L</mi><mn>5</mn></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Lagrange_point"
+    alias:
+     - lagrangian-point
+     - l-point
+     - libration-point
+  
+  - concept: laguerre-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: laguerre polynomial of $a1
+    property: "indexed function"
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><mrow intent='laguerre-polynomial($a1)'><mi>L</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LaguerrePolynomial.html"
+     - "https://en.wikipedia.org/wiki/Laguerre_polynomials"
+     - "https://dlmf.nist.gov/18.3"
+     - "https://dlmf.nist.gov/18.1#I1.ix7.p1"
+     - "https://dlmf.nist.gov/18.3#T1.t1.r27"
+     - "https://www.encyclopediaofmath.org/index.php/Laguerre_polynomials"
+  
+  - concept: landau-constant
+    arity: 0
+    arguments: []
+    speech:
       en: landau constant
-      property: constant
-      area: "complex analysis"
-      mathml:
-       - "<math><mi intent='landau-constant'>A</mi></math>"
-       - "<math><mi intent='landau-constant'>B</mi></math>"
-       - "<math><mi intent='landau-constant'>L</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LandauConstant.html"
-       - "https://en.wikipedia.org/wiki/Landau%27s_constants"
-    
-    - concept: laplace-operator
-      arity: 1
-      en: laplace operator of $1
-      property: "embellished operator"
-      area: "differential operators"
-      mathml:
-       - "<math><mrow intent='laplace-operator($a1)'><msup><mo>∇</mo><mn>2</mn></msup><mi arg='a1'>f</mi></mrow></math>"
-       - "<math><mrow intent='laplace-operator($a1)'><mo>∇</mo><mo>·</mo><mo>∇</mo><mi arg='a1'>f</mi></mrow></math>"
-       - "<math><mrow intent='laplace-operator($a1)'><mi>Δ</mi><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Laplace_operator"
-       - "https://ncatlab.org/nlab/show/Laplace+operator"
-       - "https://www.encyclopediaofmath.org/index.php/Laplace_operator"
-    
-    - concept: laplace-transform
-      arity: 1
-      en: laplace transform of $1
-      property: operator
-      area: "integral transforms"
-      mathml:
-       - "<math><mrow intent='laplace-transform($a1)'><mi>ℒ⁡</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LaplaceTransform.html"
-       - "https://en.wikipedia.org/wiki/Laplace_transform"
-       - "https://dlmf.nist.gov/1.14#E17"
-       - "https://www.encyclopediaofmath.org/index.php/Laplace_transform"
-    
-    - concept: laplacian-matrix
-      arity: 0
+    property: constant
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mi intent='landau-constant'>A</mi></math>"
+     - "<math><mi intent='landau-constant'>B</mi></math>"
+     - "<math><mi intent='landau-constant'>L</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LandauConstant.html"
+     - "https://en.wikipedia.org/wiki/Landau%27s_constants"
+  
+  - concept: laplace-operator
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: laplace operator of $a1
+    property: "embellished operator"
+    subject-area: "differential operators"
+    mathml:
+     - "<math><mrow intent='laplace-operator($a1)'><msup><mo>∇</mo><mn>2</mn></msup><mi arg='a1'>f</mi></mrow></math>"
+     - "<math><mrow intent='laplace-operator($a1)'><mo>∇</mo><mo>·</mo><mo>∇</mo><mi arg='a1'>f</mi></mrow></math>"
+     - "<math><mrow intent='laplace-operator($a1)'><mi>Δ</mi><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Laplace_operator"
+     - "https://ncatlab.org/nlab/show/Laplace+operator"
+     - "https://www.encyclopediaofmath.org/index.php/Laplace_operator"
+  
+  - concept: laplace-transform
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: laplace transform of $a1
+    property: operator
+    subject-area: "integral transforms"
+    mathml:
+     - "<math><mrow intent='laplace-transform($a1)'><mi>ℒ⁡</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LaplaceTransform.html"
+     - "https://en.wikipedia.org/wiki/Laplace_transform"
+     - "https://dlmf.nist.gov/1.14#E17"
+     - "https://www.encyclopediaofmath.org/index.php/Laplace_transform"
+  
+  - concept: laplacian-matrix
+    arity: 0
+    arguments: []
+    speech:
       en: laplacian matrix
-      property: symbol
-      area: "graph theory"
-      mathml:
-       - "<math><mi intent='laplacian-matrix'>L</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LaplacianMatrix.html"
-       - "https://en.wikipedia.org/wiki/Laplacian_matrix"
-    
-    - concept: latin-rectangle
-      arity: 1
-      en: latin rectangle $1
-      property: mtable
-      area: "combinatorial mathematics"
-      mathml:
-       - "<math><mrow intent='latin-rectangle($a1)'><mtable arg='a1'><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mrow></math>"
+    property: symbol
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mi intent='laplacian-matrix'>L</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LaplacianMatrix.html"
+     - "https://en.wikipedia.org/wiki/Laplacian_matrix"
+  
+  - concept: latin-rectangle
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: latin rectangle $a1
+    property: mtable
+    subject-area: "combinatorial mathematics"
+    mathml:
+     - "<math><mrow intent='latin-rectangle($a1)'><mtable arg='a1'><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mrow></math>"
 
-      urls: 
-       - "https://mathworld.wolfram.com/LatinRectangle.html"
-       - "https://en.wikipedia.org/wiki/Latin_rectangle"
-       - "https://www.encyclopediaofmath.org/index.php/Latin_rectangle"
-    
-    - concept: latin-square
-      arity: 1
-      en: latin square $1
-      property: mtable
-      area: "combinatorial mathematics"
-      mathml:
-       - "<math><mrow intent='latin-square($a1)'><mtable arg='a1'><mtr><mtd><mi>A</mi></mtd><mtd><mi>B</mi></mtd><mtd><mi>C</mi></mtd></mtr><mtr><mtd><mi>C</mi></mtd><mtd><mi>A</mi></mtd><mtd><mi>B</mi></mtd></mtr><mtr><mtd><mi>B</mi></mtd><mtd><mi>C</mi></mtd><mtd><mi>A</mi></mtd></mtr></mtable></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LatinSquare.html"
-       - "https://en.wikipedia.org/wiki/Latin_square"
-       - "https://en.wikipedia.org/wiki/Small_Latin_squares_and_quasigroups"
-       - "https://ncatlab.org/nlab/show/Latin+square"
-       - "https://www.encyclopediaofmath.org/index.php/Latin_square"
-    
-    - concept: least-prime-factor
-      arity: 1
-      en: least prime factor of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='least-prime-factor($a1)'><mi>lpf</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LeastPrimeFactor.html"
-    
-    - concept: lebesgue-constant
-      arity: 1
-      en: lebesgue constant of $1
-      property: indexed constant
-      area: "fourier series"
-      mathml:
-       - "<math><msub intent='lebesgue-constant($a1)'><mi>L</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LebesgueConstants.html"
-       - "https://en.wikipedia.org/wiki/Lebesgue_constant_(interpolation)"
-       - "https://dlmf.nist.gov/1.8#E8"
-       - "https://www.encyclopediaofmath.org/index.php/Lebesgue_constants"
-    
-    - concept: lebesgue-integral
-      arity: 1
-      en: lebesgue integral of $1
-      property: indexed
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='lebesgue-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LebesgueIntegral.html"
-       - "https://www.encyclopediaofmath.org/index.php/Lebesgue_integral"
-    
-    - concept: leech-lattice
-      arity: 0
+    urls: 
+     - "https://mathworld.wolfram.com/LatinRectangle.html"
+     - "https://en.wikipedia.org/wiki/Latin_rectangle"
+     - "https://www.encyclopediaofmath.org/index.php/Latin_rectangle"
+  
+  - concept: latin-square
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: latin square $a1
+    property: mtable
+    subject-area: "combinatorial mathematics"
+    mathml:
+     - "<math><mrow intent='latin-square($a1)'><mtable arg='a1'><mtr><mtd><mi>A</mi></mtd><mtd><mi>B</mi></mtd><mtd><mi>C</mi></mtd></mtr><mtr><mtd><mi>C</mi></mtd><mtd><mi>A</mi></mtd><mtd><mi>B</mi></mtd></mtr><mtr><mtd><mi>B</mi></mtd><mtd><mi>C</mi></mtd><mtd><mi>A</mi></mtd></mtr></mtable></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LatinSquare.html"
+     - "https://en.wikipedia.org/wiki/Latin_square"
+     - "https://en.wikipedia.org/wiki/Small_Latin_squares_and_quasigroups"
+     - "https://ncatlab.org/nlab/show/Latin+square"
+     - "https://www.encyclopediaofmath.org/index.php/Latin_square"
+  
+  - concept: least-prime-factor
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: least prime factor of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='least-prime-factor($a1)'><mi>lpf</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LeastPrimeFactor.html"
+  
+  - concept: lebesgue-constant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lebesgue constant of $a1
+    property: indexed constant
+    subject-area: "fourier series"
+    mathml:
+     - "<math><msub intent='lebesgue-constant($a1)'><mi>L</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LebesgueConstants.html"
+     - "https://en.wikipedia.org/wiki/Lebesgue_constant_(interpolation)"
+     - "https://dlmf.nist.gov/1.8#E8"
+     - "https://www.encyclopediaofmath.org/index.php/Lebesgue_constants"
+  
+  - concept: lebesgue-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lebesgue integral of $a1
+    property: indexed
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='lebesgue-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LebesgueIntegral.html"
+     - "https://www.encyclopediaofmath.org/index.php/Lebesgue_integral"
+  
+  - concept: leech-lattice
+    arity: 0
+    arguments: []
+    speech:
       en: leech lattice
-      property: symbol
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='leech-lattice'><mo>Λ</mo><mn>24</mn></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LeechLattice.html"
-       - "https://en.wikipedia.org/wiki/Leech_lattice"
-       - "https://ncatlab.org/nlab/show/Leech+lattice"
-    
-    - concept: left-adjoint
-      arity: 2
-      en: $1 left adjoint $2
-      property: infix
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='left-adjoint($a1,$a2)'><mi arg='a1'>X</mi><mo>⊣</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Adjoint_functors"
-    
-    - concept: left-composition
-      arity: 2
-      en: $1 left composition $2
-      property: infix
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='left-composition($a1,$a2)'><mi arg='a1'>X</mi><mo>;</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Composition_of_relations"
-      alias:
-       - left-compose
-    
-    - concept: left-derivative
-      arity: 1
-      en: left derivative of $1
-      property: operator
-      area: "calculus"
-      mathml:
-       - "<math><msub intent='left-derivative($a1)'><mo>∂</mo><mo>−</mo></msub><mi arg='a1'>f</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Left_and_right_derivative"
-    
-    - concept: legendre-chi-function
-      arity: 1
-      en: legendre chi function of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='legendre-chi-function($a1)'><mi>χ</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Legendre_chi_function"
-       - "https://mathworld.wolfram.com/LegendresChi-Function.html"
-    
-    - concept: legendre-polynomial
-      arity: 1
-      en: legendre polynomial of $1
-      property: function
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><msub intent='legendre-polynomial($a1)'><mi>P</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LegendrePolynomial.html"
-       - "https://en.wikipedia.org/wiki/Legendre_polynomials"
-       - "https://dlmf.nist.gov/18.3"
-       - "https://dlmf.nist.gov/18.3#T1.t1.r25"
-       - "https://ncatlab.org/nlab/show/Legendre+polynomial"
-    
-    - concept: legendre-symbol
-      arity: 2
+    property: symbol
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='leech-lattice'><mo>Λ</mo><mn>24</mn></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LeechLattice.html"
+     - "https://en.wikipedia.org/wiki/Leech_lattice"
+     - "https://ncatlab.org/nlab/show/Leech+lattice"
+  
+  - concept: left-adjoint
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 left adjoint $a2
+    property: infix
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='left-adjoint($a1,$a2)'><mi arg='a1'>X</mi><mo>⊣</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Adjoint_functors"
+  
+  - concept: left-composition
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 left composition $a2
+    property: infix
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='left-composition($a1,$a2)'><mi arg='a1'>X</mi><mo>;</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Composition_of_relations"
+    alias:
+     - left-compose
+  
+  - concept: left-derivative
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: left derivative of $a1
+    property: operator
+    subject-area: "calculus"
+    mathml:
+     - "<math><msub intent='left-derivative($a1)'><mo>∂</mo><mo>−</mo></msub><mi arg='a1'>f</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Left_and_right_derivative"
+  
+  - concept: legendre-chi-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: legendre chi function of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='legendre-chi-function($a1)'><mi>χ</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Legendre_chi_function"
+     - "https://mathworld.wolfram.com/LegendresChi-Function.html"
+  
+  - concept: legendre-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: legendre polynomial of $a1
+    property: function
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><msub intent='legendre-polynomial($a1)'><mi>P</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LegendrePolynomial.html"
+     - "https://en.wikipedia.org/wiki/Legendre_polynomials"
+     - "https://dlmf.nist.gov/18.3"
+     - "https://dlmf.nist.gov/18.3#T1.t1.r25"
+     - "https://ncatlab.org/nlab/show/Legendre+polynomial"
+  
+  - concept: legendre-symbol
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: legendre symbol
-      property: fenced, fenced stacked
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='legendre-symbol($a1,$a2)'><mo>(</mo><mi arg='a1'>a</mi><mo>|</mo><mi arg='a2'>p</mi><mo>)</mo></mrow></math>"
-       - "<math><mrow intent='legendre-symbol($a1,$a2)'><mo>(</mo><mfrac><mi arg='a1'>a</mi><mi arg='a2'>p</mi></mfrac><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LegendreSymbol.html"
-       - "https://en.wikipedia.org/wiki/Legendre_symbol"
-       - "https://dlmf.nist.gov/27.9"
-    
-    - concept: lehmer-mean
-      arity: 1
-      en: lehmer mean of $1
-      property: "indexed function"
-      area: "means"
-      mathml:
-       - "<math><msub intent='lehmer-mean($a1)'><mi>L</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LehmerMean.html"
-       - "https://en.wikipedia.org/wiki/Lehmer_mean"
-    
-    - concept: lehmer-number
-      arity: 1
-      en: lehmer number of $1
-      property: "indexed function"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='lehmer-number($a1)'><mi>U</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LehmerNumber.html"
-       - "https://mathworld.wolfram.com/LehmersNumber.html"
-       - "https://en.wikipedia.org/wiki/Lehmer_number"
-    
-    - concept: level
-      arity: 1
-      en: level of $1
-      property: function
-      area: "scales of measurement"
-      mathml:
-       - "<math><msub intent='level($a1)'><mi>L</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Level_(logarithmic_quantity)"
-       - "https://en.wikipedia.org/wiki/Categorical_variable"
-       - "https://ncatlab.org/nlab/show/level"
-    
-    - concept: levi-civita-symbol
-      arity: 3
-      en: levi civita symbol  of $1, $2 and $3
-      property: "indexed symbol"
-      area: "combinatorics"
-      mathml:
-       - "<math><msub intent='levi-civita-symbol($1,$2,$3)'><mi>&#x03f5;</mi><mrow><mi arg='a1'>i</mi><mi arg='a2'>j</mi><mi arg='a3'>k</mi></mrow></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Levi-CivitaSymbol.html"
-       - "https://en.wikipedia.org/wiki/Levi-Civita_symbol"
-       - "https://dlmf.nist.gov/1.6#E14"
-      alias:
-       - permutation-symbol
-    
-    - concept: levy-prokhorov-metric
-      arity: 1
-      en: levy prokhorov metric of $1
-      property: function
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='levy-prokhorov-metric($a1)'><mi>π</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/L%C3%A9vy%E2%80%93Prokhorov_metric"
-       - "https://encyclopediaofmath.org/wiki/L%C3%A9vy-Prokhorov_metric"
-    
-    - concept: lexicographic-product
-      arity: 2
-      en: $1 lexicographic product $2
-      property: infix, mixfix
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='lexicographic-product($a1,$a2)'><mi arg='a1'>G</mi><mo>∙</mo><mi arg='a2'>H</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Lexicographic_product_of_graphs"
-      alias:
-       - graph-composition
-    
-    - concept: lexicographic-order
-      arity: 2
-      en: $1 lexicographic order $2
-      property: infix
-      area: "discrete mathematics"
-      mathml:
-       - "<math><mrow intent='lexicographic-order($a1,$a2)'><mi arg='a1'>X</mi><mo>&lt;</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Lexicographic_order"
-       - "https://mathworld.wolfram.com/LexicographicOrder.html"
-       - "https://ncatlab.org/nlab/show/lexicographic+order"
-      alias:
-       - dictionary-order
-    
-    - concept: lie-derivative
-      arity: 1
-      en: lie derivative of $1
-      property: "indexed operator"
-      area: "lie algebra"
-      mathml:
-       - "<math><msub intent='lie-derivative($a1)'><mi>ℒ</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LieDerivative.html"
-       - "https://en.wikipedia.org/wiki/Lie_derivative"
-       - "https://ncatlab.org/nlab/show/Lie+derivative"
-    
-    - concept: lie-superbracket
-      arity: 2
+    property: fenced, fenced stacked
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='legendre-symbol($a1,$a2)'><mo>(</mo><mi arg='a1'>a</mi><mo>|</mo><mi arg='a2'>p</mi><mo>)</mo></mrow></math>"
+     - "<math><mrow intent='legendre-symbol($a1,$a2)'><mo>(</mo><mfrac><mi arg='a1'>a</mi><mi arg='a2'>p</mi></mfrac><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LegendreSymbol.html"
+     - "https://en.wikipedia.org/wiki/Legendre_symbol"
+     - "https://dlmf.nist.gov/27.9"
+  
+  - concept: lehmer-mean
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lehmer mean of $a1
+    property: "indexed function"
+    subject-area: "means"
+    mathml:
+     - "<math><msub intent='lehmer-mean($a1)'><mi>L</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LehmerMean.html"
+     - "https://en.wikipedia.org/wiki/Lehmer_mean"
+  
+  - concept: lehmer-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lehmer number of $a1
+    property: "indexed function"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='lehmer-number($a1)'><mi>U</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LehmerNumber.html"
+     - "https://mathworld.wolfram.com/LehmersNumber.html"
+     - "https://en.wikipedia.org/wiki/Lehmer_number"
+  
+  - concept: level
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: level of $a1
+    property: function
+    subject-area: "scales of measurement"
+    mathml:
+     - "<math><msub intent='level($a1)'><mi>L</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Level_(logarithmic_quantity)"
+     - "https://en.wikipedia.org/wiki/Categorical_variable"
+     - "https://ncatlab.org/nlab/show/level"
+  
+  - concept: levi-civita-symbol
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: levi civita symbol  of $a1, $a2 and $a3
+    property: "indexed symbol"
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><msub intent='levi-civita-symbol($a1,$a2,$a3)'><mi>&#x03f5;</mi><mrow><mi arg='a1'>i</mi><mi arg='a2'>j</mi><mi arg='a3'>k</mi></mrow></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Levi-CivitaSymbol.html"
+     - "https://en.wikipedia.org/wiki/Levi-Civita_symbol"
+     - "https://dlmf.nist.gov/1.6#E14"
+    alias:
+     - permutation-symbol
+  
+  - concept: levy-prokhorov-metric
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: levy prokhorov metric of $a1
+    property: function
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='levy-prokhorov-metric($a1)'><mi>π</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/L%C3%A9vy%E2%80%93Prokhorov_metric"
+     - "https://encyclopediaofmath.org/wiki/L%C3%A9vy-Prokhorov_metric"
+  
+  - concept: lexicographic-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 lexicographic product $a2
+    property: infix, mixfix
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='lexicographic-product($a1,$a2)'><mi arg='a1'>G</mi><mo>∙</mo><mi arg='a2'>H</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Lexicographic_product_of_graphs"
+    alias:
+     - graph-composition
+  
+  - concept: lexicographic-order
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 lexicographic order $a2
+    property: infix
+    subject-area: "discrete mathematics"
+    mathml:
+     - "<math><mrow intent='lexicographic-order($a1,$a2)'><mi arg='a1'>X</mi><mo>&lt;</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Lexicographic_order"
+     - "https://mathworld.wolfram.com/LexicographicOrder.html"
+     - "https://ncatlab.org/nlab/show/lexicographic+order"
+    alias:
+     - dictionary-order
+  
+  - concept: lie-derivative
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lie derivative of $a1
+    property: "indexed operator"
+    subject-area: "lie algebra"
+    mathml:
+     - "<math><msub intent='lie-derivative($a1)'><mi>ℒ</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LieDerivative.html"
+     - "https://en.wikipedia.org/wiki/Lie_derivative"
+     - "https://ncatlab.org/nlab/show/Lie+derivative"
+  
+  - concept: lie-superbracket
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: lie superbracket
-      property: fenced
-      area: "lie algebra"
-      mathml:
-       - "<math><mrow intent='lie-superbracket($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Lie_superalgebra"
-      alias:
-       - supercommutator
-    
-    - concept: like-charge
-      arity: 2
-      en: $1 like charge $2
-      property: infix
-      area: "physics"
-      mathml:
-       - "<math><mrow intent='like-charge($a1,$a2)'><mi arg='a1'>X</mi><mo>⇈</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://youtu.be/HZ7a9YkF204?t=4719"
-    
-    - concept: line-graph
-      arity: 1
-      en: line graph of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='line-graph($a1)'><mi>L</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LineGraph.html"
-       - "https://en.wikipedia.org/wiki/Line_graph"
-    
-    - concept: line-integral
-      arity: 1
-      en: line integral of $1
-      property: indexed
-      area: "analysis"
-      mathml:
-       - "<math><mrow intent='line-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LineIntegral.html"
-       - "https://en.wikipedia.org/wiki/Line_integral"
-       - "https://ncatlab.org/nlab/show/line+integral"
-      alias:
-       - curve-integral
-       - path-integral
-       - curvilinear-integral
-       - contour-integral
-    
-    - concept: linear-span
-      arity: 1
-      en: linear span of $1
-      property: function
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='linear-span($a1)'><mi>span</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LinearSpan.html"
-       - "https://en.wikipedia.org/wiki/Linear_span"
-      alias:
-       - span
-       - linear-hull
-    
-    - concept: link
-      arity: 1
-      en: link of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='link($a1)'><mi>Lk</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Link.html"
-    
-    - concept: gunter-link
-      arity: 1
-      en: gunter link of $1
-      property: unit
-      area: "units"
-      mathml:
-       - "<math><mrow intent='gunter-link($a1)'><mi>l.</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='gunter-link($a1)'><mi>li.</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='gunter-link($a1)'><mi>lnk.</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Link_(unit)"
-    
-    - concept: liouville-constant
-      arity: 0
+    property: fenced
+    subject-area: "lie algebra"
+    mathml:
+     - "<math><mrow intent='lie-superbracket($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Lie_superalgebra"
+    alias:
+     - supercommutator
+  
+  - concept: like-charge
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 like charge $a2
+    property: infix
+    subject-area: "physics"
+    mathml:
+     - "<math><mrow intent='like-charge($a1,$a2)'><mi arg='a1'>X</mi><mo>⇈</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://youtu.be/HZ7a9YkF204?t=4719"
+  
+  - concept: line-graph
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: line graph of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='line-graph($a1)'><mi>L</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LineGraph.html"
+     - "https://en.wikipedia.org/wiki/Line_graph"
+  
+  - concept: line-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: line integral of $a1
+    property: indexed
+    subject-area: "analysis"
+    mathml:
+     - "<math><mrow intent='line-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LineIntegral.html"
+     - "https://en.wikipedia.org/wiki/Line_integral"
+     - "https://ncatlab.org/nlab/show/line+integral"
+    alias:
+     - curve-integral
+     - path-integral
+     - curvilinear-integral
+     - contour-integral
+  
+  - concept: linear-span
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: linear span of $a1
+    property: function
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='linear-span($a1)'><mi>span</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LinearSpan.html"
+     - "https://en.wikipedia.org/wiki/Linear_span"
+    alias:
+     - span
+     - linear-hull
+  
+  - concept: link
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: link of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='link($a1)'><mi>Lk</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Link.html"
+  
+  - concept: gunter-link
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: gunter link of $a1
+    property: unit
+    subject-area: "units"
+    mathml:
+     - "<math><mrow intent='gunter-link($a1)'><mi>l.</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='gunter-link($a1)'><mi>li.</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='gunter-link($a1)'><mi>lnk.</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Link_(unit)"
+  
+  - concept: liouville-constant
+    arity: 0
+    arguments: []
+    speech:
       en: liouville constant
-      property: constant
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='liouville-constant'>L</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LiouvillesConstant.html"
-      alias:
-       - liouville-number
-    
-    - concept: liouville-function
-      arity: 1
-      en: liouville function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='liouville-function($a1)'><mi>λ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LiouvilleFunction.html"
-       - "https://en.wikipedia.org/wiki/Liouville_function"
-       - "https://dlmf.nist.gov/27.2#E13"
-    
-    - concept: localization
-      arity: 2
-      en: localization of $2 by $1
-      property: mixfix
-      area: "module theory"
-      mathml:
-       - "<math><mrow intent='localization($a1,$a2)'><msup><mi arg='a1'>S</mi><mn>−1</mn></msup><mi arg='a2'>R</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Localization.html"
-       - "https://en.wikipedia.org/wiki/Localization_(algebra)"
-       - "https://en.wikipedia.org/wiki/Localization_of_a_ring"
-       - "https://ncatlab.org/nlab/show/localization"
-       - "https://ncatlab.org/nlab/show/localization+of+a+module"
-    
-    - concept: logarithmic-integral
-      arity: 1
-      en: logarithmic integral of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='logarithmic-integral($a1)'><mi>li</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LogarithmicIntegral.html"
-       - "https://dlmf.nist.gov/6.2#i"
-       - "https://dlmf.nist.gov/6.2#E8"
-    
-    - concept: logarithmic-moment-of-function
-      arity: 2
-      en: $1<i>th</i> logarithmic moment of $2
-      property: "mixfix"
-      area: "mathematics"
-      mathml:
-       - "<math><mrow intent='logarithmic-moment-of-function($a1,$a2)'><mi>E</mi><mrow><mo>[</mo><msup><mi>ln</mi><mi arg='a1'>n</mi></msup><mrow><mo>(</mo><mi arg='a2'>X</mi><mo>)</mo></mrow><mo>]</mo></mrow></mrow></math>"
-      notation: "E [ msup ln $1 /msup ( $2 ) ]"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Moment_(mathematics)"
-      alias:
-       - logarithmic-moment
-    
-    - concept: logit
-      arity: 1
-      en: logit of $1
-      property: function
-      area: "statistics"
-      mathml:
-       - "<math><mrow intent='logit($a1)'><mi>logit</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Logit"
-    
-    - concept: lommel-function
-      arity: 2
-      en: $1 ,$2 lommel function
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='lommel-function($a1,$a2)'><msub><mi>s</mi><mrow><mo>(</mo><mi arg='a1'>u</mi><mi arg='a2'>v</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LommelFunction.html"
-       - "https://en.wikipedia.org/wiki/Lommel_function"
-       - "https://dlmf.nist.gov/11.9"
-       - "https://dlmf.nist.gov/11.9#E5"
-       - "https://dlmf.nist.gov/11.9#E3"
-    
-    - concept: long-division
-      arity: 1
-      en: long division of $1 by $2
-      property: mfrac
-      area: "arithmetic"
-      comments:
-       - "long division display layout"
-      urls: 
-       - "https://mathworld.wolfram.com/LongDivision.html"
-       - "https://en.wikipedia.org/wiki/Long_division"
-    
-    - concept: loop-space
-      arity: 1
-      en: loop space of $1
-      property: function
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='loop-space($a1)'><mi>Ω</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LoopSpace.html"
-       - "https://en.wikipedia.org/wiki/Loop_space"
-       - "https://ncatlab.org/nlab/show/loop+space"
-    
-    - concept: lower-closure-poset
-      arity: 1
-      en: lower closure poset of $1
-      property: prefix
-      area: "order theory"
-      mathml:
-       - "<math><mrow intent='lower-closure-poset($a1)'><mo>↓</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Upper_set#Upper_closure_and_lower_closure"
-    
-    - concept: lower-darboux-integral
-      arity: 1
-      en: lower darboux integral of $1
-      property: indexed
-      area: "real analysis"
-      mathml:
-       - "<math><mrow intent='lower-darboux-integral($a1)'><munder><munderover><mo>∫</mo><mi>a</mi><mi>b</mi></munderover><mo>_</mo></munder><mi arg='a1'>f</mi></mrow></math>"
-      notation: "munder ¯"
-      urls: 
-       - "https://mathworld.wolfram.com/DarbouxIntegral.html"
-       - "https://en.wikipedia.org/wiki/Darboux_integral"
-       - "https://www.encyclopediaofmath.org/index.php/Darboux_integral"
-    
-    - concept: lower-dini-derivative
-      arity: 1
-      en: lower dini derivative of $1
-      property: decorated function
-      area: "analysis"
-      mathml:
-       - "<math><mrow intent='lower-dini-derivative($a1)'><msub><msup><mi arg='a1'>f</mi><mo>′</mo></msup><mo>-</mo></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DiniDerivative.html"
-       - "https://en.wikipedia.org/wiki/Dini_derivative"
-       - "https://www.encyclopediaofmath.org/index.php/Dini_derivative"
-    
-    - concept: lower-shadow
-      arity: 1
-      en: lower shadow of $1
-      property: function
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='lower-shadow($a1)'><mi>𝜕</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      notationa: "msub 𝜕 -"
-      urls: 
-       - "http://qk206.user.srcf.net/notes/combinatorics.pdf"
-      alias:
-       - shadow
-    
-    - concept: lucas-number
-      arity: 1
-      en: lucas number of $1
-      property: "indexed symbol"
-      area: "integer sequences"
-      mathml:
-       - "<math><msub intent='lucas-number($a1)'><mi>L</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LucasNumber.html"
-       - "https://en.wikipedia.org/wiki/Lucas_number"
-       - "https://en.wikipedia.org/wiki/Lucas_prime"
-    
-    - concept: lucas-sequence
-      arity: 1
-      en: lucas sequence of $1
-      property: "indexed function"
-      area: "integer sequences"
-      mathml:
-       - "<math><msub intent='lucas-sequence($a1)'><mi>U</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='lucas-sequence($a1)'><mi>V</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LucasSequence.html"
-       - "https://en.wikipedia.org/wiki/Lucas_sequence"
-    
-    - concept: lyapunov-candidate-function
-      arity: 1
-      en: lyapunov candidate function of $1
-      property: function
-      area: "stability theory"
-      mathml:
-       - "<math><mrow intent='lyapunov-candidate-function($a1)'><mi>V</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LyapunovFunction.html"
-       - "https://en.wikipedia.org/wiki/Lyapunov_function"
-       - "https://www.encyclopediaofmath.org/index.php/Lyapunov_function"
-      alias:
-       - lyapunov-function
-    
-    - concept: macdonald-polynomial
-      arity: 1
-      en: macdonald polynomial of $1
-      property: function
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><mrow intent='macdonald-polynomial($a1)'><msub><mi>P</mi><mi>λ</mi></msub><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>;</mo><mi>t</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Macdonald_polynomials"
-       - "https://ncatlab.org/nlab/show/Macdonald+polynomial"
-    
-    - concept: mahler-measure
-      arity: 1
-      en: mahler measure of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='mahler-measure($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MahlerMeasure.html"
-       - "https://en.wikipedia.org/wiki/Mahler_measure"
-       - "https://www.encyclopediaofmath.org/index.php/Mahler_measure"
-    
-    - concept: mangoldt-function
-      arity: 1
-      en: mangoldt function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='mangoldt-function($a1)'><mi>Λ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MangoldtFunction.html"
-       - "https://dlmf.nist.gov/27.2#E14"
-       - "https://www.encyclopediaofmath.org/index.php/Mangoldt_function"
-      alias:
-       - von-mangoldt-function
-    
-    - concept: mapping-class-group
-      arity: 1
-      en: mapping class group of $1
-      property: function
-      area: "geometric topology"
-      mathml:
-       - "<math><mrow intent='mapping-class-group($a1)'><mi>MCG</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Mapping_class_group"
-       - "https://ncatlab.org/nlab/show/mapping+class+group"
-    
-    - concept: mapping-cone
-      arity: 1
-      en: mapping cone of $1
-      property: "indexed symbol"
-      area: "homotopy theory"
-      mathml:
-       - "<math><msub intent='mapping-cone($a1)'><mi>C</mi><mi arg='a1'>x</mi></msub></math>"
-      notationa: "mrow C $1"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Mapping_cone_(topology)"
-       - "https://en.wikipedia.org/wiki/Mapping_cone_(homological_algebra)"
-       - "https://ncatlab.org/nlab/show/mapping+cone"
-      alias:
-       - homotopy-cofiber
-    
-    - concept: matching-polynomial
-      arity: 1
-      en: matching polynomial of $1
-      property: "indexed function"
-      area: "graph theory"
-      mathml:
-       - "<math><msub intent='matching-polynomial($a1)'><mi>m</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='matching-polynomial($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='matching-polynomial($a1)'><mi>μ</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Matching_polynomial"
-    
-    - concept: mathieu-function-of-first-kind
-      arity: 1
-      en: mathieu function of first kind of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='mathieu-function-of-first-kind($a1)'><mi>ce</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='mathieu-function-of-first-kind($a1)'><mi>se</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MathieuFunction.html"
-       - "https://en.wikipedia.org/wiki/Mathieu_function"
-       - "https://dlmf.nist.gov/28#PT2"
-       - "https://dlmf.nist.gov/28#PT3"
-       - "https://dlmf.nist.gov/28.2#SS6.p1"
-       - "https://dlmf.nist.gov/28.26#i"
-       - "https://dlmf.nist.gov/28.26#i"
-       - "https://dlmf.nist.gov/28.26#i"
-       - "https://dlmf.nist.gov/28.26#i"
-       - "https://dlmf.nist.gov/28.12#SS2.p2"
-       - "https://dlmf.nist.gov/28.2#SS6.p1"
-       - "https://www.encyclopediaofmath.org/index.php/Mathieu_functions"
-      alias:
-       - angular-mathieu-function
-       - mathieu-function
-    
-    - concept: mathieu-function-of-second-kind
-      arity: 1
-      en: mathieu function of second kind of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='mathieu-function-of-second-kind($a1)'><mi>fe</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='mathieu-function-of-second-kind($a1)'><mi>ge</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MathieuFunction.html"
-       - "https://en.wikipedia.org/wiki/Mathieu_function"
-       - "https://dlmf.nist.gov/28#PT2"
-       - "https://dlmf.nist.gov/28#PT3"
-       - "https://dlmf.nist.gov/28.2#SS6.p1"
-       - "https://dlmf.nist.gov/28.26#i"
-       - "https://dlmf.nist.gov/28.26#i"
-       - "https://dlmf.nist.gov/28.26#i"
-       - "https://dlmf.nist.gov/28.26#i"
-       - "https://dlmf.nist.gov/28.12#SS2.p2"
-       - "https://dlmf.nist.gov/28.2#SS6.p1"
-       - "https://www.encyclopediaofmath.org/index.php/Mathieu_functions"
-      alias:
-       - angular-mathieu-function
-       - mathieu-function
-    
-    - concept: mathieu-group
-      arity: 1
-      en: mathieu group $1
-      property: "indexed symbol"
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='mathieu-group($a1)'><mi>M</mi><mn arg='a1'>11</mn></msub></math>"
-       - "<math><msub intent='mathieu-group($a1)'><mi>M</mi><mn arg='a1'>12</mn></msub></math>"
-       - "<math><msub intent='mathieu-group($a1)'><mi>M</mi><mn arg='a1'>22</mn></msub></math>"
-       - "<math><msub intent='mathieu-group($a1)'><mi>M</mi><mn arg='a1'>23</mn></msub></math>"
-       - "<math><msub intent='mathieu-group($a1)'><mi>M</mi><mn arg='a1'>24</mn></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MathieuGroups.html"
-       - "https://en.wikipedia.org/wiki/Multiply_transitive_group"
-       - "https://en.wikipedia.org/wiki/Mathieu_group"
-       - "https://en.wikipedia.org/wiki/Mathieu_group_M11"
-       - "https://en.wikipedia.org/wiki/Mathieu_group_M12"
-       - "https://en.wikipedia.org/wiki/Mathieu_group_M22"
-       - "https://en.wikipedia.org/wiki/Mathieu_group_M23"
-       - "https://en.wikipedia.org/wiki/Mathieu_group_M24"
-       - "https://ncatlab.org/nlab/show/Mathieu+group"
-       - "https://www.encyclopediaofmath.org/index.php/Mathieu_group"
-    
-    - concept: matrix
-      arity: 1
-      en: matrix $1
-      property: mtable, fenced
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='matrix($a1)'><mo>(</mo><mtable arg='a1'><mtr><mtd><mtext>...</mtext></mtd></mtr><mtr><mtd><mtext>...</mtext></mtd></mtr></mtable><mo>)</mo></mrow></math>"
-       - "<math><mrow intent='matrix($a1)'><mo>[</mo><mtable arg='a1'><mtr><mtd><mtext>...</mtext></mtd></mtr><mtr><mtd><mtext>...</mtext></mtd></mtr></mtable><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Matrix.html"
-       - "https://mathworld.wolfram.com/SquareBracket.html"
-       - "https://en.wikipedia.org/wiki/Matrix_(mathematics)"
-       - "https://en.wikipedia.org/wiki/List_of_matrices"
-       - "https://en.wikipedia.org/wiki/Skew-symmetric_matrix"
-       - "https://en.wikipedia.org/wiki/Prenex_normal_form"
-       - "https://en.wikipedia.org/wiki/Matrix_isolation"
-       - "https://ncatlab.org/nlab/show/matrix"
-       - "https://www.encyclopediaofmath.org/index.php/Matrix"
-    
-    - concept: matrix-ring
-      arity: 1
-      en: matrix ring of $1
-      property: function
-      area: "abstract algebra"
-      mathml:
-       - "<math><msub intent='matrix-ring($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Matrix_ring"
-       - "https://www.encyclopediaofmath.org/index.php/Matrix_ring"
-    
-    - concept: maximum-degree
-      arity: 1
-      en: maximum degree of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='maximum-degree($a1)'><mi>Δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MaximumDegree.html"
-       - "https://en.wikipedia.org/wiki/Degree_(graph_theory)"
-       - "https://en.wikipedia.org/wiki/Degree_sequence"
-    
-    - concept: mean-curvature
-      arity: 1
-      en: mean curvature of $1
-      property: function
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='mean-curvature($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MeanCurvature.html"
-       - "https://en.wikipedia.org/wiki/Mean_curvature"
-       - "https://www.encyclopediaofmath.org/index.php/Mean_curvature"
-    
-    - concept: mean-squared-error
-      arity: 1
-      en: mean squared error of $1
-      property: function
-      area: "statistics"
-      mathml:
-       - "<math><mrow intent='mean-squared-error($a1)'><mi>MSE</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Mean_squared_error"
-    
-    - concept: meixner-pollaczek-polynomial
-      arity: 1
-      en: meixner pollaczek polynomial of $1
-      property: "indexed function"
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><mrow intent='meixner-pollaczek-polynomial($a1)'><mi>P</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Meixner-PollaczekPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Meixner%E2%80%93Pollaczek_polynomials"
-       - "https://dlmf.nist.gov/18.19#P3.p1"
-    
-    - concept: mellin-transform
-      arity: 1
-      en: mellin transform of $1
-      property: operator
-      area: "integral transforms"
-      mathml:
-       - "<math><mrow intent='mellin-transform($a1)'><mi>ℳ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MellinTransform.html"
-       - "https://en.wikipedia.org/wiki/Mellin_transform"
-       - "https://dlmf.nist.gov/1.14#E32"
-       - "https://www.encyclopediaofmath.org/index.php/Mellin_transform"
-    
-    - concept: meridian-radius-of-curvature
-      arity: 1
-      en: meridian radius of curvature of $1
-      property: function
-      area: "geodesy"
-      mathml:
-       - "<math><mrow intent='meridian-radius-of-curvature($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Meridian_arc"
-       - "https://en.wikipedia.org/wiki/Meridian_arc"
-    
-    - concept: meridian-distance
-      arity: 1
-      en: meridian distance of $1
-      property: function
-      area: "geodesy"
-      mathml:
-       - "<math><mrow intent='meridian-distance($a1)'><mi>m</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Meridian.html"
-    
-    - concept: mersenne-number
-      arity: 1
-      en: mersenne number of $1
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='mersenne-number($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MersenneNumber.html"
-       - "https://www.encyclopediaofmath.org/index.php/Mersenne_number"
-    
-    - concept: mersenne-prime
-      arity: 1
-      en: mersenne prime of $1
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='mersenne-prime($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MersennePrime.html"
-       - "https://en.wikipedia.org/wiki/Mersenne_number"
-       - "https://en.wikipedia.org/wiki/Mersenne_prime"
-    
-    - concept: merten-function
-      arity: 1
-      en: merten function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='merten-function($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MertensFunction.html"
-       - "https://en.wikipedia.org/wiki/Mertens_function"
-    
-    - concept: meson
-      arity: 1
-      en: meson of $1
-      property: 
-      urls: 
-       - "https://en.wikipedia.org/wiki/Meson"
-       - "https://en.wikipedia.org/wiki/List_of_mesons"
-       - "https://ncatlab.org/nlab/show/meson"
-    
-    - concept: metaplectic-group
-      arity: 1
+    property: constant
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='liouville-constant'>L</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LiouvillesConstant.html"
+    alias:
+     - liouville-number
+  
+  - concept: liouville-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: liouville function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='liouville-function($a1)'><mi>λ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LiouvilleFunction.html"
+     - "https://en.wikipedia.org/wiki/Liouville_function"
+     - "https://dlmf.nist.gov/27.2#E13"
+  
+  - concept: localization
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: localization of $a2 by $a1
+    property: mixfix
+    subject-area: "module theory"
+    mathml:
+     - "<math><mrow intent='localization($a1,$a2)'><msup><mi arg='a1'>S</mi><mn>−1</mn></msup><mi arg='a2'>R</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Localization.html"
+     - "https://en.wikipedia.org/wiki/Localization_(algebra)"
+     - "https://en.wikipedia.org/wiki/Localization_of_a_ring"
+     - "https://ncatlab.org/nlab/show/localization"
+     - "https://ncatlab.org/nlab/show/localization+of+a+module"
+  
+  - concept: logarithmic-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: logarithmic integral of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='logarithmic-integral($a1)'><mi>li</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LogarithmicIntegral.html"
+     - "https://dlmf.nist.gov/6.2#i"
+     - "https://dlmf.nist.gov/6.2#E8"
+  
+  - concept: logarithmic-moment-of-function
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1<i>th</i> logarithmic moment of $a2
+    property: "mixfix"
+    subject-area: "mathematics"
+    mathml:
+     - "<math><mrow intent='logarithmic-moment-of-function($a1,$a2)'><mi>E</mi><mrow><mo>[</mo><msup><mi>ln</mi><mi arg='a1'>n</mi></msup><mrow><mo>(</mo><mi arg='a2'>X</mi><mo>)</mo></mrow><mo>]</mo></mrow></mrow></math>"
+    notation: "E [ msup ln $a1 /msup ( $a2 ) ]"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Moment_(mathematics)"
+    alias:
+     - logarithmic-moment
+  
+  - concept: logit
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: logit of $a1
+    property: function
+    subject-area: "statistics"
+    mathml:
+     - "<math><mrow intent='logit($a1)'><mi>logit</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Logit"
+  
+  - concept: lommel-function
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 ,$a2 lommel function
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='lommel-function($a1,$a2)'><msub><mi>s</mi><mrow><mo>(</mo><mi arg='a1'>u</mi><mi arg='a2'>v</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LommelFunction.html"
+     - "https://en.wikipedia.org/wiki/Lommel_function"
+     - "https://dlmf.nist.gov/11.9"
+     - "https://dlmf.nist.gov/11.9#E5"
+     - "https://dlmf.nist.gov/11.9#E3"
+  
+  - concept: long-division
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: long division of $a1 by $a2
+    property: mfrac
+    subject-area: "arithmetic"
+    comments:
+     - "long division display layout"
+    urls: 
+     - "https://mathworld.wolfram.com/LongDivision.html"
+     - "https://en.wikipedia.org/wiki/Long_division"
+  
+  - concept: loop-space
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: loop space of $a1
+    property: function
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='loop-space($a1)'><mi>Ω</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LoopSpace.html"
+     - "https://en.wikipedia.org/wiki/Loop_space"
+     - "https://ncatlab.org/nlab/show/loop+space"
+  
+  - concept: lower-closure-poset
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lower closure poset of $a1
+    property: prefix
+    subject-area: "order theory"
+    mathml:
+     - "<math><mrow intent='lower-closure-poset($a1)'><mo>↓</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Upper_set#Upper_closure_and_lower_closure"
+  
+  - concept: lower-darboux-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lower darboux integral of $a1
+    property: indexed
+    subject-area: "real analysis"
+    mathml:
+     - "<math><mrow intent='lower-darboux-integral($a1)'><munder><munderover><mo>∫</mo><mi>a</mi><mi>b</mi></munderover><mo>_</mo></munder><mi arg='a1'>f</mi></mrow></math>"
+    notation: "munder ¯"
+    urls: 
+     - "https://mathworld.wolfram.com/DarbouxIntegral.html"
+     - "https://en.wikipedia.org/wiki/Darboux_integral"
+     - "https://www.encyclopediaofmath.org/index.php/Darboux_integral"
+  
+  - concept: lower-dini-derivative
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lower dini derivative of $a1
+    property: decorated function
+    subject-area: "analysis"
+    mathml:
+     - "<math><mrow intent='lower-dini-derivative($a1)'><msub><msup><mi arg='a1'>f</mi><mo>′</mo></msup><mo>-</mo></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DiniDerivative.html"
+     - "https://en.wikipedia.org/wiki/Dini_derivative"
+     - "https://www.encyclopediaofmath.org/index.php/Dini_derivative"
+  
+  - concept: lower-shadow
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lower shadow of $a1
+    property: function
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='lower-shadow($a1)'><mi>𝜕</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    notationa: "msub 𝜕 -"
+    urls: 
+     - "http://qk206.user.srcf.net/notes/combinatorics.pdf"
+    alias:
+     - shadow
+  
+  - concept: lucas-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lucas number of $a1
+    property: "indexed symbol"
+    subject-area: "integer sequences"
+    mathml:
+     - "<math><msub intent='lucas-number($a1)'><mi>L</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LucasNumber.html"
+     - "https://en.wikipedia.org/wiki/Lucas_number"
+     - "https://en.wikipedia.org/wiki/Lucas_prime"
+  
+  - concept: lucas-sequence
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lucas sequence of $a1
+    property: "indexed function"
+    subject-area: "integer sequences"
+    mathml:
+     - "<math><msub intent='lucas-sequence($a1)'><mi>U</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='lucas-sequence($a1)'><mi>V</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LucasSequence.html"
+     - "https://en.wikipedia.org/wiki/Lucas_sequence"
+  
+  - concept: lyapunov-candidate-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: lyapunov candidate function of $a1
+    property: function
+    subject-area: "stability theory"
+    mathml:
+     - "<math><mrow intent='lyapunov-candidate-function($a1)'><mi>V</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LyapunovFunction.html"
+     - "https://en.wikipedia.org/wiki/Lyapunov_function"
+     - "https://www.encyclopediaofmath.org/index.php/Lyapunov_function"
+    alias:
+     - lyapunov-function
+  
+  - concept: macdonald-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: macdonald polynomial of $a1
+    property: function
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><mrow intent='macdonald-polynomial($a1)'><msub><mi>P</mi><mi>λ</mi></msub><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>;</mo><mi>t</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Macdonald_polynomials"
+     - "https://ncatlab.org/nlab/show/Macdonald+polynomial"
+  
+  - concept: mahler-measure
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mahler measure of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='mahler-measure($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MahlerMeasure.html"
+     - "https://en.wikipedia.org/wiki/Mahler_measure"
+     - "https://www.encyclopediaofmath.org/index.php/Mahler_measure"
+  
+  - concept: mangoldt-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mangoldt function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='mangoldt-function($a1)'><mi>Λ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MangoldtFunction.html"
+     - "https://dlmf.nist.gov/27.2#E14"
+     - "https://www.encyclopediaofmath.org/index.php/Mangoldt_function"
+    alias:
+     - von-mangoldt-function
+  
+  - concept: mapping-class-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mapping class group of $a1
+    property: function
+    subject-area: "geometric topology"
+    mathml:
+     - "<math><mrow intent='mapping-class-group($a1)'><mi>MCG</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Mapping_class_group"
+     - "https://ncatlab.org/nlab/show/mapping+class+group"
+  
+  - concept: mapping-cone
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mapping cone of $a1
+    property: "indexed symbol"
+    subject-area: "homotopy theory"
+    mathml:
+     - "<math><msub intent='mapping-cone($a1)'><mi>C</mi><mi arg='a1'>x</mi></msub></math>"
+    notationa: "mrow C $a1"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Mapping_cone_(topology)"
+     - "https://en.wikipedia.org/wiki/Mapping_cone_(homological_algebra)"
+     - "https://ncatlab.org/nlab/show/mapping+cone"
+    alias:
+     - homotopy-cofiber
+  
+  - concept: matching-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: matching polynomial of $a1
+    property: "indexed function"
+    subject-area: "graph theory"
+    mathml:
+     - "<math><msub intent='matching-polynomial($a1)'><mi>m</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='matching-polynomial($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='matching-polynomial($a1)'><mi>μ</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Matching_polynomial"
+  
+  - concept: mathieu-function-of-first-kind
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mathieu function of first kind of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='mathieu-function-of-first-kind($a1)'><mi>ce</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='mathieu-function-of-first-kind($a1)'><mi>se</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MathieuFunction.html"
+     - "https://en.wikipedia.org/wiki/Mathieu_function"
+     - "https://dlmf.nist.gov/28#PT2"
+     - "https://dlmf.nist.gov/28#PT3"
+     - "https://dlmf.nist.gov/28.2#SS6.p1"
+     - "https://dlmf.nist.gov/28.26#i"
+     - "https://dlmf.nist.gov/28.26#i"
+     - "https://dlmf.nist.gov/28.26#i"
+     - "https://dlmf.nist.gov/28.26#i"
+     - "https://dlmf.nist.gov/28.12#SS2.p2"
+     - "https://dlmf.nist.gov/28.2#SS6.p1"
+     - "https://www.encyclopediaofmath.org/index.php/Mathieu_functions"
+    alias:
+     - angular-mathieu-function
+     - mathieu-function
+  
+  - concept: mathieu-function-of-second-kind
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mathieu function of second kind of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='mathieu-function-of-second-kind($a1)'><mi>fe</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='mathieu-function-of-second-kind($a1)'><mi>ge</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MathieuFunction.html"
+     - "https://en.wikipedia.org/wiki/Mathieu_function"
+     - "https://dlmf.nist.gov/28#PT2"
+     - "https://dlmf.nist.gov/28#PT3"
+     - "https://dlmf.nist.gov/28.2#SS6.p1"
+     - "https://dlmf.nist.gov/28.26#i"
+     - "https://dlmf.nist.gov/28.26#i"
+     - "https://dlmf.nist.gov/28.26#i"
+     - "https://dlmf.nist.gov/28.26#i"
+     - "https://dlmf.nist.gov/28.12#SS2.p2"
+     - "https://dlmf.nist.gov/28.2#SS6.p1"
+     - "https://www.encyclopediaofmath.org/index.php/Mathieu_functions"
+    alias:
+     - angular-mathieu-function
+     - mathieu-function
+  
+  - concept: mathieu-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mathieu group $a1
+    property: "indexed symbol"
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='mathieu-group($a1)'><mi>M</mi><mn arg='a1'>11</mn></msub></math>"
+     - "<math><msub intent='mathieu-group($a1)'><mi>M</mi><mn arg='a1'>12</mn></msub></math>"
+     - "<math><msub intent='mathieu-group($a1)'><mi>M</mi><mn arg='a1'>22</mn></msub></math>"
+     - "<math><msub intent='mathieu-group($a1)'><mi>M</mi><mn arg='a1'>23</mn></msub></math>"
+     - "<math><msub intent='mathieu-group($a1)'><mi>M</mi><mn arg='a1'>24</mn></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MathieuGroups.html"
+     - "https://en.wikipedia.org/wiki/Multiply_transitive_group"
+     - "https://en.wikipedia.org/wiki/Mathieu_group"
+     - "https://en.wikipedia.org/wiki/Mathieu_group_M11"
+     - "https://en.wikipedia.org/wiki/Mathieu_group_M12"
+     - "https://en.wikipedia.org/wiki/Mathieu_group_M22"
+     - "https://en.wikipedia.org/wiki/Mathieu_group_M23"
+     - "https://en.wikipedia.org/wiki/Mathieu_group_M24"
+     - "https://ncatlab.org/nlab/show/Mathieu+group"
+     - "https://www.encyclopediaofmath.org/index.php/Mathieu_group"
+  
+  - concept: matrix
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: matrix $a1
+    property: mtable, fenced
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='matrix($a1)'><mo>(</mo><mtable arg='a1'><mtr><mtd><mtext>...</mtext></mtd></mtr><mtr><mtd><mtext>...</mtext></mtd></mtr></mtable><mo>)</mo></mrow></math>"
+     - "<math><mrow intent='matrix($a1)'><mo>[</mo><mtable arg='a1'><mtr><mtd><mtext>...</mtext></mtd></mtr><mtr><mtd><mtext>...</mtext></mtd></mtr></mtable><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Matrix.html"
+     - "https://mathworld.wolfram.com/SquareBracket.html"
+     - "https://en.wikipedia.org/wiki/Matrix_(mathematics)"
+     - "https://en.wikipedia.org/wiki/List_of_matrices"
+     - "https://en.wikipedia.org/wiki/Skew-symmetric_matrix"
+     - "https://en.wikipedia.org/wiki/Prenex_normal_form"
+     - "https://en.wikipedia.org/wiki/Matrix_isolation"
+     - "https://ncatlab.org/nlab/show/matrix"
+     - "https://www.encyclopediaofmath.org/index.php/Matrix"
+  
+  - concept: matrix-ring
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: matrix ring of $a1
+    property: function
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><msub intent='matrix-ring($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Matrix_ring"
+     - "https://www.encyclopediaofmath.org/index.php/Matrix_ring"
+  
+  - concept: maximum-degree
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: maximum degree of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='maximum-degree($a1)'><mi>Δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MaximumDegree.html"
+     - "https://en.wikipedia.org/wiki/Degree_(graph_theory)"
+     - "https://en.wikipedia.org/wiki/Degree_sequence"
+  
+  - concept: mean-curvature
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mean curvature of $a1
+    property: function
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='mean-curvature($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MeanCurvature.html"
+     - "https://en.wikipedia.org/wiki/Mean_curvature"
+     - "https://www.encyclopediaofmath.org/index.php/Mean_curvature"
+  
+  - concept: mean-squared-error
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mean squared error of $a1
+    property: function
+    subject-area: "statistics"
+    mathml:
+     - "<math><mrow intent='mean-squared-error($a1)'><mi>MSE</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Mean_squared_error"
+  
+  - concept: meixner-pollaczek-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: meixner pollaczek polynomial of $a1
+    property: "indexed function"
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><mrow intent='meixner-pollaczek-polynomial($a1)'><mi>P</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Meixner-PollaczekPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Meixner%E2%80%93Pollaczek_polynomials"
+     - "https://dlmf.nist.gov/18.19#P3.p1"
+  
+  - concept: mellin-transform
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mellin transform of $a1
+    property: operator
+    subject-area: "integral transforms"
+    mathml:
+     - "<math><mrow intent='mellin-transform($a1)'><mi>ℳ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MellinTransform.html"
+     - "https://en.wikipedia.org/wiki/Mellin_transform"
+     - "https://dlmf.nist.gov/1.14#E32"
+     - "https://www.encyclopediaofmath.org/index.php/Mellin_transform"
+  
+  - concept: meridian-radius-of-curvature
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: meridian radius of curvature of $a1
+    property: function
+    subject-area: "geodesy"
+    mathml:
+     - "<math><mrow intent='meridian-radius-of-curvature($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Meridian_arc"
+     - "https://en.wikipedia.org/wiki/Meridian_arc"
+  
+  - concept: meridian-distance
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: meridian distance of $a1
+    property: function
+    subject-area: "geodesy"
+    mathml:
+     - "<math><mrow intent='meridian-distance($a1)'><mi>m</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Meridian.html"
+  
+  - concept: mersenne-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mersenne number of $a1
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='mersenne-number($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MersenneNumber.html"
+     - "https://www.encyclopediaofmath.org/index.php/Mersenne_number"
+  
+  - concept: mersenne-prime
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mersenne prime of $a1
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='mersenne-prime($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MersennePrime.html"
+     - "https://en.wikipedia.org/wiki/Mersenne_number"
+     - "https://en.wikipedia.org/wiki/Mersenne_prime"
+  
+  - concept: merten-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: merten function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='merten-function($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MertensFunction.html"
+     - "https://en.wikipedia.org/wiki/Mertens_function"
+  
+  - concept: meson
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: meson of $a1
+    property: 
+    urls: 
+     - "https://en.wikipedia.org/wiki/Meson"
+     - "https://en.wikipedia.org/wiki/List_of_mesons"
+     - "https://ncatlab.org/nlab/show/meson"
+  
+  - concept: metaplectic-group
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: metaplectic group
-      property: symbol
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='metaplectic-group($a1)'><msub><mi>Mp</mi><mrow><mn>2</mn><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi arg='a1'>R</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MetaplecticGroup.html"
-       - "https://en.wikipedia.org/wiki/Metaplectic_group"
-       - "https://ncatlab.org/nlab/show/metaplectic+group"
-    
-    - concept: mills-constant
-      arity: 0
+    property: symbol
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='metaplectic-group($a1)'><msub><mi>Mp</mi><mrow><mn>2</mn><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi arg='a1'>R</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MetaplecticGroup.html"
+     - "https://en.wikipedia.org/wiki/Metaplectic_group"
+     - "https://ncatlab.org/nlab/show/metaplectic+group"
+  
+  - concept: mills-constant
+    arity: 0
+    arguments: []
+    speech:
       en: mills constant
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='mills-constant'>A</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MillsConstant.html"
-       - "https://en.wikipedia.org/wiki/Mills%27_constant"
-       - "https://en.wikipedia.org/wiki/Mills_prime"
-    
-    - concept: mills-ratio
-      arity: 1
-      en: mills ratio of $1
-      property: function
-      area: "probability theory"
-      mathml:
-       - "<math><mrow intent='mills-ratio($a1)'><mi>m</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='mills-ratio($a1)'><mi>M</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MillsRatio.html"
-       - "https://en.wikipedia.org/wiki/Mills_ratio"
-       - "https://dlmf.nist.gov/7.8#E1"
-    
-    - concept: minimum-degree
-      arity: 1
-      en: minimum degree of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='minimum-degree($a1)'><mi>δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MinimumDegree.html"
-       - "https://en.wikipedia.org/wiki/Degree_(graph_theory)"
-       - "https://en.wikipedia.org/wiki/Degree_sequence"
-    
-    - concept: minkowski-difference
-      arity: 2
-      en: $1 minkowski difference $2
-      property: infix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='minkowski-difference($a1,$a2)'><mi arg='a1'>X</mi><mo>-</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Minkowski_addition"
-      alias:
-       - geometric-difference
-    
-    - concept: minkowski-sum
-      arity: 2
-      en: $1 minkowski sum $2
-      property: infix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='minkowski-sum($a1,$a2)'><mi arg='a1'>X</mi><mo>+</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MinkowskiSum.html"
-       - "https://en.wikipedia.org/wiki/Minkowski_addition"
-      alias:
-       - dilation
-    
-    - concept: mittag-leffler-function
-      arity: 1
-      en: mittag leffler function of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='mittag-leffler-function($a1)'><mi>E</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Mittag-LefflerFunction.html"
-       - "https://en.wikipedia.org/wiki/Mittag-Leffler_function"
-       - "https://dlmf.nist.gov/10.46#E3"
-       - "https://www.encyclopediaofmath.org/index.php/Mittag-Leffler_function"
-    
-    - concept: mobius-function
-      arity: 1
-      en: mobius function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='mobius-function($a1)'><mi>μ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MoebiusFunction.html"
-       - "https://en.wikipedia.org/wiki/%CE%9C(n)"
-       - "https://en.wikipedia.org/wiki/M%C3%B6bius_function"
-       - "https://dlmf.nist.gov/27.2#E12"
-       - "https://www.encyclopediaofmath.org/index.php/Möbius_function"
-    
-    - concept: modified-bessel-function-of-first-kind
-      arity: 1
-      en: modified bessel function of first kind of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='modified-bessel-function-of-first-kind($a1)'><mi>I</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://dlmf.nist.gov/10#PT3"
-       - "https://dlmf.nist.gov/10.25#E2"
-       - "https://dlmf.nist.gov/10.25#E3"
-    
-    - concept: modified-bessel-function-of-second-kind
-      arity: 1
-      en: modified bessel function of second kind of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='modified-bessel-function-of-second-kind($a1)'><mi>K</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://dlmf.nist.gov/10#PT3"
-       - "https://dlmf.nist.gov/10.25#E2"
-       - "https://dlmf.nist.gov/10.25#E3"
-    
-    - concept: modified-mathieu-function
-      arity: 1
-      en: modified mathieu function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='modified-mathieu-function($a1)'><mi>Ce</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='modified-mathieu-function($a1)'><mi>Se</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='modified-mathieu-function($a1)'><mi>Me</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='modified-mathieu-function($a1)'><mi>Fe</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='modified-mathieu-function($a1)'><mi>Ge</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://dlmf.nist.gov/28#PT4"
-       - "https://dlmf.nist.gov/28.20#E3"
-       - "https://dlmf.nist.gov/28.20#E6"
-       - "https://dlmf.nist.gov/28.20#E7"
-       - "https://dlmf.nist.gov/28.20#E17"
-       - "https://dlmf.nist.gov/28.20#E18"
-       - "https://dlmf.nist.gov/28.20#E19"
-       - "https://dlmf.nist.gov/28.20#E20"
-       - "https://dlmf.nist.gov/28.20#SS3.p1"
-       - "https://dlmf.nist.gov/28.20#E5"
-       - "https://dlmf.nist.gov/28.20#E4"
-    
-    - concept: modified-spherical-bessel-function
-      arity: 1
-      en: modified spherical bessel function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='modified-spherical-bessel-function($a1)'><msubsup><mi>i</mi><mi>n</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mrow><mo>(</mo><mi arg='a1'>z</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='modified-spherical-bessel-function($a1)'><msubsup><mi>i</mi><mi>n</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup><mrow><mo>(</mo><mi arg='a1'>z</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='modified-spherical-bessel-function($a1)'><msub><mi>k</mi><mi>n</mi></msub><mrow><mo>(</mo><mi arg='a1'>z</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ModifiedSphericalBesselFunction.html"
-       - "https://dlmf.nist.gov/10.47#E7"
-       - "https://dlmf.nist.gov/10.47#E8"
-       - "https://dlmf.nist.gov/10.47#E9"
-    
-    - concept: modified-struve-function
-      arity: 1
-      en: modified struve function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='modified-struve-function($a1)'><mi>L</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ModifiedStruveFunction.html"
-       - "https://dlmf.nist.gov/11.2#E2"
-       - "https://dlmf.nist.gov/11.2#E6"
-    
-    - concept: modular-discriminant
-      arity: 1
-      en: modular discriminant of $1
-      property: operator
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='modular-discriminant($a1)'><mi>Δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ModularDiscriminant.html"
-       - "https://en.wikipedia.org/wiki/Modular_form#The_modular_discriminant"
-    
-    - concept: modulo
-      arity: 2
-      en: $1 modulo $2
-      property: infix, mixfix
-      area: "modular arithmetic"
-      mathml:
-       - "<math><mrow intent='modulo($a1,$a2)'><mi arg='a1'>x</mi><mrow><mspace width='1em'/><mo>(</mo><mi>mod</mi><mi arg='a2'>p</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Modulo.html"
-       - "https://en.wikipedia.org/wiki/Modulo_(jargon)"
-       - "https://en.wikipedia.org/wiki/Modulo_operation"
-       - "https://dlmf.nist.gov/front/introduction#Sx4.p2.t1.r10"
-      alias:
-       - mod
-    
-    - concept: moebius-function
-      arity: 1
-      en: moebius function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='moebius-function($a1)'><mi>μ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://www.encyclopediaofmath.org/index.php/Moebius_function"
-       - "https://en.wikipedia.org/wiki/M%C3%B6bius_function"
-    
-    - concept: moment-of-function
-      arity: 
-      en: $1<i>th</i> moment 
-      property: "msub, mixfix"
-      area: "mathematics"
-      mathml:
-       - "<math><mrow intent='moment-of-function($a1)'><msub><mi>μ</mi><mi arg='a1'>n</mi></msub></mrow></math>"
-      notationa: "mrow E [ msup $1 $2 ]"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Moment_(mathematics)"
-      alias:
-       - moment
-    
-    - concept: moment
-      arity: 0
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='mills-constant'>A</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MillsConstant.html"
+     - "https://en.wikipedia.org/wiki/Mills%27_constant"
+     - "https://en.wikipedia.org/wiki/Mills_prime"
+  
+  - concept: mills-ratio
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mills ratio of $a1
+    property: function
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mrow intent='mills-ratio($a1)'><mi>m</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='mills-ratio($a1)'><mi>M</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MillsRatio.html"
+     - "https://en.wikipedia.org/wiki/Mills_ratio"
+     - "https://dlmf.nist.gov/7.8#E1"
+  
+  - concept: minimum-degree
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: minimum degree of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='minimum-degree($a1)'><mi>δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MinimumDegree.html"
+     - "https://en.wikipedia.org/wiki/Degree_(graph_theory)"
+     - "https://en.wikipedia.org/wiki/Degree_sequence"
+  
+  - concept: minkowski-difference
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 minkowski difference $a2
+    property: infix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='minkowski-difference($a1,$a2)'><mi arg='a1'>X</mi><mo>-</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Minkowski_addition"
+    alias:
+     - geometric-difference
+  
+  - concept: minkowski-sum
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 minkowski sum $a2
+    property: infix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='minkowski-sum($a1,$a2)'><mi arg='a1'>X</mi><mo>+</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MinkowskiSum.html"
+     - "https://en.wikipedia.org/wiki/Minkowski_addition"
+    alias:
+     - dilation
+  
+  - concept: mittag-leffler-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mittag leffler function of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='mittag-leffler-function($a1)'><mi>E</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Mittag-LefflerFunction.html"
+     - "https://en.wikipedia.org/wiki/Mittag-Leffler_function"
+     - "https://dlmf.nist.gov/10.46#E3"
+     - "https://www.encyclopediaofmath.org/index.php/Mittag-Leffler_function"
+  
+  - concept: mobius-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mobius function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='mobius-function($a1)'><mi>μ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MoebiusFunction.html"
+     - "https://en.wikipedia.org/wiki/%CE%9C(n)"
+     - "https://en.wikipedia.org/wiki/M%C3%B6bius_function"
+     - "https://dlmf.nist.gov/27.2#E12"
+     - "https://www.encyclopediaofmath.org/index.php/Möbius_function"
+  
+  - concept: modified-bessel-function-of-first-kind
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: modified bessel function of first kind of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='modified-bessel-function-of-first-kind($a1)'><mi>I</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://dlmf.nist.gov/10#PT3"
+     - "https://dlmf.nist.gov/10.25#E2"
+     - "https://dlmf.nist.gov/10.25#E3"
+  
+  - concept: modified-bessel-function-of-second-kind
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: modified bessel function of second kind of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='modified-bessel-function-of-second-kind($a1)'><mi>K</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://dlmf.nist.gov/10#PT3"
+     - "https://dlmf.nist.gov/10.25#E2"
+     - "https://dlmf.nist.gov/10.25#E3"
+  
+  - concept: modified-mathieu-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: modified mathieu function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='modified-mathieu-function($a1)'><mi>Ce</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='modified-mathieu-function($a1)'><mi>Se</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='modified-mathieu-function($a1)'><mi>Me</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='modified-mathieu-function($a1)'><mi>Fe</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='modified-mathieu-function($a1)'><mi>Ge</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://dlmf.nist.gov/28#PT4"
+     - "https://dlmf.nist.gov/28.20#E3"
+     - "https://dlmf.nist.gov/28.20#E6"
+     - "https://dlmf.nist.gov/28.20#E7"
+     - "https://dlmf.nist.gov/28.20#E17"
+     - "https://dlmf.nist.gov/28.20#E18"
+     - "https://dlmf.nist.gov/28.20#E19"
+     - "https://dlmf.nist.gov/28.20#E20"
+     - "https://dlmf.nist.gov/28.20#SS3.p1"
+     - "https://dlmf.nist.gov/28.20#E5"
+     - "https://dlmf.nist.gov/28.20#E4"
+  
+  - concept: modified-spherical-bessel-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: modified spherical bessel function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='modified-spherical-bessel-function($a1)'><msubsup><mi>i</mi><mi>n</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mrow><mo>(</mo><mi arg='a1'>z</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='modified-spherical-bessel-function($a1)'><msubsup><mi>i</mi><mi>n</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup><mrow><mo>(</mo><mi arg='a1'>z</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='modified-spherical-bessel-function($a1)'><msub><mi>k</mi><mi>n</mi></msub><mrow><mo>(</mo><mi arg='a1'>z</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ModifiedSphericalBesselFunction.html"
+     - "https://dlmf.nist.gov/10.47#E7"
+     - "https://dlmf.nist.gov/10.47#E8"
+     - "https://dlmf.nist.gov/10.47#E9"
+  
+  - concept: modified-struve-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: modified struve function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='modified-struve-function($a1)'><mi>L</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ModifiedStruveFunction.html"
+     - "https://dlmf.nist.gov/11.2#E2"
+     - "https://dlmf.nist.gov/11.2#E6"
+  
+  - concept: modular-discriminant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: modular discriminant of $a1
+    property: operator
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='modular-discriminant($a1)'><mi>Δ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ModularDiscriminant.html"
+     - "https://en.wikipedia.org/wiki/Modular_form#The_modular_discriminant"
+  
+  - concept: modulo
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 modulo $a2
+    property: infix, mixfix
+    subject-area: "modular arithmetic"
+    mathml:
+     - "<math><mrow intent='modulo($a1,$a2)'><mi arg='a1'>x</mi><mrow><mspace width='1em'/><mo>(</mo><mi>mod</mi><mi arg='a2'>p</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Modulo.html"
+     - "https://en.wikipedia.org/wiki/Modulo_(jargon)"
+     - "https://en.wikipedia.org/wiki/Modulo_operation"
+     - "https://dlmf.nist.gov/front/introduction#Sx4.p2.t1.r10"
+    alias:
+     - mod
+  
+  - concept: moebius-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: moebius function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='moebius-function($a1)'><mi>μ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://www.encyclopediaofmath.org/index.php/Moebius_function"
+     - "https://en.wikipedia.org/wiki/M%C3%B6bius_function"
+  
+  - concept: moment-of-function
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1<i>th</i> moment 
+    property: "msub, mixfix"
+    subject-area: "mathematics"
+    mathml:
+     - "<math><mrow intent='moment-of-function($a1)'><msub><mi>μ</mi><mi arg='a1'>n</mi></msub></mrow></math>"
+    notationa: "mrow E [ msup $a1 $a2 ]"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Moment_(mathematics)"
+    alias:
+     - moment
+  
+  - concept: moment
+    arity: 0
+    arguments: []
+    speech:
       en: moment
-      property: symbol
-      area: "mechanics"
-      mathml:
-       - "<math><mi intent='moment'>M</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Moment.html"
-       - "https://en.wikipedia.org/wiki/Moment_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Torque"
-       - "https://ncatlab.org/nlab/show/moment"
-       - "https://www.encyclopediaofmath.org/index.php/Moment"
-    
-    - concept: moment-of-inertia
-      arity: 0
+    property: symbol
+    subject-area: "mechanics"
+    mathml:
+     - "<math><mi intent='moment'>M</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Moment.html"
+     - "https://en.wikipedia.org/wiki/Moment_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Torque"
+     - "https://ncatlab.org/nlab/show/moment"
+     - "https://www.encyclopediaofmath.org/index.php/Moment"
+  
+  - concept: moment-of-inertia
+    arity: 0
+    arguments: []
+    speech:
       en: moment of inertia
-      property: symbol
-      area: "physics"
-      mathml:
-       - "<math><mi intent='moment-of-inertia'>I</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MomentofInertia.html"
-       - "https://en.wikipedia.org/wiki/Moment_of_inertia"
-       - "https://ncatlab.org/nlab/show/moment+of+inertia"
-      alias:
-       - mass-moment-of-inertia
-       - angular-mass
-       - rotational-inertia
-    
-    - concept: momentum
-      arity: 0
+    property: symbol
+    subject-area: "physics"
+    mathml:
+     - "<math><mi intent='moment-of-inertia'>I</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MomentofInertia.html"
+     - "https://en.wikipedia.org/wiki/Moment_of_inertia"
+     - "https://ncatlab.org/nlab/show/moment+of+inertia"
+    alias:
+     - mass-moment-of-inertia
+     - angular-mass
+     - rotational-inertia
+  
+  - concept: momentum
+    arity: 0
+    arguments: []
+    speech:
       en: momentum
-      property: symbol
-      area: "mechanics"
-      mathml:
-       - "<math><mi intent='momentum'>p</mi></math>"
-       - "<math><mi intent='momentum'>mip</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Momentum"
-       - "https://ncatlab.org/nlab/show/momentum"
-      alias:
-       - linear-momentum
-       - translational-momentum
-    
-    - concept: monster-group
-      arity: 0
+    property: symbol
+    subject-area: "mechanics"
+    mathml:
+     - "<math><mi intent='momentum'>p</mi></math>"
+     - "<math><mi intent='momentum'>mip</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Momentum"
+     - "https://ncatlab.org/nlab/show/momentum"
+    alias:
+     - linear-momentum
+     - translational-momentum
+  
+  - concept: monster-group
+    arity: 0
+    arguments: []
+    speech:
       en: monster group
-      property: symbol
-      area: "group theory"
-      mathml:
-       - "<math><mi intent='monster-group'>M</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MonsterGroup.html"
-       - "https://en.wikipedia.org/wiki/Monster_group"
-       - "https://ncatlab.org/nlab/show/Monster+group"
-      alias:
-       - friendly-giant
-    
-    - concept: moore-penrose-inverse
-      arity: 1
-      en: moore penrose inverse of $1
-      property: msup
-      area: "linear algebra"
-      mathml:
-       - "<math><msup intent='moore-penrose-inverse($a1)'><mi arg='a1'>X</mi><mo>+</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse"
-      alias:
-       - moore-penrose-pseudoinverse
-    
-    - concept: moore-smith-sequence
-      arity: 1
-      en: moore smith sequence of $1
-      property: fenced
-      area: "topology"
-      mathml:
-       - "<math><msub intent='moore-smith-sequence($a1)'><mrow><mo>(</mo><msub><mi arg='a1'>x</mi><mi>a</mi></msub><mo>)</mo></mrow><mrow><mi>a</mi><mo>∈</mo><mi>A</mi></mrow></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Moore%E2%80%93Smith_limit"
-       - "https://en.wikipedia.org/wiki/Net_(mathematics)"
-      alias:
-       - net
-    
-    - concept: motzkin-number
-      arity: 1
-      en: motzkin number of $1
-      property: "indexed symbol"
-      area: "combinatorial analysis"
-      mathml:
-       - "<math><msub intent='motzkin-number($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><mrow intent='motzkin-number($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MotzkinNumber.html"
-       - "https://en.wikipedia.org/wiki/Motzkin_number"
-       - "https://en.wikipedia.org/wiki/Motzkin_prime"
-       - "https://dlmf.nist.gov/26.6#E2"
-    
-    - concept: multiple-integral
-      arity: 1
-      en: multiple integral of $1
-      property: indexed
-      area: "multivariable calculus"
-      mathml:
-       - "<math><mrow intent='multiple-integral($a1)'><mrow><mo>∫</mo><mo>⋯</mo><mo>∫</mo></mrow><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MultipleIntegral.html"
-       - "https://en.wikipedia.org/wiki/%E2%88%AB%E2%88%ABf(x,y)dxdy"
-       - "https://en.wikipedia.org/wiki/Multiple_integral"
-       - "https://www.encyclopediaofmath.org/index.php/Multiple_integral"
-    
-    - concept: multiplicative-inverse
-      arity: 1
-      en: multiplicative inverse of $1
-      property: msup, mixfix
-      area: "abstract algebra"
-      mathml:
-       - "<math><msup intent='multiplicative-inverse($a1)'><mi arg='a1'>x</mi><mn>-1</mn></msup></math>"
-       - "<math><mrow intent='multiplicative-inverse($a1)'><mn>1</mn><mo>/</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Inverse.html"
-       - "https://en.wikipedia.org/wiki/Inverse_function"
-       - "https://en.wikipedia.org/wiki/Inverse_functions_and_differentiation"
-       - "https://ncatlab.org/nlab/show/inverse"
-       - "https://mathworld.wolfram.com/MultiplicativeInverse.html"
-       - "https://en.wikipedia.org/wiki/Multiplicative_inverse"
-      alias:
-       - inverse
-    
-    - concept: multiplicative-order
-      arity: 1
-      en: multiplicative order of $1
-      property: "indexed function"
-      area: "modular arithmetic"
-      mathml:
-       - "<math><msub intent='multiplicative-order($a1)'><mi>O</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='multiplicative-order($a1)'><mi>ord</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MultiplicativeOrder.html"
-       - "https://en.wikipedia.org/wiki/Multiplicative_order"
-    
-    - concept: multiplier-algebra
-      arity: 1
-      en: multiplier algebra of $1
-      property: function
-      area: "functional analysis"
-      mathml:
-       - "<math><mrow intent='multiplier-algebra($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>A</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MultiplierAlgebra.html"
-       - "https://en.wikipedia.org/wiki/Multiplier_algebra"
-       - "https://ncatlab.org/nlab/show/multiplier+algebra"
-    
-    - concept: multichoose
-      arity: 2
+    property: symbol
+    subject-area: "group theory"
+    mathml:
+     - "<math><mi intent='monster-group'>M</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MonsterGroup.html"
+     - "https://en.wikipedia.org/wiki/Monster_group"
+     - "https://ncatlab.org/nlab/show/Monster+group"
+    alias:
+     - friendly-giant
+  
+  - concept: moore-penrose-inverse
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: moore penrose inverse of $a1
+    property: msup
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><msup intent='moore-penrose-inverse($a1)'><mi arg='a1'>X</mi><mo>+</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse"
+    alias:
+     - moore-penrose-pseudoinverse
+  
+  - concept: moore-smith-sequence
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: moore smith sequence of $a1
+    property: fenced
+    subject-area: "topology"
+    mathml:
+     - "<math><msub intent='moore-smith-sequence($a1)'><mrow><mo>(</mo><msub><mi arg='a1'>x</mi><mi>a</mi></msub><mo>)</mo></mrow><mrow><mi>a</mi><mo>∈</mo><mi>A</mi></mrow></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Moore%E2%80%93Smith_limit"
+     - "https://en.wikipedia.org/wiki/Net_(mathematics)"
+    alias:
+     - net
+  
+  - concept: motzkin-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: motzkin number of $a1
+    property: "indexed symbol"
+    subject-area: "combinatorial analysis"
+    mathml:
+     - "<math><msub intent='motzkin-number($a1)'><mi>M</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><mrow intent='motzkin-number($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MotzkinNumber.html"
+     - "https://en.wikipedia.org/wiki/Motzkin_number"
+     - "https://en.wikipedia.org/wiki/Motzkin_prime"
+     - "https://dlmf.nist.gov/26.6#E2"
+  
+  - concept: multiple-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: multiple integral of $a1
+    property: indexed
+    subject-area: "multivariable calculus"
+    mathml:
+     - "<math><mrow intent='multiple-integral($a1)'><mrow><mo>∫</mo><mo>⋯</mo><mo>∫</mo></mrow><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MultipleIntegral.html"
+     - "https://en.wikipedia.org/wiki/%E2%88%AB%E2%88%ABf(x,y)dxdy"
+     - "https://en.wikipedia.org/wiki/Multiple_integral"
+     - "https://www.encyclopediaofmath.org/index.php/Multiple_integral"
+  
+  - concept: multiplicative-inverse
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: multiplicative inverse of $a1
+    property: msup, mixfix
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><msup intent='multiplicative-inverse($a1)'><mi arg='a1'>x</mi><mn>-1</mn></msup></math>"
+     - "<math><mrow intent='multiplicative-inverse($a1)'><mn>1</mn><mo>/</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Inverse.html"
+     - "https://en.wikipedia.org/wiki/Inverse_function"
+     - "https://en.wikipedia.org/wiki/Inverse_functions_and_differentiation"
+     - "https://ncatlab.org/nlab/show/inverse"
+     - "https://mathworld.wolfram.com/MultiplicativeInverse.html"
+     - "https://en.wikipedia.org/wiki/Multiplicative_inverse"
+    alias:
+     - inverse
+  
+  - concept: multiplicative-order
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: multiplicative order of $a1
+    property: "indexed function"
+    subject-area: "modular arithmetic"
+    mathml:
+     - "<math><msub intent='multiplicative-order($a1)'><mi>O</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='multiplicative-order($a1)'><mi>ord</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MultiplicativeOrder.html"
+     - "https://en.wikipedia.org/wiki/Multiplicative_order"
+  
+  - concept: multiplier-algebra
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: multiplier algebra of $a1
+    property: function
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><mrow intent='multiplier-algebra($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>A</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MultiplierAlgebra.html"
+     - "https://en.wikipedia.org/wiki/Multiplier_algebra"
+     - "https://ncatlab.org/nlab/show/multiplier+algebra"
+  
+  - concept: multichoose
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: multichoose
-      property: fenced-stacked
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='multichoose($a1,$a2)'><mo style='font-weight:bold'>(</mo><mfrac linethickness='0pt'><mi arg='a1'>m</mi><mi arg='a2'>n</mi></mfrac><mo style='font-weight:bold'>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Multiset.html"
-    
-    - concept: multiset-coefficient
-      arity: 2
+    property: fenced-stacked
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='multichoose($a1,$a2)'><mo style='font-weight:bold'>(</mo><mfrac linethickness='0pt'><mi arg='a1'>m</mi><mi arg='a2'>n</mi></mfrac><mo style='font-weight:bold'>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Multiset.html"
+  
+  - concept: multiset-coefficient
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: multiset coefficient
-      property: fenced-stacked
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='multiset-coefficient($a1,$a2)'><mo>⦅</mo><mfrac linethickness='0pt'><mi arg='a1'>n</mi><mi arg='a2'>n</mi></mfrac><mo>⦆</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Multiset"
-      alias:
-       - multiset-number
-    
-    - concept: multivariate-gaussian-distribution
-      arity: 1
+    property: fenced-stacked
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='multiset-coefficient($a1,$a2)'><mo>⦅</mo><mfrac linethickness='0pt'><mi arg='a1'>n</mi><mi arg='a2'>n</mi></mfrac><mo>⦆</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Multiset"
+    alias:
+     - multiset-number
+  
+  - concept: multivariate-gaussian-distribution
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: multivariate gaussian distribution
-      property: symbol
-      area: "probability theory"
-      mathml:
-       - "<math><msub intent='multivariate-gaussian-distribution($a1)'><mi>𝒩</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Multivariate_normal_distribution"
-      alias:
-       - multivariate-normal-distribution
-       - joint-normal-distribution
-    
-    - concept: mutation
-      arity: 2
+    property: symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><msub intent='multivariate-gaussian-distribution($a1)'><mi>𝒩</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Multivariate_normal_distribution"
+    alias:
+     - multivariate-normal-distribution
+     - joint-normal-distribution
+  
+  - concept: mutation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: mutation
-      property: msup
-      area: "abstract algebra"
-      mathml:
-       - "<math><msub intent='mutation($a1,$a2)'><mi arg='a1'>A</mi><mi arg='a2'>y</mi></msub></math>"
-      notation: "msup $1 $2"
-      urls: 
-       - "https://mathworld.wolfram.com/Mutation.html"
-       - "https://en.wikipedia.org/wiki/Mutation_(knot_theory)"
-       - "https://en.wikipedia.org/wiki/Mutation_(Jordan_algebra)"
-       - "https://en.wikipedia.org/wiki/Hua%27s_identity_(Jordan_algebra)"
-       - "https://en.wikipedia.org/wiki/Mutation_(algebra)"
-       - "https://en.wikipedia.org/wiki/Mutation_(genetic_algorithm)"
-      alias:
-       - homotope
-    
-    - concept: mutual-information
-      arity: 1
-      en: mutual information of $1
-      property: function
-      area: "information theory"
-      mathml:
-       - "<math><mrow intent='mutual-information($a1)'><mi>I</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/MutualInformation.html"
-       - "https://en.wikipedia.org/wiki/Mutual_information"
-    
-    - concept: narayana-number
-      arity: 2
+    property: msup
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><msub intent='mutation($a1,$a2)'><mi arg='a1'>A</mi><mi arg='a2'>y</mi></msub></math>"
+    notation: "msup $a1 $a2"
+    urls: 
+     - "https://mathworld.wolfram.com/Mutation.html"
+     - "https://en.wikipedia.org/wiki/Mutation_(knot_theory)"
+     - "https://en.wikipedia.org/wiki/Mutation_(Jordan_algebra)"
+     - "https://en.wikipedia.org/wiki/Hua%27s_identity_(Jordan_algebra)"
+     - "https://en.wikipedia.org/wiki/Mutation_(algebra)"
+     - "https://en.wikipedia.org/wiki/Mutation_(genetic_algorithm)"
+    alias:
+     - homotope
+  
+  - concept: mutual-information
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: mutual information of $a1
+    property: function
+    subject-area: "information theory"
+    mathml:
+     - "<math><mrow intent='mutual-information($a1)'><mi>I</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/MutualInformation.html"
+     - "https://en.wikipedia.org/wiki/Mutual_information"
+  
+  - concept: narayana-number
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: narayana number
-      property: function
-      area: "combinatorial analysis"
-      mathml:
-       - "<math><mrow intent='narayana-number($a1,$a2)'><mi>N</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>,</mo><mi arg='a2'>k</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/NarayanaNumber.html"
-       - "https://en.wikipedia.org/wiki/Narayana_number"
-       - "https://dlmf.nist.gov/26.6#E3"
-    
-    - concept: narrow-denjoy-integral
-      arity: 1
-      en: narrow denjoy integral of $1
-      property: indexed
-      area: "calculus"
-      mathml:
-       - "<math><mrow intent='narrow-denjoy-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DenjoyIntegral.html"
-       - "https://en.wikipedia.org/wiki/Henstock%E2%80%93Kurzweil_integral"
-       - "https://www.encyclopediaofmath.org/index.php/Denjoy_integral"
-      alias:
-       - henstock-kurzweil-integral
-       - luzin-integral
-       - perron-integral
-    
-    - concept: negative-binomial-distribution
-      arity: 0
+    property: function
+    subject-area: "combinatorial analysis"
+    mathml:
+     - "<math><mrow intent='narayana-number($a1,$a2)'><mi>N</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>,</mo><mi arg='a2'>k</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/NarayanaNumber.html"
+     - "https://en.wikipedia.org/wiki/Narayana_number"
+     - "https://dlmf.nist.gov/26.6#E3"
+  
+  - concept: narrow-denjoy-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: narrow denjoy integral of $a1
+    property: indexed
+    subject-area: "calculus"
+    mathml:
+     - "<math><mrow intent='narrow-denjoy-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DenjoyIntegral.html"
+     - "https://en.wikipedia.org/wiki/Henstock%E2%80%93Kurzweil_integral"
+     - "https://www.encyclopediaofmath.org/index.php/Denjoy_integral"
+    alias:
+     - henstock-kurzweil-integral
+     - luzin-integral
+     - perron-integral
+  
+  - concept: negative-binomial-distribution
+    arity: 0
+    arguments: []
+    speech:
       en: negative binomial distribution
-      property: symbol
-      area: "probability theory"
-      mathml:
-       - "<math><mi intent='negative-binomial-distribution'>NB</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/NegativeBinomialDistribution.html"
-       - "https://en.wikipedia.org/wiki/Negative_binomial_distribution"
-       - "https://www.encyclopediaofmath.org/index.php/Negative_binomial_distribution"
-    
-    - concept: negative-hypergeometric-distribution
-      arity: 1
-      en: negative hypergeometric distribution of $1
-      property: "indexed symbol"
-      area: "probability theory"
-      mathml:
-       - "<math><mrow intent='negative-hypergeometric-distribution($a1)'><mi>NHG</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Negative_hypergeometric_distribution"
-       - "https://www.encyclopediaofmath.org/index.php/Negative_hypergeometric_distribution"
-    
-    - concept: neighbourhood
-      arity: 2
-      en: neighbourhood of $2 in $1
-      property: "indexed function, function"
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='neighbourhood($a1,$a2)'><msub><mi>N</mi><mi arg='a2'>v</mi></msub><mrow><mo>(</mo><mi arg='a1'>G</mi><mo>)</mo></mrow></mrow></math>"
-      notation: "msub N $1 ( $2 )"
-      notationa: "mrow N ( $1"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Neighbourhood_(graph_theory)"
-      alias:
-       - open-neighbourhood
-    
-    - concept: neighbourhood-filter
-      arity: 1
-      en: neighbourhood filter of $1
-      property: function
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='neighbourhood-filter($a1)'><mi>𝒩</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Neighbourhood_system"
-      alias:
-       - neighbourhood-system
-       - complete-system-of-neighbourhoods
-    
-    - concept: neron-severi-group
-      arity: 1
-      en: neron severi group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='neron-severi-group($a1)'><mi>NS</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Neron-SeveriGroup.html"
-       - "https://encyclopediaofmath.org/wiki/N%C3%A9ron-Severi_group"
-    
-    - concept: neron-tate-height
-      arity: 0
+    property: symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mi intent='negative-binomial-distribution'>NB</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/NegativeBinomialDistribution.html"
+     - "https://en.wikipedia.org/wiki/Negative_binomial_distribution"
+     - "https://www.encyclopediaofmath.org/index.php/Negative_binomial_distribution"
+  
+  - concept: negative-hypergeometric-distribution
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: negative hypergeometric distribution of $a1
+    property: "indexed symbol"
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mrow intent='negative-hypergeometric-distribution($a1)'><mi>NHG</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Negative_hypergeometric_distribution"
+     - "https://www.encyclopediaofmath.org/index.php/Negative_hypergeometric_distribution"
+  
+  - concept: neighbourhood
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: neighbourhood of $a2 in $a1
+    property: "indexed function, function"
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='neighbourhood($a1,$a2)'><msub><mi>N</mi><mi arg='a2'>v</mi></msub><mrow><mo>(</mo><mi arg='a1'>G</mi><mo>)</mo></mrow></mrow></math>"
+    notation: "msub N $a1 ( $a2 )"
+    notationa: "mrow N ( $a1"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Neighbourhood_(graph_theory)"
+    alias:
+     - open-neighbourhood
+  
+  - concept: neighbourhood-filter
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: neighbourhood filter of $a1
+    property: function
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='neighbourhood-filter($a1)'><mi>𝒩</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Neighbourhood_system"
+    alias:
+     - neighbourhood-system
+     - complete-system-of-neighbourhoods
+  
+  - concept: neron-severi-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: neron severi group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='neron-severi-group($a1)'><mi>NS</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Neron-SeveriGroup.html"
+     - "https://encyclopediaofmath.org/wiki/N%C3%A9ron-Severi_group"
+  
+  - concept: neron-tate-height
+    arity: 0
+    arguments: []
+    speech:
       en: neron tate height
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><mover intent='neron-tate-height'><mi>h</mi><mo>^</mo></mover></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/N%C3%A9ron%E2%80%93Tate_height"
-      alias:
-       - canonical-height
-    
-    - concept: nerve
-      arity: 1
-      en: nerve of $1
-      property: function
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='nerve($a1)'><mi>N</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Nerve.html"
-       - "https://en.wikipedia.org/wiki/Nerve_(category_theory)"
-       - "https://ncatlab.org/nlab/show/nerve"
-    
-    - concept: nome
-      arity: 1
-      en: nome of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='nome($a1)'><mi>q</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Nome.html"
-       - "https://en.wikipedia.org/wiki/Nome_(mathematics)"
-    
-    - concept: non-oriented-angle
-      arity: 1
-      en: non oriented angle of $1
-      property: prefix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='non-oriented-angle($a1)'><mo>∠</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Orientation_(vector_space)"
-       - "https://en.wikipedia.org/wiki/Euclidean_space#Angle"
-      alias:
-       - angle
-    
-    - concept: nor
-      arity: 2
-      en: $1 nor $2
-      property: infix
-      area: "logic"
-      mathml:
-       - "<math><mrow intent='nor($a1,$a2)'><mi arg='a1'>X</mi><mo>↓</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Nor.html"
-       - "https://mathworld.wolfram.com/NOR.html"
-      alias:
-       - joint-denial
-    
-    - concept: norm
-      arity: 1
-      en: norm of $1
-      property: fenced
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='norm($a1)'><mo>‖</mo><mi arg='a1'>x</mi><mo>‖</mo></mrow></math>"
-      notationa: "mrow | $1"
-      urls: 
-       - "https://mathworld.wolfram.com/Norm.html"
-       - "https://en.wikipedia.org/wiki/Norm_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Norm_(abelian_group)"
-       - "https://ncatlab.org/nlab/show/norm"
-       - "https://www.encyclopediaofmath.org/index.php/Norm"
-    
-    - concept: normalizer
-      arity: 1
-      en: normalizer of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='normalizer($a1)'><mi>N</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Normalizer.html"
-       - "https://en.wikipedia.org/wiki/Centralizer_and_normalizer"
-       - "https://ncatlab.org/nlab/show/normalizer"
-    
-    - concept: not-divisible-by
-      arity: 2
-      en: $1 not divisible by $2
-      property: infix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='not-divisible-by($a1,$a2)'><mi arg='a1'>X</mi><mo>∤</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Divisor"
-    
-    - concept: null-graph
-      arity: 1
-      en: null graph of order $1
-      property: symbol
-      area: "graph theory"
-      mathml:
-       - "<math><msub intent='null-graph($a1)'><mover><mi>K</mi><mo>¯</mo></mover><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/NullGraph.html"
-       - "https://en.wikipedia.org/wiki/Null_graph"
-       - "https://en.wikipedia.org/wiki/Order-zero_graph"
-      alias:
-       - edgeless-graph
-    
-    - concept: numerical-part
-      arity: 1
-      en: numerical part of $1
-      property: fenced
-      area: "SI units"
-      mathml:
-       - "<math><mrow intent='numerical-part($a1)'><mo>{</mo><mi arg='a1'>x</mi><mo>}</mo></mrow></math>"
-      urls: 
-       - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values"
-    
-    - concept: object
-      arity: 1
-      en: object of $1
-      property: prefix
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='object($a1)'><mi>Obj</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Object.html"
-       - "https://en.wikipedia.org/wiki/Lattice-based_access_control"
-       - "https://ncatlab.org/nlab/show/object"
-    
-    - concept: octant
-      arity: 3
-      en: octant  of $1, $2 and $3
-      property: fenced
-      area: "euclidean solid geometry"
-      mathml:
-       - "<math><mrow intent='octant($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>±</mi><mo>,</mo><mi arg='a2'>±</mi><mo>,</mo><mi arg='a3'>±</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Octant.html"
-       - "https://en.wikipedia.org/wiki/Octant_(plane_geometry)"
-       - "https://en.wikipedia.org/wiki/Octant_(solid_geometry)"
-       - "https://www.encyclopediaofmath.org/index.php/Octant"
-    
-    - concept: octonions
-      arity: 0
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><mover intent='neron-tate-height'><mi>h</mi><mo>^</mo></mover></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/N%C3%A9ron%E2%80%93Tate_height"
+    alias:
+     - canonical-height
+  
+  - concept: nerve
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: nerve of $a1
+    property: function
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='nerve($a1)'><mi>N</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Nerve.html"
+     - "https://en.wikipedia.org/wiki/Nerve_(category_theory)"
+     - "https://ncatlab.org/nlab/show/nerve"
+  
+  - concept: nome
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: nome of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='nome($a1)'><mi>q</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Nome.html"
+     - "https://en.wikipedia.org/wiki/Nome_(mathematics)"
+  
+  - concept: non-oriented-angle
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: non oriented angle of $a1
+    property: prefix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='non-oriented-angle($a1)'><mo>∠</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Orientation_(vector_space)"
+     - "https://en.wikipedia.org/wiki/Euclidean_space#Angle"
+    alias:
+     - angle
+  
+  - concept: nor
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 nor $a2
+    property: infix
+    subject-area: "logic"
+    mathml:
+     - "<math><mrow intent='nor($a1,$a2)'><mi arg='a1'>X</mi><mo>↓</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Nor.html"
+     - "https://mathworld.wolfram.com/NOR.html"
+    alias:
+     - joint-denial
+  
+  - concept: norm
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: norm of $a1
+    property: fenced
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='norm($a1)'><mo>‖</mo><mi arg='a1'>x</mi><mo>‖</mo></mrow></math>"
+    notationa: "mrow | $a1"
+    urls: 
+     - "https://mathworld.wolfram.com/Norm.html"
+     - "https://en.wikipedia.org/wiki/Norm_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Norm_(abelian_group)"
+     - "https://ncatlab.org/nlab/show/norm"
+     - "https://www.encyclopediaofmath.org/index.php/Norm"
+  
+  - concept: normalizer
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: normalizer of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='normalizer($a1)'><mi>N</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Normalizer.html"
+     - "https://en.wikipedia.org/wiki/Centralizer_and_normalizer"
+     - "https://ncatlab.org/nlab/show/normalizer"
+  
+  - concept: not-divisible-by
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 not divisible by $a2
+    property: infix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='not-divisible-by($a1,$a2)'><mi arg='a1'>X</mi><mo>∤</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Divisor"
+  
+  - concept: null-graph
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: null graph of order $a1
+    property: symbol
+    subject-area: "graph theory"
+    mathml:
+     - "<math><msub intent='null-graph($a1)'><mover><mi>K</mi><mo>¯</mo></mover><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/NullGraph.html"
+     - "https://en.wikipedia.org/wiki/Null_graph"
+     - "https://en.wikipedia.org/wiki/Order-zero_graph"
+    alias:
+     - edgeless-graph
+  
+  - concept: numerical-part
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: numerical part of $a1
+    property: fenced
+    subject-area: "SI units"
+    mathml:
+     - "<math><mrow intent='numerical-part($a1)'><mo>{</mo><mi arg='a1'>x</mi><mo>}</mo></mrow></math>"
+    urls: 
+     - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values"
+  
+  - concept: object
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: object of $a1
+    property: prefix
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='object($a1)'><mi>Obj</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Object.html"
+     - "https://en.wikipedia.org/wiki/Lattice-based_access_control"
+     - "https://ncatlab.org/nlab/show/object"
+  
+  - concept: octant
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: octant  of $a1, $a2 and $a3
+    property: fenced
+    subject-area: "euclidean solid geometry"
+    mathml:
+     - "<math><mrow intent='octant($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>±</mi><mo>,</mo><mi arg='a2'>±</mi><mo>,</mo><mi arg='a3'>±</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Octant.html"
+     - "https://en.wikipedia.org/wiki/Octant_(plane_geometry)"
+     - "https://en.wikipedia.org/wiki/Octant_(solid_geometry)"
+     - "https://www.encyclopediaofmath.org/index.php/Octant"
+  
+  - concept: octonions
+    arity: 0
+    arguments: []
+    speech:
       en: octonions
-      property: symbol
-      area: "compositional algebra"
-      mathml:
-       - "<math><mi intent='octonions'>𝕆</mi></math>"
-       - "<math><mi intent='octonions'>O</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Octonion.html"
-       - "https://en.wikipedia.org/wiki/Octonion"
-       - "https://ncatlab.org/nlab/show/octonion"
-       - "https://www.encyclopediaofmath.org/index.php/Octonion"
-      alias:
-       - cayley-numbers
-    
-    - concept: odds-ratio
-      arity: 0
+    property: symbol
+    subject-area: "compositional algebra"
+    mathml:
+     - "<math><mi intent='octonions'>𝕆</mi></math>"
+     - "<math><mi intent='octonions'>O</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Octonion.html"
+     - "https://en.wikipedia.org/wiki/Octonion"
+     - "https://ncatlab.org/nlab/show/octonion"
+     - "https://www.encyclopediaofmath.org/index.php/Octonion"
+    alias:
+     - cayley-numbers
+  
+  - concept: odds-ratio
+    arity: 0
+    arguments: []
+    speech:
       en: odds ratio
-      property: symbol
-      area: "statistics"
-      mathml:
-       - "<math><mi intent='odds-ratio'>OR</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Odds_ratio"
-    
-    - concept: onsager-machlup-function
-      arity: 1
-      en: onsager machlup function of $1
-      property: function
-      area: "functional analysis"
-      mathml:
-       - "<math><mrow intent='onsager-machlup-function($a1)'><mi>L</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Onsager%E2%80%93Machlup_function"
-       - "https://www.encyclopediaofmath.org/index.php/Onsager-Machlup_function"
-    
-    
-    - concept: open-ball
-      arity: 2
-      en: open ball $1 $2
-      property: mixfix
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='open-ball($a1,$a2)'><msub><mi>B</mi><mi arg='a1'>r</mi></msub><mrow><mo>(</mo><mi arg='a2'>p</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/OpenBall.html"
-       - "https://en.wikipedia.org/wiki/Ball_(mathematics)"
-      alias:
-       - open-metric-ball
-    
-    - concept: open-interval
-      arity: 2
+    property: symbol
+    subject-area: "statistics"
+    mathml:
+     - "<math><mi intent='odds-ratio'>OR</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Odds_ratio"
+  
+  - concept: onsager-machlup-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: onsager machlup function of $a1
+    property: function
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><mrow intent='onsager-machlup-function($a1)'><mi>L</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Onsager%E2%80%93Machlup_function"
+     - "https://www.encyclopediaofmath.org/index.php/Onsager-Machlup_function"
+  
+  
+  - concept: open-ball
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: open ball $a1 $a2
+    property: mixfix
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='open-ball($a1,$a2)'><msub><mi>B</mi><mi arg='a1'>r</mi></msub><mrow><mo>(</mo><mi arg='a2'>p</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/OpenBall.html"
+     - "https://en.wikipedia.org/wiki/Ball_(mathematics)"
+    alias:
+     - open-metric-ball
+  
+  - concept: open-interval
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: open interval
-      property: fenced
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='open-interval($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
-       - "<math><mrow intent='open-interval($a1,$a2)'><mo>]</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>[</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/OpenInterval.html"
-       - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r28"
-    
-    - concept: open-real-interval
-      arity: 2
-      en: open real interval $1 to $2
-      property: fenced
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='open-real-interval($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://proofwiki.org/wiki/Definition: Real_Interval/Open"
-    
-    - concept: opposite
-      arity: 1
-      en: opposite of $1
-      property: msup
-      area: "category theory,, group theory"
-      mathml:
-       - "<math><msup intent='opposite($a1)'><mi arg='a1'>X</mi><mi>op</mi></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Opposite_category"
-       - "https://ncatlab.org/nlab/show/opposite+category"
-       - "https://en.wikipedia.org/wiki/Opposite_group"
-       - "https://en.wikipedia.org/wiki/Opposite_ring"
-      alias:
-       - dual
-    
-    - concept: opposite-charge
-      arity: 2
-      en: $1 opposite charge $2
-      property: infix
-      area: "physics"
-      mathml:
-       - "<math><mrow intent='opposite-charge($a1,$a2)'><mi arg='a1'>X</mi><mo>⇅</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://youtu.be/HZ7a9YkF204?t=4657"
-    
-    - concept: or-product
-      arity: 2
-      en: $1 or product $2
-      property: infix
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='or-product($a1,$a2)'><mi arg='a1'>X</mi><mo>*</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Graph_product"
-      alias:
-       - disjunctive-product
-       - co-normal-product
-    
-    - concept: order-of-group
-      arity: 1
-      en: order of group of $1
-      property: "function, fenced"
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='order-of-group($a1)'><mi>ord</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='order-of-group($a1)'><mo>|</mo><mi arg='a1'>x</mi><mo>|</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Order_(group_theory))"
-    
-    - concept: orthocomplement
-      arity: 1
-      en: orthocomplement of $1
-      property: msup
-      area: "lattice theory"
-      mathml:
-       - "<math><msup intent='orthocomplement($a1)'><mi arg='a1'>X</mi><mo>⊥</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Complemented_lattice"
-    
-    - concept: orthogonal
-      arity: 2
-      en: $1 orthogonal $2
-      property: infix
-      area: "geometry,, algebra"
-      mathml:
-       - "<math><mrow intent='orthogonal($a1,$a2)'><mi arg='a1'>X</mi><mo>⊥</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Orthogonal.html"
-       - "https://en.1wikipedia.org/wiki/Orthogonal_functions"
-       - "https://en.wikipedia.org/wiki/Orthogonality_(term_rewriting)"
-       - "https://en.wikipedia.org/wiki/Orthogonality"
-       - "https://ncatlab.org/nlab/show/orthogonality"
-       - "https://www.encyclopediaofmath.org/index.php/Orthogonality"
-      alias:
-       - perpendicular
-    
-    - concept: orthogonal-group
-      arity: 1
-      en: orthogonal group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='orthogonal-group($a1)'><mi>O</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/OrthogonalGroup.html"
-       - "https://en.wikipedia.org/wiki/Orthogonal_group"
-       - "https://en.wikipedia.org/wiki/Special_orthogonal_Lie_algebra"
-       - "https://ncatlab.org/nlab/show/orthogonal+group"
-       - "https://www.encyclopediaofmath.org/index.php/Orthogonal_group"
-    
-    - concept: outer-automorphism-group
-      arity: 1
-      en: outer automorphism group of $1
-      property: function
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='outer-automorphism-group($a1)'><mi>Out</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/OuterAutomorphismGroup.html"
-       - "https://en.wikipedia.org/wiki/Outer_automorphism_group"
-      alias:
-       - outer-automorphism
-    
-    - concept: outer-jordan-measure
-      arity: 1
-      en: outer jordan measure of $1
-      property: function
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='outer-jordan-measure($a1)'><msup><mi>m</mi><mo>*</mo></msup><mrow><mo>(</mo><mi arg='a1'>N</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/JordanMeasure.html"
-       - "https://en.wikipedia.org/wiki/Jordan_measure"
-       - "https://www.encyclopediaofmath.org/index.php/Jordan_measure"
-    
-    - concept: outer-product
-      arity: 2
-      en: $1 outer product $2
-      property: infix
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='outer-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⊗</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/OuterProduct.html"
-       - "https://en.wikipedia.org/wiki/Outer_product"
-       - "https://en.wikipedia.org/wiki/Tensor_product"
-    
-    - concept: p-core
-      arity: 1
-      en: p core of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='p-core($a1)'><msub><mi>O</mi><mi>p</mi></msub><mrow><mo>(</mo><mi arg='a1'>G</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Core_(group)"
-       - "https://en.wikipedia.org/wiki/P-soluble_group"
-       - "https://en.wikipedia.org/wiki/P-core"
-       - "https://en.wikipedia.org/wiki/Upper_p-series"
-    
-    - concept: pade-approximant
-      arity: 3
-      en: pade approximant  of $1, $2 and $3
-      property: mixfix
-      area: "numerical analysis"
-      mathml:
-       - "<math><msub intent='pade-approximant($a1,$a2,$a3)'><mrow><mo>[</mo><mi arg='a1'>X</mi><mo>/</mo><mi arg='a2'>Y</mi><mo>]</mo></mrow><mi arg='a3'>f</mi></msub></math>"
-      urls: 
-       - "https://dlmf.nist.gov/3.11#SS4.p1"
-       - "https://mathworld.wolfram.com/PadeApproximant.html"
-       - "https://en.wikipedia.org/wiki/Pad%C3%A9_approximant"
-    
-    - concept: padovan-sequence
-      arity: 1
-      en: padovan sequence of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='padovan-sequence($a1)'><mi>P</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PadovanSequence.html"
-       - "https://en.wikipedia.org/wiki/Padovan_sequence"
-    
-    - concept: paraboloidal-coordinate
-      arity: 3
-      en: paraboloidal coordinate of $1, $2 and $3
-      property: fenced
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='paraboloidal-coordinate($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ParaboloidalCoordinates.html"
-       - "https://en.wikipedia.org/wiki/Paraboloidal_coordinates"
-       - "https://www.encyclopediaofmath.org/index.php/Paraboloidal_coordinates"
-    
-    - concept: parallel
-      arity: 2
-      en: $1 parallel $2
-      property: infix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='parallel($a1,$a2)'><mi arg='a1'>X</mi><mo>∥</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Parallel.html"
-       - "https://en.wikipedia.org/wiki/Parallel_(geometry)"
-       - "https://en.wikipedia.org/wiki/Parallel_curve"
-    
-    - concept: parallel-morphism
-      arity: 2
+    property: fenced
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='open-interval($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
+     - "<math><mrow intent='open-interval($a1,$a2)'><mo>]</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>[</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/OpenInterval.html"
+     - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r28"
+  
+  - concept: open-real-interval
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: open real interval $a1 to $a2
+    property: fenced
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='open-real-interval($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://proofwiki.org/wiki/Definition: Real_Interval/Open"
+  
+  - concept: opposite
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: opposite of $a1
+    property: msup
+    subject-area: "category theory,, group theory"
+    mathml:
+     - "<math><msup intent='opposite($a1)'><mi arg='a1'>X</mi><mi>op</mi></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Opposite_category"
+     - "https://ncatlab.org/nlab/show/opposite+category"
+     - "https://en.wikipedia.org/wiki/Opposite_group"
+     - "https://en.wikipedia.org/wiki/Opposite_ring"
+    alias:
+     - dual
+  
+  - concept: opposite-charge
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 opposite charge $a2
+    property: infix
+    subject-area: "physics"
+    mathml:
+     - "<math><mrow intent='opposite-charge($a1,$a2)'><mi arg='a1'>X</mi><mo>⇅</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://youtu.be/HZ7a9YkF204?t=4657"
+  
+  - concept: or-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 or product $a2
+    property: infix
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='or-product($a1,$a2)'><mi arg='a1'>X</mi><mo>*</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Graph_product"
+    alias:
+     - disjunctive-product
+     - co-normal-product
+  
+  - concept: order-of-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: order of group of $a1
+    property: "function, fenced"
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='order-of-group($a1)'><mi>ord</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='order-of-group($a1)'><mo>|</mo><mi arg='a1'>x</mi><mo>|</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Order_(group_theory))"
+  
+  - concept: orthocomplement
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: orthocomplement of $a1
+    property: msup
+    subject-area: "lattice theory"
+    mathml:
+     - "<math><msup intent='orthocomplement($a1)'><mi arg='a1'>X</mi><mo>⊥</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Complemented_lattice"
+  
+  - concept: orthogonal
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 orthogonal $a2
+    property: infix
+    subject-area: "geometry,, algebra"
+    mathml:
+     - "<math><mrow intent='orthogonal($a1,$a2)'><mi arg='a1'>X</mi><mo>⊥</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Orthogonal.html"
+     - "https://en.1wikipedia.org/wiki/Orthogonal_functions"
+     - "https://en.wikipedia.org/wiki/Orthogonality_(term_rewriting)"
+     - "https://en.wikipedia.org/wiki/Orthogonality"
+     - "https://ncatlab.org/nlab/show/orthogonality"
+     - "https://www.encyclopediaofmath.org/index.php/Orthogonality"
+    alias:
+     - perpendicular
+  
+  - concept: orthogonal-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: orthogonal group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='orthogonal-group($a1)'><mi>O</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/OrthogonalGroup.html"
+     - "https://en.wikipedia.org/wiki/Orthogonal_group"
+     - "https://en.wikipedia.org/wiki/Special_orthogonal_Lie_algebra"
+     - "https://ncatlab.org/nlab/show/orthogonal+group"
+     - "https://www.encyclopediaofmath.org/index.php/Orthogonal_group"
+  
+  - concept: outer-automorphism-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: outer automorphism group of $a1
+    property: function
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='outer-automorphism-group($a1)'><mi>Out</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/OuterAutomorphismGroup.html"
+     - "https://en.wikipedia.org/wiki/Outer_automorphism_group"
+    alias:
+     - outer-automorphism
+  
+  - concept: outer-jordan-measure
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: outer jordan measure of $a1
+    property: function
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='outer-jordan-measure($a1)'><msup><mi>m</mi><mo>*</mo></msup><mrow><mo>(</mo><mi arg='a1'>N</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/JordanMeasure.html"
+     - "https://en.wikipedia.org/wiki/Jordan_measure"
+     - "https://www.encyclopediaofmath.org/index.php/Jordan_measure"
+  
+  - concept: outer-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 outer product $a2
+    property: infix
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='outer-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⊗</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/OuterProduct.html"
+     - "https://en.wikipedia.org/wiki/Outer_product"
+     - "https://en.wikipedia.org/wiki/Tensor_product"
+  
+  - concept: p-core
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: p core of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='p-core($a1)'><msub><mi>O</mi><mi>p</mi></msub><mrow><mo>(</mo><mi arg='a1'>G</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Core_(group)"
+     - "https://en.wikipedia.org/wiki/P-soluble_group"
+     - "https://en.wikipedia.org/wiki/P-core"
+     - "https://en.wikipedia.org/wiki/Upper_p-series"
+  
+  - concept: pade-approximant
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: pade approximant  of $a1, $a2 and $a3
+    property: mixfix
+    subject-area: "numerical analysis"
+    mathml:
+     - "<math><msub intent='pade-approximant($a1,$a2,$a3)'><mrow><mo>[</mo><mi arg='a1'>X</mi><mo>/</mo><mi arg='a2'>Y</mi><mo>]</mo></mrow><mi arg='a3'>f</mi></msub></math>"
+    urls: 
+     - "https://dlmf.nist.gov/3.11#SS4.p1"
+     - "https://mathworld.wolfram.com/PadeApproximant.html"
+     - "https://en.wikipedia.org/wiki/Pad%C3%A9_approximant"
+  
+  - concept: padovan-sequence
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: padovan sequence of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='padovan-sequence($a1)'><mi>P</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PadovanSequence.html"
+     - "https://en.wikipedia.org/wiki/Padovan_sequence"
+  
+  - concept: paraboloidal-coordinate
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: paraboloidal coordinate of $a1, $a2 and $a3
+    property: fenced
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='paraboloidal-coordinate($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ParaboloidalCoordinates.html"
+     - "https://en.wikipedia.org/wiki/Paraboloidal_coordinates"
+     - "https://www.encyclopediaofmath.org/index.php/Paraboloidal_coordinates"
+  
+  - concept: parallel
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 parallel $a2
+    property: infix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='parallel($a1,$a2)'><mi arg='a1'>X</mi><mo>∥</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Parallel.html"
+     - "https://en.wikipedia.org/wiki/Parallel_(geometry)"
+     - "https://en.wikipedia.org/wiki/Parallel_curve"
+  
+  - concept: parallel-morphism
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: parallel morphism
-      property: embellished infix
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='parallel-morphism($a1,$a2)'><mi arg='a1'>x</mi><mo>⇉</mo><mi arg='a2'>y</mi></mrow></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/parallel+morphisms"
-    
-    - concept: partial-charge
-      arity: 1
+    property: embellished infix
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='parallel-morphism($a1,$a2)'><mi arg='a1'>x</mi><mo>⇉</mo><mi arg='a2'>y</mi></mrow></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/parallel+morphisms"
+  
+  - concept: partial-charge
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: partial charge
-      property: symbol
-      area: "chemistry"
-      mathml:
-       - "<math><mrow intent='partial-charge($a1)'><mi>δ</mi><mo arg='a1'>+</mo></mrow></math>"
-       - "<math><msup intent='partial-charge($a1)'><mi>δ</mi><mo arg='a1'>+</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Partial_charge"
-       - "https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/08._Basic_Concepts_of_Chemical_Bonding/8.S%3A_Basic_Concepts_of_Chemical_Bonding_(Summary)"
-      alias:
-       - delta-sign
-    
-    - concept: partition
-      arity: 2
-      en: $1 partition $2
-      property: infix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='partition($a1,$a2)'><mi arg='a1'>X</mi><mo>⊢</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Partition.html"
-       - "https://mathworld.wolfram.com/FrequencyRepresentation.html"
-       - "https://en.wikipedia.org/wiki/Partition_(number_theory)"
-       - "https://en.wikipedia.org/wiki/List_of_partition_topics"
-    
-    - concept: partition-frequency-representation
-      arity: ">=0"
-      en: "partition $1 sup $2, $2 sup $3, ..."
-      property: mixfix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='partition-frequency-representation($a1,$a2)'><mo>(</mo><msup arg='a1'><mn>1</mn><mi>a</mi></msup><msup arg='a2'><mn>2</mn><mi>b</mi></msup><msup arg='a3'><mn>3</mn><mi>c</mi></msup><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/FrequencyRepresentation.html"
-    
-    - concept: partition-function
-      arity: 1
-      en: partition function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='partition-function($a1)'><mi>p</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Partition_(number_theory)"
-    
-    - concept: pauli-matrix
-      arity: 1
-      en: pauli matrix of $1
-      property: "indexed symbol"
-      area: "mathematical physics"
-      mathml:
-       - "<math><msub intent='pauli-matrix($a1)'><mi>σ</mi><mi arg='a1'>G</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PauliMatrices.html"
-       - "https://mathworld.wolfram.com/PauliMatrix.html"
-       - "https://en.wikipedia.org/wiki/Pauli_matrices"
-       - "https://www.encyclopediaofmath.org/index.php/Pauli_matrices"
-    
-    - concept: peclet-number
-      arity: 1
-      en: peclet number of $1
-      property: "indexed symbol"
-      area: "fluid dynamics"
-      mathml:
-       - "<math><msub intent='peclet-number($a1)'><mi>Pe</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/P%C3%A9clet_number"
-       - "https://www.encyclopediaofmath.org/index.php/Peclet_number"
-       - "https://www.encyclopediaofmath.org/index.php/Péclet_number"
-    
-    - concept: peirce-arrow
-      arity: 2
-      en: $1 peirce arrow $2
-      property: infix
-      area: "logic"
-      mathml:
-       - "<math><mrow intent='peirce-arrow($a1,$a2)'><mi arg='a1'>X</mi><mo>↓</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://www.encyclopediaofmath.org/index.php/Peirce_arrow"
-    
-    - concept: pell-number
-      arity: 1
+    property: symbol
+    subject-area: "chemistry"
+    mathml:
+     - "<math><mrow intent='partial-charge($a1)'><mi>δ</mi><mo arg='a1'>+</mo></mrow></math>"
+     - "<math><msup intent='partial-charge($a1)'><mi>δ</mi><mo arg='a1'>+</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Partial_charge"
+     - "https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/08._Basic_Concepts_of_Chemical_Bonding/8.S%3A_Basic_Concepts_of_Chemical_Bonding_(Summary)"
+    alias:
+     - delta-sign
+  
+  - concept: partition
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 partition $a2
+    property: infix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='partition($a1,$a2)'><mi arg='a1'>X</mi><mo>⊢</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Partition.html"
+     - "https://mathworld.wolfram.com/FrequencyRepresentation.html"
+     - "https://en.wikipedia.org/wiki/Partition_(number_theory)"
+     - "https://en.wikipedia.org/wiki/List_of_partition_topics"
+  
+  - concept: partition-frequency-representation
+    arity: ">=0"
+    speech:
+      en: "partition $a1 sup $a2, $a2 sup $a3, ..."
+    property: mixfix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='partition-frequency-representation($a1,$a2)'><mo>(</mo><msup arg='a1'><mn>1</mn><mi>a</mi></msup><msup arg='a2'><mn>2</mn><mi>b</mi></msup><msup arg='a3'><mn>3</mn><mi>c</mi></msup><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/FrequencyRepresentation.html"
+  
+  - concept: partition-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: partition function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='partition-function($a1)'><mi>p</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Partition_(number_theory)"
+  
+  - concept: pauli-matrix
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: pauli matrix of $a1
+    property: "indexed symbol"
+    subject-area: "mathematical physics"
+    mathml:
+     - "<math><msub intent='pauli-matrix($a1)'><mi>σ</mi><mi arg='a1'>G</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PauliMatrices.html"
+     - "https://mathworld.wolfram.com/PauliMatrix.html"
+     - "https://en.wikipedia.org/wiki/Pauli_matrices"
+     - "https://www.encyclopediaofmath.org/index.php/Pauli_matrices"
+  
+  - concept: peclet-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: peclet number of $a1
+    property: "indexed symbol"
+    subject-area: "fluid dynamics"
+    mathml:
+     - "<math><msub intent='peclet-number($a1)'><mi>Pe</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/P%C3%A9clet_number"
+     - "https://www.encyclopediaofmath.org/index.php/Peclet_number"
+     - "https://www.encyclopediaofmath.org/index.php/Péclet_number"
+  
+  - concept: peirce-arrow
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 peirce arrow $a2
+    property: infix
+    subject-area: "logic"
+    mathml:
+     - "<math><mrow intent='peirce-arrow($a1,$a2)'><mi arg='a1'>X</mi><mo>↓</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://www.encyclopediaofmath.org/index.php/Peirce_arrow"
+  
+  - concept: pell-number
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: pell number
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='pell-number($a1)'><mi>P</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PellNumber.html"
-       - "https://en.wikipedia.org/wiki/Pell_number"
-    
-    - concept: pell-luca-number
-      arity: 1
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='pell-number($a1)'><mi>P</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PellNumber.html"
+     - "https://en.wikipedia.org/wiki/Pell_number"
+  
+  - concept: pell-luca-number
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: pell luca number
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='pell-luca-number($a1)'><mi>Q</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Pell-LucasNumber.html"
-       - "https://en.wikipedia.org/wiki/Pell_number"
-    
-    - concept: periodic-continued-fraction
-      arity: 1
-      en: periodic continued fraction $1
-      property: mfrac
-      area: "mathematical analysis"
-      mathml:
-       - "<math><mrow intent='periodic-continued-fraction($a1)'><msub><mi>a</mi><mn>0</mn></msub><mo>+</mo><mfrac arg='a1'><mn>1</mn><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>+</mo><mo>⋱</mo></mrow></mfrac></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PeriodicContinuedFraction.html"
-       - "https://en.wikipedia.org/wiki/Periodic_continued_fraction"
-    
-    - concept: permanent
-      arity: 1
-      en: permanent of $1
-      property: function
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='permanent($a1)'><mi>perm</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Permanent.html"
-       - "https://en.wikipedia.org/wiki/Permanent"
-       - "https://www.encyclopediaofmath.org/index.php/Permanent"
-    
-    - concept: permutation
-      arity: 1
-      en: permutation $1
-      property: fenced, mtable, mixfix
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='permutation($a1)'><mtable arg='a1'><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></mrow></math>"
-       - "<math><mrow intent='permutation($a1)'><mrow arg='a1'><mrow><mo>(</mo><mn>1</mn><mn>2</mn><mn>4</mn><mo>)</mo></mrow><mrow><mo>(</mo><mn>3</mn><mn>5</mn><mo>)</mo></mrow></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Permutation.html"
-       - "https://en.wikipedia.org/wiki/Permutation"
-       - "https://en.wikipedia.org/wiki/Permutation_(music)"
-       - "https://ncatlab.org/nlab/show/permutation"
-       - "https://www.encyclopediaofmath.org/index.php/Permutation"
-    
-    - concept: perpendicular
-      arity: 2
-      en: $1 perpendicular $2
-      property: infix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='perpendicular($a1,$a2)'><mi arg='a1'>X</mi><mo>⟂</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Perpendicular"
-       - "https://www.encyclopediaofmath.org/index.php/Perpendicular"
-    
-    - concept: perrin-sequence
-      arity: 1
-      en: perrin sequence of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='perrin-sequence($a1)'><mi>P</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PerrinNumber.html"
-       - "https://en.wikipedia.org/wiki/Perrin_number"
-    
-    - concept: pfaffian
-      arity: 1
-      en: pfaffian of $1
-      property: function
-      area: "multilinear algebra"
-      mathml:
-       - "<math><mrow intent='pfaffian($a1)'><mi>Pf</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='pfaffian($a1)'><mi>pf</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Pfaffian.html"
-       - "https://en.wikipedia.org/wiki/Pfaffian"
-       - "https://ncatlab.org/nlab/show/Pfaffian"
-       - "https://ncatlab.org/nlab/show/Pfaffian"
-       - "https://www.encyclopediaofmath.org/index.php/Pfaffian"
-    
-    - concept: ph
-      arity: 0
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='pell-luca-number($a1)'><mi>Q</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Pell-LucasNumber.html"
+     - "https://en.wikipedia.org/wiki/Pell_number"
+  
+  - concept: periodic-continued-fraction
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: periodic continued fraction $a1
+    property: mfrac
+    subject-area: "mathematical analysis"
+    mathml:
+     - "<math><mrow intent='periodic-continued-fraction($a1)'><msub><mi>a</mi><mn>0</mn></msub><mo>+</mo><mfrac arg='a1'><mn>1</mn><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>+</mo><mo>⋱</mo></mrow></mfrac></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PeriodicContinuedFraction.html"
+     - "https://en.wikipedia.org/wiki/Periodic_continued_fraction"
+  
+  - concept: permanent
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: permanent of $a1
+    property: function
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='permanent($a1)'><mi>perm</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Permanent.html"
+     - "https://en.wikipedia.org/wiki/Permanent"
+     - "https://www.encyclopediaofmath.org/index.php/Permanent"
+  
+  - concept: permutation
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: permutation $a1
+    property: fenced, mtable, mixfix
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='permutation($a1)'><mtable arg='a1'><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></mrow></math>"
+     - "<math><mrow intent='permutation($a1)'><mrow arg='a1'><mrow><mo>(</mo><mn>1</mn><mn>2</mn><mn>4</mn><mo>)</mo></mrow><mrow><mo>(</mo><mn>3</mn><mn>5</mn><mo>)</mo></mrow></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Permutation.html"
+     - "https://en.wikipedia.org/wiki/Permutation"
+     - "https://en.wikipedia.org/wiki/Permutation_(music)"
+     - "https://ncatlab.org/nlab/show/permutation"
+     - "https://www.encyclopediaofmath.org/index.php/Permutation"
+  
+  - concept: perpendicular
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 perpendicular $a2
+    property: infix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='perpendicular($a1,$a2)'><mi arg='a1'>X</mi><mo>⟂</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Perpendicular"
+     - "https://www.encyclopediaofmath.org/index.php/Perpendicular"
+  
+  - concept: perrin-sequence
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: perrin sequence of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='perrin-sequence($a1)'><mi>P</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PerrinNumber.html"
+     - "https://en.wikipedia.org/wiki/Perrin_number"
+  
+  - concept: pfaffian
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: pfaffian of $a1
+    property: function
+    subject-area: "multilinear algebra"
+    mathml:
+     - "<math><mrow intent='pfaffian($a1)'><mi>Pf</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='pfaffian($a1)'><mi>pf</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Pfaffian.html"
+     - "https://en.wikipedia.org/wiki/Pfaffian"
+     - "https://ncatlab.org/nlab/show/Pfaffian"
+     - "https://ncatlab.org/nlab/show/Pfaffian"
+     - "https://www.encyclopediaofmath.org/index.php/Pfaffian"
+  
+  - concept: ph
+    arity: 0
+    arguments: []
+    speech:
       en: p h
-      property: symbol
-      area: "chemistry"
-      mathml:
-       - "<math><mi intent='ph'>pH</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/PH"
-      alias:
-       - potential-of-hydrogen
-       - power-of-hydrogen
-    
-    - concept: phase
-      arity: 1
-      en: phase of $1
-      property: function
-      area: "physics"
-      mathml:
-       - "<math><mrow intent='phase($a1)'><mi>ϕ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='phase($a1)'><mi>ph</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Phase.html"
-       - "https://en.wikipedia.org/wiki/Phase_(waves)"
-       - "https://dlmf.nist.gov/1.9#E7"
-       - "https://ncatlab.org/nlab/show/phase"
-    
-    - concept: phi-coefficient
-      arity: 0
+    property: symbol
+    subject-area: "chemistry"
+    mathml:
+     - "<math><mi intent='ph'>pH</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/PH"
+    alias:
+     - potential-of-hydrogen
+     - power-of-hydrogen
+  
+  - concept: phase
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: phase of $a1
+    property: function
+    subject-area: "physics"
+    mathml:
+     - "<math><mrow intent='phase($a1)'><mi>ϕ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='phase($a1)'><mi>ph</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Phase.html"
+     - "https://en.wikipedia.org/wiki/Phase_(waves)"
+     - "https://dlmf.nist.gov/1.9#E7"
+     - "https://ncatlab.org/nlab/show/phase"
+  
+  - concept: phi-coefficient
+    arity: 0
+    arguments: []
+    speech:
       en: phi coefficient
-      property: symbol
-      area: "statistics"
-      mathml:
-       - "<math><mi intent='phi-coefficient'>φ</mi></math>"
-      notationa: "msub r φ"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Phi_coefficient"
-      alias:
-       - mean-square-contingency-coefficient
-    
-    - concept: picard-group
-      arity: 1
-      en: picard group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='picard-group($a1)'><mi>Pic</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PicardGroup.html"
-       - "https://en.wikipedia.org/wiki/Picard_group"
-       - "https://ncatlab.org/nlab/show/Picard+group"
-       - "https://www.encyclopediaofmath.org/index.php/Picard_group"
-    
-    - concept: planck-constant
-      arity: 0
+    property: symbol
+    subject-area: "statistics"
+    mathml:
+     - "<math><mi intent='phi-coefficient'>φ</mi></math>"
+    notationa: "msub r φ"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Phi_coefficient"
+    alias:
+     - mean-square-contingency-coefficient
+  
+  - concept: picard-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: picard group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='picard-group($a1)'><mi>Pic</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PicardGroup.html"
+     - "https://en.wikipedia.org/wiki/Picard_group"
+     - "https://ncatlab.org/nlab/show/Picard+group"
+     - "https://www.encyclopediaofmath.org/index.php/Picard_group"
+  
+  - concept: planck-constant
+    arity: 0
+    arguments: []
+    speech:
       en: planck constant
-      property: constant
-      area: "physics"
-      mathml:
-       - "<math><mi intent='planck-constant'>h</mi></math>"
-       - "<math><mi intent='planck-constant'>ℎ</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Planck_constant"
-       - "https://ncatlab.org/nlab/show/Planck's+constant"
-       - "https://www.encyclopediaofmath.org/index.php/Planck_constant"
-    
-    - concept: plastic-constant
-      arity: 0
+    property: constant
+    subject-area: "physics"
+    mathml:
+     - "<math><mi intent='planck-constant'>h</mi></math>"
+     - "<math><mi intent='planck-constant'>ℎ</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Planck_constant"
+     - "https://ncatlab.org/nlab/show/Planck's+constant"
+     - "https://www.encyclopediaofmath.org/index.php/Planck_constant"
+  
+  - concept: plastic-constant
+    arity: 0
+    arguments: []
+    speech:
       en: plastic constant
-      property: constant
-      area: "geometry"
-      mathml:
-       - "<math><mi intent='plastic-constant'>P</mi></math>"
-       - "<math><mi intent='plastic-constant'>p</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PlasticConstant.html"
-       - "https://en.wikipedia.org/wiki/Plastic_number"
-      alias:
-       - plastic-number
-       - platin-number
-       - minimal-pisot-number
-       - plastic-ratio
-       - siegel-number
-       - le-nombre-radiant
-    
-    - concept: playing-card-suit
-      arity: 1
+    property: constant
+    subject-area: "geometry"
+    mathml:
+     - "<math><mi intent='plastic-constant'>P</mi></math>"
+     - "<math><mi intent='plastic-constant'>p</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PlasticConstant.html"
+     - "https://en.wikipedia.org/wiki/Plastic_number"
+    alias:
+     - plastic-number
+     - platin-number
+     - minimal-pisot-number
+     - plastic-ratio
+     - siegel-number
+     - le-nombre-radiant
+  
+  - concept: playing-card-suit
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: playing card suit
-      property: unit
-      area: "game theory"
-      mathml:
-       - "<math><mrow intent='playing-card-suit($a1)'><mo arg='a1'>♣</mo></mrow></math>"
-       - "<math><mrow intent='playing-card-suit($a1)'><mo arg='a1'>♠</mo></mrow></math>"
-       - "<math><mrow intent='playing-card-suit($a1)'><mo arg='a1'>♦</mo></mrow></math>"
-       - "<math><mrow intent='playing-card-suit($a1)'><mo arg='a1'>♥</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Playing_card_suit"
-       - "https://en.wikipedia.org/wiki/Poker_probability"
-    
-    
-    - concept: plethysm
-      arity: 2
-      en: plethysm $1 $2
-      property: mixfix
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='plethysm($a1,$a2)'><mrow><mo>{</mo><mi arg='a1'>λ</mi><mo>}</mo></mrow><mo>⊗</mo><mrow><mo>{</mo><mi arg='a2'>μ</mi><mo>}</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Plethysm.html"
-       - "https://en.wikipedia.org/wiki/Plethysm"
-       - "https://ncatlab.org/nlab/show/plethysm"
-    
-    - concept: plucker-coordinate
-      arity: 2
+    property: unit
+    subject-area: "game theory"
+    mathml:
+     - "<math><mrow intent='playing-card-suit($a1)'><mo arg='a1'>♣</mo></mrow></math>"
+     - "<math><mrow intent='playing-card-suit($a1)'><mo arg='a1'>♠</mo></mrow></math>"
+     - "<math><mrow intent='playing-card-suit($a1)'><mo arg='a1'>♦</mo></mrow></math>"
+     - "<math><mrow intent='playing-card-suit($a1)'><mo arg='a1'>♥</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Playing_card_suit"
+     - "https://en.wikipedia.org/wiki/Poker_probability"
+  
+  
+  - concept: plethysm
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: plethysm $a1 $a2
+    property: mixfix
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='plethysm($a1,$a2)'><mrow><mo>{</mo><mi arg='a1'>λ</mi><mo>}</mo></mrow><mo>⊗</mo><mrow><mo>{</mo><mi arg='a2'>μ</mi><mo>}</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Plethysm.html"
+     - "https://en.wikipedia.org/wiki/Plethysm"
+     - "https://ncatlab.org/nlab/show/plethysm"
+  
+  - concept: plucker-coordinate
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: plucker coordinate
-      property: fenced
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='plucker-coordinate($a1,$a2)'><mo>(</mo><mi arg='a1'>𝐝</mi><mo>:</mo><mi arg='a2'>𝐦</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PlueckerCoordinates.html"
-       - "https://en.wikipedia.org/wiki/Pl%C3%BCcker_coordinates"
-       - "https://www.encyclopediaofmath.org/index.php/Plücker_coordinates"
-    
-    - concept: pointwise-convergent
-      arity: 1
-      en: $1 converges pointwise
-      property: postfix
-      area: "convergence"
-      mathml:
-       - "<math><mrow intent='pointwise-convergent($a1)'><mi arg='a1'>f</mi><mi>pointwise</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PointwiseConvergence.html"
-       - "https://en.wikipedia.org/wiki/Pointwise_convergence"
-       - "https://www.encyclopediaofmath.org/index.php/Pointwise_convergence"
-    
-    - concept: poisson-bracket
-      arity: 2
+    property: fenced
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='plucker-coordinate($a1,$a2)'><mo>(</mo><mi arg='a1'>𝐝</mi><mo>:</mo><mi arg='a2'>𝐦</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PlueckerCoordinates.html"
+     - "https://en.wikipedia.org/wiki/Pl%C3%BCcker_coordinates"
+     - "https://www.encyclopediaofmath.org/index.php/Plücker_coordinates"
+  
+  - concept: pointwise-convergent
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1 converges pointwise
+    property: postfix
+    subject-area: "convergence"
+    mathml:
+     - "<math><mrow intent='pointwise-convergent($a1)'><mi arg='a1'>f</mi><mi>pointwise</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PointwiseConvergence.html"
+     - "https://en.wikipedia.org/wiki/Pointwise_convergence"
+     - "https://www.encyclopediaofmath.org/index.php/Pointwise_convergence"
+  
+  - concept: poisson-bracket
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: poisson bracket
-      property: fenced
-      area: "classical mechanics"
-      mathml:
-       - "<math><mrow intent='poisson-bracket($a1,$a2)'><mo>{</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>}</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PoissonBracket.html"
-       - "https://en.wikipedia.org/wiki/Poisson_bracket"
-       - "https://www.encyclopediaofmath.org/index.php/Poisson_brackets"
-    
-    - concept: poisson-distribution
-      arity: 0
+    property: fenced
+    subject-area: "classical mechanics"
+    mathml:
+     - "<math><mrow intent='poisson-bracket($a1,$a2)'><mo>{</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>}</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PoissonBracket.html"
+     - "https://en.wikipedia.org/wiki/Poisson_bracket"
+     - "https://www.encyclopediaofmath.org/index.php/Poisson_brackets"
+  
+  - concept: poisson-distribution
+    arity: 0
+    arguments: []
+    speech:
       en: poisson distribution
-      property: symbol
-      area: "probability theory"
-      mathml:
-       - "<math><mi intent='poisson-distribution'>Pois</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PoissonDistribution.html"
-       - "https://en.wikipedia.org/wiki/Poisson_distribution"
-       - "https://en.wikipedia.org/wiki/Poisson_random_numbers"
-       - "https://www.encyclopediaofmath.org/index.php/Poisson_distribution"
-    
-    - concept: polar-set
-      arity: 1
-      en: polar set of $1
-      property: msup
-      area: "functional analysis"
-      mathml:
-       - "<math><msup intent='polar-set($a1)'><mi arg='a1'>X</mi><mo>°</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Polar_set"
-       - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)"
-       - "https://www.encyclopediaofmath.org/index.php/Polar_set"
-    
-    - concept: pollaczek-polynomial
-      arity: 1
-      en: $1<i>th</i> pollaczek polynomial
-      property: "indexed function"
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><msubsup intent='pollaczek-polynomial($a1)'><mi>P</mi><mi arg='a1'>n</mi><mrow><mo>(</mo><mi>λ</mi><mo>)</mo></mrow></msubsup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PollaczekPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Meixner%E2%80%93Pollaczek_polynomials"
-       - "https://dlmf.nist.gov/18.35#E4"
-    
-    - concept: polygamma-function
-      arity: 1
-      en: polygamma function of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='polygamma-function($a1)'><mi>ψ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PolygammaFunction.html"
-       - "https://en.wikipedia.org/wiki/Polygamma_function"
-       - "https://dlmf.nist.gov/5.15"
-       - "https://dlmf.nist.gov/5.15"
-    
-    - concept: polynomial-ring
-      arity: 2
-      en: polynomial ring $1 $2
-      property: mixfix
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='polynomial-ring($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>[</mo><mi arg='a2'>x</mi><mo>]</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Polynomial_ring#Definition_(univariate_case)"
-      alias:
-       - polynomial-algebra
-    
-    - concept: polylogarithm
-      arity: 1
-      en: polylogarithm of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='polylogarithm($a1)'><mi>Li</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Polylogarithm.html"
-       - "https://en.wikipedia.org/wiki/Polylogarithm"
-       - "https://dlmf.nist.gov/25.12#ii"
-       - "https://dlmf.nist.gov/25.12#E10"
-       - "https://ncatlab.org/nlab/show/polylogarithm"
-    
-    - concept: pontrjagin-dual
-      arity: 1
-      en: pontrjagin dual of $1
-      property: mover
-      area: "harmonic analysis"
-      mathml:
-       - "<math><mover intent='pontrjagin-dual($a1)'><mi arg='a1'>G</mi><mo>^</mo></mover></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/Pontrjagin+dual"
-       - "https://en.wikipedia.org/wiki/Pontryagin_duality#Definition"
-    
-    - concept: pontryagin-class
-      arity: 1
-      en: pontryagin class of $1
-      property: "indexed symbol"
-      area: "differential topology"
-      mathml:
-       - "<math><msub intent='pontryagin-class($a1)'><mi>p</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PontryaginClass.html"
-       - "https://en.wikipedia.org/wiki/Pontryagin_class"
-       - "https://ncatlab.org/nlab/show/Pontryagin+class"
-       - "https://www.encyclopediaofmath.org/index.php/Pontryagin_class"
-    
-    - concept: positive-part
-      arity: 1
-      en: positive part of $1
-      property: msup, msub
-      area: "elementary mathematics"
-      mathml:
-       - "<math><msup intent='positive-part($a1)'><mi arg='a1'>X</mi><mo>+</mo></msup></math>"
-      notationa: "msub $1 +"
-      urls: 
-       - "https://mathworld.wolfram.com/PositiveElement.html"
-       - "https://en.wikipedia.org/wiki/Positive_and_negative_parts"
-       - "https://www.encyclopediaofmath.org/index.php/Positive_element"
-    
-    - concept: positivitiy-predicate
-      arity: 1
-      en: positivitiy predicate of $1
-      property: prefix
-      area: "predicative mathematics"
-      mathml:
-       - "<math><mrow intent='positivitiy-predicate($a1)'><mo>◊</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/positive+element"
-    
-    - concept: post-canonical-system
-      arity: 3
-      en: post canonical system  $1 $2 $3
-      property: fenced
-      area: "formal languages"
-      mathml:
-       - "<math><mrow intent='post-canonical-system($a1)'><mo>(</mo><mi arg='a1'>A</mi><mo>,</mo><mi arg='a2'>I</mi><mo>,</mo><mi arg='a3'>R</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Post_canonical_system"
-       - "https://en.wikipedia.org/wiki/Tag_system"
-       - "https://www.encyclopediaofmath.org/index.php/Post_canonical_system"
-    
-    - concept: power-set
-      arity: 1
-      en: power set of $1
-      property: "function, msup"
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='power-set($a1)'><mi>P</mi><mi arg='a1'>X</mi></mrow></math>"
-       - "<math><mrow intent='power-set($a1)'><mi>𝒫</mi><mi arg='a1'>X</mi></mrow></math>"
-       - "<math><mrow intent='power-set($a1)'><mi>ℙ</mi><mi arg='a1'>X</mi></mrow></math>"
-       - "<math><mrow intent='power-set($a1)'><mi>℘</mi><mi arg='a1'>X</mi></mrow></math>"
-       - "<math><msup intent='power-set($a1)'><mn>2</mn><mi arg='a1'>X</mi></msup></math>"
-      notationa: "msup 2 $1"
-      urls: 
-       - "https://mathworld.wolfram.com/PowerSet.html"
-       - "https://en.wikipedia.org/wiki/Power_set"
-       - "https://ncatlab.org/nlab/show/power+set"
-    
-    - concept: preregular-space
-      arity: 0
+    property: symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mi intent='poisson-distribution'>Pois</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PoissonDistribution.html"
+     - "https://en.wikipedia.org/wiki/Poisson_distribution"
+     - "https://en.wikipedia.org/wiki/Poisson_random_numbers"
+     - "https://www.encyclopediaofmath.org/index.php/Poisson_distribution"
+  
+  - concept: polar-set
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: polar set of $a1
+    property: msup
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><msup intent='polar-set($a1)'><mi arg='a1'>X</mi><mo>°</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Polar_set"
+     - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)"
+     - "https://www.encyclopediaofmath.org/index.php/Polar_set"
+  
+  - concept: pollaczek-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> pollaczek polynomial
+    property: "indexed function"
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><msubsup intent='pollaczek-polynomial($a1)'><mi>P</mi><mi arg='a1'>n</mi><mrow><mo>(</mo><mi>λ</mi><mo>)</mo></mrow></msubsup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PollaczekPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Meixner%E2%80%93Pollaczek_polynomials"
+     - "https://dlmf.nist.gov/18.35#E4"
+  
+  - concept: polygamma-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: polygamma function of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='polygamma-function($a1)'><mi>ψ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PolygammaFunction.html"
+     - "https://en.wikipedia.org/wiki/Polygamma_function"
+     - "https://dlmf.nist.gov/5.15"
+     - "https://dlmf.nist.gov/5.15"
+  
+  - concept: polynomial-ring
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: polynomial ring $a1 $a2
+    property: mixfix
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='polynomial-ring($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>[</mo><mi arg='a2'>x</mi><mo>]</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Polynomial_ring#Definition_(univariate_case)"
+    alias:
+     - polynomial-algebra
+  
+  - concept: polylogarithm
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: polylogarithm of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='polylogarithm($a1)'><mi>Li</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Polylogarithm.html"
+     - "https://en.wikipedia.org/wiki/Polylogarithm"
+     - "https://dlmf.nist.gov/25.12#ii"
+     - "https://dlmf.nist.gov/25.12#E10"
+     - "https://ncatlab.org/nlab/show/polylogarithm"
+  
+  - concept: pontrjagin-dual
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: pontrjagin dual of $a1
+    property: mover
+    subject-area: "harmonic analysis"
+    mathml:
+     - "<math><mover intent='pontrjagin-dual($a1)'><mi arg='a1'>G</mi><mo>^</mo></mover></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/Pontrjagin+dual"
+     - "https://en.wikipedia.org/wiki/Pontryagin_duality#Definition"
+  
+  - concept: pontryagin-class
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: pontryagin class of $a1
+    property: "indexed symbol"
+    subject-area: "differential topology"
+    mathml:
+     - "<math><msub intent='pontryagin-class($a1)'><mi>p</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PontryaginClass.html"
+     - "https://en.wikipedia.org/wiki/Pontryagin_class"
+     - "https://ncatlab.org/nlab/show/Pontryagin+class"
+     - "https://www.encyclopediaofmath.org/index.php/Pontryagin_class"
+  
+  - concept: positive-part
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: positive part of $a1
+    property: msup, msub
+    subject-area: "elementary mathematics"
+    mathml:
+     - "<math><msup intent='positive-part($a1)'><mi arg='a1'>X</mi><mo>+</mo></msup></math>"
+    notationa: "msub $a1 +"
+    urls: 
+     - "https://mathworld.wolfram.com/PositiveElement.html"
+     - "https://en.wikipedia.org/wiki/Positive_and_negative_parts"
+     - "https://www.encyclopediaofmath.org/index.php/Positive_element"
+  
+  - concept: positivitiy-predicate
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: positivitiy predicate of $a1
+    property: prefix
+    subject-area: "predicative mathematics"
+    mathml:
+     - "<math><mrow intent='positivitiy-predicate($a1)'><mo>◊</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/positive+element"
+  
+  - concept: post-canonical-system
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: post canonical system  $a1 $a2 $a3
+    property: fenced
+    subject-area: "formal languages"
+    mathml:
+     - "<math><mrow intent='post-canonical-system($a1)'><mo>(</mo><mi arg='a1'>A</mi><mo>,</mo><mi arg='a2'>I</mi><mo>,</mo><mi arg='a3'>R</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Post_canonical_system"
+     - "https://en.wikipedia.org/wiki/Tag_system"
+     - "https://www.encyclopediaofmath.org/index.php/Post_canonical_system"
+  
+  - concept: power-set
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: power set of $a1
+    property: "function, msup"
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='power-set($a1)'><mi>P</mi><mi arg='a1'>X</mi></mrow></math>"
+     - "<math><mrow intent='power-set($a1)'><mi>𝒫</mi><mi arg='a1'>X</mi></mrow></math>"
+     - "<math><mrow intent='power-set($a1)'><mi>ℙ</mi><mi arg='a1'>X</mi></mrow></math>"
+     - "<math><mrow intent='power-set($a1)'><mi>℘</mi><mi arg='a1'>X</mi></mrow></math>"
+     - "<math><msup intent='power-set($a1)'><mn>2</mn><mi arg='a1'>X</mi></msup></math>"
+    notationa: "msup 2 $a1"
+    urls: 
+     - "https://mathworld.wolfram.com/PowerSet.html"
+     - "https://en.wikipedia.org/wiki/Power_set"
+     - "https://ncatlab.org/nlab/show/power+set"
+  
+  - concept: preregular-space
+    arity: 0
+    arguments: []
+    speech:
       en: preregular space
-      property: constant
-      area: "topology"
-      mathml:
-       - "<math><msub intent='preregular-space'><mi>R</mi><mn>1</mn></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions)s"
-    
-    - concept: present-value
-      arity: 0
+    property: constant
+    subject-area: "topology"
+    mathml:
+     - "<math><msub intent='preregular-space'><mi>R</mi><mn>1</mn></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions)s"
+  
+  - concept: present-value
+    arity: 0
+    arguments: []
+    speech:
       en: present value
-      property: symbol
-      area: "economics"
-      mathml:
-       - "<math><mi intent='present-value'>PV</mi></math>"
-       - "<math><mi intent='present-value'>v</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PresentValue.html"
-       - "https://en.wikipedia.org/wiki/Present_value"
-    
-    - concept: prime-constant
-      arity: 0
+    property: symbol
+    subject-area: "economics"
+    mathml:
+     - "<math><mi intent='present-value'>PV</mi></math>"
+     - "<math><mi intent='present-value'>v</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PresentValue.html"
+     - "https://en.wikipedia.org/wiki/Present_value"
+  
+  - concept: prime-constant
+    arity: 0
+    arguments: []
+    speech:
       en: prime constant
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='prime-constant'>P</mi></math>"
-       - "<math><mi intent='prime-constant'>ρ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PrimeConstant.html"
-       - "https://en.wikipedia.org/wiki/Prime_constant"
-    
-    
-    
-    - concept: prime-counting-function
-      arity: 1
-      en: prime counting function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='prime-counting-function($a1)'><mi>π</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PrimeCountingFunction.html"
-    
-    - concept: prime-difference-function
-      arity: 1
-      en: prime difference function of $1
-      property: "indexed function"
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='prime-difference-function($a1)'><mi>d</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PrimeDifferenceFunction.html"
-    
-    - concept: prime-gap
-      arity: 1
-      en: prime gap of $1
-      property: "indexed function"
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='prime-gap($a1)'><mi>G</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='prime-gap($a1)'><mi>g</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PrimeGaps.html"
-       - "https://en.wikipedia.org/wiki/Prime_gap"
-    
-    - concept: primorial
-      arity: 1
-      en: primorial of $1
-      property: postfix
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='primorial($a1)'><mi arg='a1'>x</mi><mo>#</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Primorial.html"
-       - "https://en.wikipedia.org/wiki/Primorial"
-    
-    - concept: principal-value
-      arity: 1
-      en: principal value of $1
-      property: function
-      area: "complex analysis"
-      mathml:
-       - "<math><mrow intent='principal-value($a1)'><mi>Log</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Complex_logarithm#Principal_value"
-    
-    - concept: probability-limit
-      arity: 1
-      en: probability limit of $1
-      property: "indexed function"
-      area: "probability theory"
-      mathml:
-       - "<math><mrow intent='probability-limit($a1)'><mi>plim</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_probability"
-      alias:
-       - convergence-in-probability
-    
-    - concept: product-integral
-      arity: 1
-      en: product integral of $1
-      property: indexed
-      area: "calculus"
-      mathml:
-       - "<math><mrow intent='product-integral($a1)'><mo>∏</mo><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Continuous_product"
-       - "https://en.wikipedia.org/wiki/Product_integral"
-       - "https://www.encyclopediaofmath.org/index.php/Product_integral"
-    
-    - concept: product-measure
-      arity: 2
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='prime-constant'>P</mi></math>"
+     - "<math><mi intent='prime-constant'>ρ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PrimeConstant.html"
+     - "https://en.wikipedia.org/wiki/Prime_constant"
+  
+  
+  
+  - concept: prime-counting-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: prime counting function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='prime-counting-function($a1)'><mi>π</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PrimeCountingFunction.html"
+  
+  - concept: prime-difference-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: prime difference function of $a1
+    property: "indexed function"
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='prime-difference-function($a1)'><mi>d</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PrimeDifferenceFunction.html"
+  
+  - concept: prime-gap
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: prime gap of $a1
+    property: "indexed function"
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='prime-gap($a1)'><mi>G</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='prime-gap($a1)'><mi>g</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PrimeGaps.html"
+     - "https://en.wikipedia.org/wiki/Prime_gap"
+  
+  - concept: primorial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: primorial of $a1
+    property: postfix
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='primorial($a1)'><mi arg='a1'>x</mi><mo>#</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Primorial.html"
+     - "https://en.wikipedia.org/wiki/Primorial"
+  
+  - concept: principal-value
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: principal value of $a1
+    property: function
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mrow intent='principal-value($a1)'><mi>Log</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Complex_logarithm#Principal_value"
+  
+  - concept: probability-limit
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: probability limit of $a1
+    property: "indexed function"
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mrow intent='probability-limit($a1)'><mi>plim</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_probability"
+    alias:
+     - convergence-in-probability
+  
+  - concept: product-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: product integral of $a1
+    property: indexed
+    subject-area: "calculus"
+    mathml:
+     - "<math><mrow intent='product-integral($a1)'><mo>∏</mo><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Continuous_product"
+     - "https://en.wikipedia.org/wiki/Product_integral"
+     - "https://www.encyclopediaofmath.org/index.php/Product_integral"
+  
+  - concept: product-measure
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: product measure
-      property: function
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='product-measure($a1,$a2)'><mi arg='a1'>x</mi><mo>×</mo><mi arg='a2'>y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ProductMeasure.html"
-       - "https://en.wikipedia.org/wiki/Product_measure"
-    
-    - concept: projective-line
-      arity: 1
-      en: projective line of $1
-      property: function
-      area: "projective geometry"
-      mathml:
-       - "<math><mrow intent='projective-line($a1)'><mi>P</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Projective_line"
-       - "https://ncatlab.org/nlab/show/projective+line"
-    
-    - concept: projective-space
-      arity: 0
+    property: function
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='product-measure($a1,$a2)'><mi arg='a1'>x</mi><mo>×</mo><mi arg='a2'>y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ProductMeasure.html"
+     - "https://en.wikipedia.org/wiki/Product_measure"
+  
+  - concept: projective-line
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: projective line of $a1
+    property: function
+    subject-area: "projective geometry"
+    mathml:
+     - "<math><mrow intent='projective-line($a1)'><mi>P</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Projective_line"
+     - "https://ncatlab.org/nlab/show/projective+line"
+  
+  - concept: projective-space
+    arity: 0
+    arguments: []
+    speech:
       en: projective space
-      property: symbol
-      area: "projective geometry"
-      mathml:
-       - "<math><mi intent='projective-space'>ℙ</mi></math>"
-      notationa: "mi ℝ⁢ ℙ"
-      urls: 
-       - "https://mathworld.wolfram.com/ProjectiveSpace.html"
-       - "https://en.wikipedia.org/wiki/Algebraic_geometry_of_projective_spaces"
-       - "https://en.wikipedia.org/wiki/Projective_space"
-       - "https://ncatlab.org/nlab/show/projective+space"
-       - "https://www.encyclopediaofmath.org/index.php/Projective_space"
-      alias:
-       - real-projective-space
-    
-    - concept: proper-subgroup
-      arity: 2
-      en: $1 proper subgroup $2
-      property: infix
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='proper-subgroup($a1,$a2)'><mi arg='a1'>X</mi><mo>&lt;</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Subgroup"
-    
-    - concept: proportional
-      arity: 2
-      en: $1 proportional $2
-      property: infix
-      area: "arithmetic"
-      mathml:
-       - "<math><mrow intent='proportional($a1,$a2)'><mi arg='a1'>X</mi><mo>∝</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='proportional($a1,$a2)'><mi arg='a1'>X</mi><mo>~</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Proportional.html"
-       - "https://en.wikipedia.org/wiki/Proportionality_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Proportional_(fair_division)"
-      alias:
-       - directly-proportional
-    
-    - concept: prouhet-thue-morse-constant
-      arity: 0
+    property: symbol
+    subject-area: "projective geometry"
+    mathml:
+     - "<math><mi intent='projective-space'>ℙ</mi></math>"
+    notationa: "mi ℝ⁢ ℙ"
+    urls: 
+     - "https://mathworld.wolfram.com/ProjectiveSpace.html"
+     - "https://en.wikipedia.org/wiki/Algebraic_geometry_of_projective_spaces"
+     - "https://en.wikipedia.org/wiki/Projective_space"
+     - "https://ncatlab.org/nlab/show/projective+space"
+     - "https://www.encyclopediaofmath.org/index.php/Projective_space"
+    alias:
+     - real-projective-space
+  
+  - concept: proper-subgroup
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 proper subgroup $a2
+    property: infix
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='proper-subgroup($a1,$a2)'><mi arg='a1'>X</mi><mo>&lt;</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Subgroup"
+  
+  - concept: proportional
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 proportional $a2
+    property: infix
+    subject-area: "arithmetic"
+    mathml:
+     - "<math><mrow intent='proportional($a1,$a2)'><mi arg='a1'>X</mi><mo>∝</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='proportional($a1,$a2)'><mi arg='a1'>X</mi><mo>~</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Proportional.html"
+     - "https://en.wikipedia.org/wiki/Proportionality_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Proportional_(fair_division)"
+    alias:
+     - directly-proportional
+  
+  - concept: prouhet-thue-morse-constant
+    arity: 0
+    arguments: []
+    speech:
       en: prouhet thue morse constant
-      property: constant
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='prouhet-thue-morse-constant'>τ</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Prouhet%E2%80%93Thue%E2%80%93Morse_constant"
-    
-    - concept: prufer-group
-      arity: 1
-      en: prufer group of $1
-      property: mixfix
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='prufer-group($a1)'><mi>𝐙</mi><mrow><mo>(</mo><msup><mi arg='a1'>p</mi><mo>∞</mo></msup><mo>)</mo></mrow></mrow></math>"
-      notation: "mrow Z ( msup $1 ∞ /msup"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Pr%C3%BCfer_group"
-      alias:
-       - quasicyclic-group
-    
-    - concept: pseudovector
-      arity: 1
-      en: pseudovector $1
-      property: mixfix
-      area: "vector calculus"
-      mathml:
-       - "<math><mrow intent='pseudovector($a1)'><mi arg='a1'>v</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Pseudovector.html"
-       - "https://en.wikipedia.org/wiki/Pseudovector"
-      alias:
-       - axial-vector
-    
-    - concept: pseudo-inner-product
-      arity: 2
+    property: constant
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='prouhet-thue-morse-constant'>τ</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Prouhet%E2%80%93Thue%E2%80%93Morse_constant"
+  
+  - concept: prufer-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: prufer group of $a1
+    property: mixfix
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='prufer-group($a1)'><mi>𝐙</mi><mrow><mo>(</mo><msup><mi arg='a1'>p</mi><mo>∞</mo></msup><mo>)</mo></mrow></mrow></math>"
+    notation: "mrow Z ( msup $a1 ∞ /msup"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Pr%C3%BCfer_group"
+    alias:
+     - quasicyclic-group
+  
+  - concept: pseudovector
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: pseudovector $a1
+    property: mixfix
+    subject-area: "vector calculus"
+    mathml:
+     - "<math><mrow intent='pseudovector($a1)'><mi arg='a1'>v</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Pseudovector.html"
+     - "https://en.wikipedia.org/wiki/Pseudovector"
+    alias:
+     - axial-vector
+  
+  - concept: pseudo-inner-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: pseudo inner product
-      property: fenced
-      area: "lie algebra"
-      mathml:
-       - "<math><mrow intent='pseudo-inner-product($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://youtu.be/mJ8ZDdA10GY?t=870"
-    
-    - concept: pullback
-      arity: 0
+    property: fenced
+    subject-area: "lie algebra"
+    mathml:
+     - "<math><mrow intent='pseudo-inner-product($a1,$a2)'><mo>(</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://youtu.be/mJ8ZDdA10GY?t=870"
+  
+  - concept: pullback
+    arity: 0
+    arguments: []
+    speech:
       en: pullback
-      property: symbol
-      area: "differential geometry"
-      mathml:
-       - "<math><msup intent='pullback'><mi>φ</mi><mo>*</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Pullback_(differential_geometry)"
-    
-    - concept: pushforward
-      arity: 2
-      en: $1 pushforward $2
-      property: infix
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='pushforward($a1,$a2)'><mi arg='a1'>X</mi><mo>*</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://youtu.be/mJ8ZDdA10GY?t=2555"
-       - "https://en.wikipedia.org/wiki/Pushforward_(differential)"
-    
-    - concept: pythagoras-constant
-      arity: 0
+    property: symbol
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><msup intent='pullback'><mi>φ</mi><mo>*</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Pullback_(differential_geometry)"
+  
+  - concept: pushforward
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 pushforward $a2
+    property: infix
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='pushforward($a1,$a2)'><mi arg='a1'>X</mi><mo>*</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://youtu.be/mJ8ZDdA10GY?t=2555"
+     - "https://en.wikipedia.org/wiki/Pushforward_(differential)"
+  
+  - concept: pythagoras-constant
+    arity: 0
+    arguments: []
+    speech:
       en: pythagoras constant
-      property: constant
-      area: "geometry"
-      mathml:
-       - "<math><msqrt intent='pythagoras-constant'><mn>2</mn></msqrt></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PythagorassConstant.html"
-       - "https://en.wikipedia.org/wiki/Sqrt(2)"
-       - "https://en.wikipedia.org/wiki/%E2%88%9A2"
-       - "https://en.wikipedia.org/wiki/Square_root_of_2"
-      alias:
-       - pythagoras-number
-    
-    - concept: pythagorean-triple
-      arity: 3
-      en: pythagorean triple  $1, $2 and $3
-      property: fenced
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='pythagorean-triple($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/PythagoreanTriple.html"
-       - "https://en.wikipedia.org/wiki/Pythagorean_triple"
-    
-    - concept: q-binomial-coefficient
-      arity: 3
-      en: $3 q binomial coefficient of $1, $2
-      property: fenced-stacked
-      area: "combinatorics"
-      mathml:
-       - "<math><msub intent='q-binomial-coefficient($a1,$a2,$a3)'><mrow><mo>[</mo><mfrac linethickness='0pt'><mi arg='a1'>n</mi><mi arg='a2'>m</mi></mfrac><mo>]</mo></mrow><mi arg='a3'>q</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/q-BinomialCoefficient.html"
-    
-    - concept: qed
-      arity: 0
+    property: constant
+    subject-area: "geometry"
+    mathml:
+     - "<math><msqrt intent='pythagoras-constant'><mn>2</mn></msqrt></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PythagorassConstant.html"
+     - "https://en.wikipedia.org/wiki/Sqrt(2)"
+     - "https://en.wikipedia.org/wiki/%E2%88%9A2"
+     - "https://en.wikipedia.org/wiki/Square_root_of_2"
+    alias:
+     - pythagoras-number
+  
+  - concept: pythagorean-triple
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: pythagorean triple  $a1, $a2 and $a3
+    property: fenced
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='pythagorean-triple($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/PythagoreanTriple.html"
+     - "https://en.wikipedia.org/wiki/Pythagorean_triple"
+  
+  - concept: q-binomial-coefficient
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: $a3 q binomial coefficient of $a1, $a2
+    property: fenced-stacked
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><msub intent='q-binomial-coefficient($a1,$a2,$a3)'><mrow><mo>[</mo><mfrac linethickness='0pt'><mi arg='a1'>n</mi><mi arg='a2'>m</mi></mfrac><mo>]</mo></mrow><mi arg='a3'>q</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/q-BinomialCoefficient.html"
+  
+  - concept: qed
+    arity: 0
+    arguments: []
+    speech:
       en: qed
-      property: symbol
-      area: "mathematical symbols"
-      mathml:
-       - "<math><mo intent='qed'>□</mo></math>"
-       - "<math><mo intent='qed'>∎</mo></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Tombstone_(typography)"
-      alias:
-       - end-of-proof
-       - quod-erat-demonstrandum
-    
-    - concept: quadratic-differential
-      arity: 1
-      en: quadratic differential of $1
-      property: mixfix
-      area: "complex manifolds"
-      mathml:
-       - "<math><mrow intent='quadratic-differential($a1)'><mi arg='a1'>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mrow><mi>d</mi><mi>z</mi></mrow><mo>⊗</mo><mrow><mi>d</mi><mi>z</mi></mrow></mrow></math>"
-      notation: "mrow d $1 d $1"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Quadratic_differential"
-       - "https://ncatlab.org/nlab/show/quadratic+differential"
-       - "https://www.encyclopediaofmath.org/index.php/Quadratic_differential"
-    
-    - concept: quadratic-variation
-      arity: 2
-      en: quadratic variation $1 $2
-      property: indexed fenced
-      area: "stochastic processes"
-      mathml:
-       - "<math><msub intent='quadratic-variation($a1,$a2)'><mrow><mo>[</mo><mi arg='a1'>X</mi><mo>]</mo></mrow><mi arg='a2'>t</mi></msub></math>"
-      notation: "msub mrow [ $1 ] /mrow $2"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Quadratic_variation"
-    
-    - concept: quadrilateral
-      arity: 1
-      en: quadrilateral of $1
-      property: prefix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='quadrilateral($a1)'><mo>◻</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Quadrangle.html"
-       - "https://en.wikipedia.org/wiki/Quadrilateral"
-       - "https://www.encyclopediaofmath.org/index.php/Quadrangle"
-      alias:
-       - quadrangle
-    
-    - concept: quotient-group
-      arity: 2
-      en: $1 quotient group $2
-      property: infix
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='quotient-group($a1,$a2)'><mi arg='a1'>X</mi><mo>/</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/QuotientGroup.html"
-       - "https://ncatlab.org/nlab/show/quotient+group"
-       - "https://www.encyclopediaofmath.org/index.php/Quotient_group"
-    
-    - concept: quotient-space
-      arity: 2
-      en: $1 quotient space $2
-      property: infix
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='quotient-space($a1,$a2)'><mi arg='a1'>X</mi><mo>/</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/QuotientSpace.html"
-       - "https://en.wikipedia.org/wiki/Quotient_space_(topology)"
-       - "https://en.wikipedia.org/wiki/Quotient_space_(linear_algebra)"
-       - "https://ncatlab.org/nlab/show/quotient+space"
-       - "https://www.encyclopediaofmath.org/index.php/Quotient_space"
-      alias:
-       - quotient-set
-    
-    - concept: r-complexity-class
-      arity: 0
+    property: symbol
+    subject-area: "mathematical symbols"
+    mathml:
+     - "<math><mo intent='qed'>□</mo></math>"
+     - "<math><mo intent='qed'>∎</mo></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Tombstone_(typography)"
+    alias:
+     - end-of-proof
+     - quod-erat-demonstrandum
+  
+  - concept: quadratic-differential
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: quadratic differential of $a1
+    property: mixfix
+    subject-area: "complex manifolds"
+    mathml:
+     - "<math><mrow intent='quadratic-differential($a1)'><mi arg='a1'>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mrow><mi>d</mi><mi>z</mi></mrow><mo>⊗</mo><mrow><mi>d</mi><mi>z</mi></mrow></mrow></math>"
+    notation: "mrow d $a1 d $a1"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Quadratic_differential"
+     - "https://ncatlab.org/nlab/show/quadratic+differential"
+     - "https://www.encyclopediaofmath.org/index.php/Quadratic_differential"
+  
+  - concept: quadratic-variation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: quadratic variation $a1 $a2
+    property: indexed fenced
+    subject-area: "stochastic processes"
+    mathml:
+     - "<math><msub intent='quadratic-variation($a1,$a2)'><mrow><mo>[</mo><mi arg='a1'>X</mi><mo>]</mo></mrow><mi arg='a2'>t</mi></msub></math>"
+    notation: "msub mrow [ $a1 ] /mrow $a2"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Quadratic_variation"
+  
+  - concept: quadrilateral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: quadrilateral of $a1
+    property: prefix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='quadrilateral($a1)'><mo>◻</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Quadrangle.html"
+     - "https://en.wikipedia.org/wiki/Quadrilateral"
+     - "https://www.encyclopediaofmath.org/index.php/Quadrangle"
+    alias:
+     - quadrangle
+  
+  - concept: quotient-group
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 quotient group $a2
+    property: infix
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='quotient-group($a1,$a2)'><mi arg='a1'>X</mi><mo>/</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/QuotientGroup.html"
+     - "https://ncatlab.org/nlab/show/quotient+group"
+     - "https://www.encyclopediaofmath.org/index.php/Quotient_group"
+  
+  - concept: quotient-space
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 quotient space $a2
+    property: infix
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='quotient-space($a1,$a2)'><mi arg='a1'>X</mi><mo>/</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/QuotientSpace.html"
+     - "https://en.wikipedia.org/wiki/Quotient_space_(topology)"
+     - "https://en.wikipedia.org/wiki/Quotient_space_(linear_algebra)"
+     - "https://ncatlab.org/nlab/show/quotient+space"
+     - "https://www.encyclopediaofmath.org/index.php/Quotient_space"
+    alias:
+     - quotient-set
+  
+  - concept: r-complexity-class
+    arity: 0
+    arguments: []
+    speech:
       en: r complexity class
-      property: symbol
-      area: "complexity theory"
-      mathml:
-       - "<math><mi intent='r-complexity-class'>R</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/R.html"
-       - "https://en.wikipedia.org/wiki/R_(complexity)"
-       - "https://en.wikipedia.org/wiki/R_(cross_section_ratio)"
-    
-    - concept: racah-polynomial
-      arity: 1
-      en: racah polynomial of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='racah-polynomial($a1)'><mi>R</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RacahPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Racah_polynomials"
-       - "https://dlmf.nist.gov/18.25#T1.t1.r4"
-    
-    - concept: radial-mathieu-function
-      arity: 1
-      en: radial mathieu function of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='radial-mathieu-function($a1)'><mi>Mc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='radial-mathieu-function($a1)'><mi>Ms</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://dlmf.nist.gov/28.20#iv"
-       - "https://dlmf.nist.gov/28.20#E15"
-       - "https://dlmf.nist.gov/28.20#E16"
-    
-    - concept: radical
-      arity: 1
-      en: radical of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='radical($a1)'><mi>rad</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Radical.html"
-       - "https://en.wikipedia.org/wiki/Radical_of_a_Lie_algebra"
-       - "https://en.wikipedia.org/wiki/Radical_of_an_integer"
-       - "https://en.wikipedia.org/wiki/Radical_of_a_module"
-       - "https://ncatlab.org/nlab/show/radical"
-       - "https://www.encyclopediaofmath.org/index.php/Radical"
-    
-    - concept: radius-vector
-      arity: 0
+    property: symbol
+    subject-area: "complexity theory"
+    mathml:
+     - "<math><mi intent='r-complexity-class'>R</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/R.html"
+     - "https://en.wikipedia.org/wiki/R_(complexity)"
+     - "https://en.wikipedia.org/wiki/R_(cross_section_ratio)"
+  
+  - concept: racah-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: racah polynomial of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='racah-polynomial($a1)'><mi>R</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RacahPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Racah_polynomials"
+     - "https://dlmf.nist.gov/18.25#T1.t1.r4"
+  
+  - concept: radial-mathieu-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: radial mathieu function of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='radial-mathieu-function($a1)'><mi>Mc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='radial-mathieu-function($a1)'><mi>Ms</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://dlmf.nist.gov/28.20#iv"
+     - "https://dlmf.nist.gov/28.20#E15"
+     - "https://dlmf.nist.gov/28.20#E16"
+  
+  - concept: radical
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: radical of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='radical($a1)'><mi>rad</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Radical.html"
+     - "https://en.wikipedia.org/wiki/Radical_of_a_Lie_algebra"
+     - "https://en.wikipedia.org/wiki/Radical_of_an_integer"
+     - "https://en.wikipedia.org/wiki/Radical_of_a_module"
+     - "https://ncatlab.org/nlab/show/radical"
+     - "https://www.encyclopediaofmath.org/index.php/Radical"
+  
+  - concept: radius-vector
+    arity: 0
+    arguments: []
+    speech:
       en: radius vector
-      property: symbol
-      area: "geometry"
-      mathml:
-       - "<math><mi intent='radius-vector'>x</mi></math>"
-       - "<math><mi intent='radius-vector'>r</mi></math>"
-       - "<math><mi intent='radius-vector'>s</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RadiusVector.html"
-       - "https://en.wikipedia.org/wiki/Position_(vector)"
-       - "https://www.encyclopediaofmath.org/index.php/Radius_vector"
-      alias:
-       - location-vector
-       - position-vector
-       - position
-    
-    - concept: ramanujan-sum
-      arity: 1
-      en: ramanujan sum of $1
-      property: "indexed function"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='ramanujan-sum($a1)'><mi>c</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RamanujansSum.html"
-       - "https://dlmf.nist.gov/27.10#E4"
-       - "https://www.encyclopediaofmath.org/index.php/Ramanujan_sums"
-    
-    - concept: ramanujan-tau-function
-      arity: 1
-      en: ramanujan tau function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='ramanujan-tau-function($a1)'><mi>τ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RamanujansTauFunction.html"
-       - "https://en.wikipedia.org/wiki/Ramanujan_tau_function"
-       - "https://dlmf.nist.gov/27.14#E18"
-    
-    - concept: ramanujan-soldner-constant
-      arity: 0
+    property: symbol
+    subject-area: "geometry"
+    mathml:
+     - "<math><mi intent='radius-vector'>x</mi></math>"
+     - "<math><mi intent='radius-vector'>r</mi></math>"
+     - "<math><mi intent='radius-vector'>s</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RadiusVector.html"
+     - "https://en.wikipedia.org/wiki/Position_(vector)"
+     - "https://www.encyclopediaofmath.org/index.php/Radius_vector"
+    alias:
+     - location-vector
+     - position-vector
+     - position
+  
+  - concept: ramanujan-sum
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: ramanujan sum of $a1
+    property: "indexed function"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='ramanujan-sum($a1)'><mi>c</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RamanujansSum.html"
+     - "https://dlmf.nist.gov/27.10#E4"
+     - "https://www.encyclopediaofmath.org/index.php/Ramanujan_sums"
+  
+  - concept: ramanujan-tau-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: ramanujan tau function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='ramanujan-tau-function($a1)'><mi>τ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RamanujansTauFunction.html"
+     - "https://en.wikipedia.org/wiki/Ramanujan_tau_function"
+     - "https://dlmf.nist.gov/27.14#E18"
+  
+  - concept: ramanujan-soldner-constant
+    arity: 0
+    arguments: []
+    speech:
       en: ramanujan soldner constant
-      property: constant
-      area: "special functions"
-      mathml:
-       - "<math><mi intent='ramanujan-soldner-constant'>μ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Ramanujan-SoldnerConstant.html"
-       - "https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Soldner_constant"
-       - "https://mathworld.wolfram.com/SoldnersConstant.html"
-      alias:
-       - soldner-constant
-    
-    - concept: ramification-index
-      arity: 1
-      en: ramification index of $1
-      property: msub
-      area: "algebraic number theory"
-      mathml:
-       - "<math><msub intent='ramification-index($a1)'><mi>e</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RamificationIndex.html"
-       - "https://en.wikipedia.org/wiki/Ramification_(mathematics)#In_algebraic_number_theory"
-    
-    - concept: ramsey-number
-      arity: 1
-      en: ramsey number of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='ramsey-number($a1)'><mi>R</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RamseyNumber.html"
-       - "https://www.encyclopediaofmath.org/index.php/Ramsey_number"
-    
-    - concept: rank
-      arity: 1
-      en: rank of $1
-      property: function
-      area: "graph theory, linear algebra, "
-      mathml:
-       - "<math><mrow intent='rank($a1)'><mi>r</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='rank($a1)'><mi>rank</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='rank($a1)'><mi>rk</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Rank.html"
-       - "https://en.wikipedia.org/wiki/Rank_(graph_theory)"
-       - "https://en.wikipedia.org/wiki/Rank_(linear_algebra)"
-       - "https://en.wikipedia.org/wiki/Rank_(differential_topology)"
-       - "https://ncatlab.org/nlab/show/rank"
-       - "https://www.encyclopediaofmath.org/index.php/Rank"
-    
-    - concept: real-bipolar
-      arity: 1
-      en: real bipolar of $1
-      property: msup
-      area: "functional analysis"
-      mathml:
-       - "<math><msup intent='real-bipolar($a1)'><mi arg='a1'>A</mi><mo>∘</mo></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Polar_set"
-       - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)"
-       - "https://www.encyclopediaofmath.org/index.php/Polar_set"
-    
-    - concept: real-part
-      arity: 1
-      en: real part of $1
-      property: function
-      area: "complex analysis"
-      mathml:
-       - "<math><mrow intent='real-part($a1)'><mi>ℜ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='real-part($a1)'><mi>Re</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='real-part($a1)'><mi>ℛℯ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RealPart.html"
-       - "https://dlmf.nist.gov/1.9#E2"
-       - "https://en.wikipedia.org/wiki/Complex_number#Notation"
-    
-    - concept: real-prepolar
-      arity: 1
-      en: real prepolar of $1
-      property: prescript
-      area: "functional analysis"
-      mathml:
-       - "<math><mmultiscripts intent='real-prepolar($a1)'><mi arg='a1'>B</mi><mprescripts/><mrow/><mo>∘</mo></mmultiscripts></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Polar_set"
-       - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)"
-       - "https://www.encyclopediaofmath.org/index.php/Polar_set"
-    
-    - concept: real-polar
-      arity: 1
-      en: real polar of $1
-      property: msup
-      area: "functional analysis"
-      mathml:
-       - "<math><msup intent='real-polar($a1)'><mi arg='a1'>X</mi><mi>r</mi></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Polar_set"
-       - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)"
-       - "https://www.encyclopediaofmath.org/index.php/Polar_set"
-    
-    - concept: recession-cone
-      arity: 1
-      en: recession cone of $1
-      property: function
-      area: "convex analysis"
-      mathml:
-       - "<math><mrow intent='recession-cone($a1)'><mi>recc</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Recession_cone"
-    
-    - concept: reciprocal-polynomial
-      arity: 1
-      en: reciprocal polynomial of $1
-      property: msup
-      area: "algebra"
-      mathml:
-       - "<math><msup intent='reciprocal-polynomial($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
-       - "<math><msup intent='reciprocal-polynomial($a1)'><mi arg='a1'>X</mi><mi>R</mi></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ReciprocalPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Reciprocal_polynomial"
-      alias:
-       - reflected-polynomial
-    
-    - concept: rectification
-      arity: 1
-      en: rectification of $1
-      property: function
-      area: "euclidean geometry"
-      mathml:
-       - "<math><mrow intent='rectification($a1)'><mi>r</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Rectification.html"
-       - "https://en.wikipedia.org/wiki/Rectification_(geometry)"
-       - "https://ncatlab.org/nlab/show/rectification"
-    
-    - concept: reduced-suspension
-      arity: 1
-      en: reduced suspension of $1
-      property: function
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='reduced-suspension($a1)'><mi>Σ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Suspension_(topology)"
-    
-    - concept: relative-homology
-      arity: 1
-      en: relative homology of $1
-      property: "indexed function"
-      area: "algebraic topology"
-      mathml:
-       - "<math><mrow intent='relative-homology($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Relative_homology"
-       - "https://ncatlab.org/nlab/show/relative+homology"
-       - "https://www.encyclopediaofmath.org/index.php/Relative_homology"
-    
-    - concept: repunit
-      arity: 1
-      en: repunit of $1
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='repunit($a1)'><mi>R</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Repunit.html"
-       - "https://en.wikipedia.org/wiki/Repunit"
-       - "https://en.wikipedia.org/wiki/Repunit_prime"
-    
-    - concept: residue
-      arity: 1
-      en: residue of $1
-      property: function
-      area: "complex analysis"
-      mathml:
-       - "<math><mrow intent='residue($a1)'><mi>Res</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='residue($a1)'><mi>res</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Residue.html"
-       - "https://en.wikipedia.org/wiki/Residue_(complex_analysis)"
-       - "https://dlmf.nist.gov/1.10#SS3.p5"
-    
-    - concept: resolvent
-      arity: 1
+    property: constant
+    subject-area: "special functions"
+    mathml:
+     - "<math><mi intent='ramanujan-soldner-constant'>μ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Ramanujan-SoldnerConstant.html"
+     - "https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Soldner_constant"
+     - "https://mathworld.wolfram.com/SoldnersConstant.html"
+    alias:
+     - soldner-constant
+  
+  - concept: ramification-index
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: ramification index of $a1
+    property: msub
+    subject-area: "algebraic number theory"
+    mathml:
+     - "<math><msub intent='ramification-index($a1)'><mi>e</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RamificationIndex.html"
+     - "https://en.wikipedia.org/wiki/Ramification_(mathematics)#In_algebraic_number_theory"
+  
+  - concept: ramsey-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: ramsey number of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='ramsey-number($a1)'><mi>R</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RamseyNumber.html"
+     - "https://www.encyclopediaofmath.org/index.php/Ramsey_number"
+  
+  - concept: rank
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: rank of $a1
+    property: function
+    subject-area: "graph theory, linear algebra, "
+    mathml:
+     - "<math><mrow intent='rank($a1)'><mi>r</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='rank($a1)'><mi>rank</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='rank($a1)'><mi>rk</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Rank.html"
+     - "https://en.wikipedia.org/wiki/Rank_(graph_theory)"
+     - "https://en.wikipedia.org/wiki/Rank_(linear_algebra)"
+     - "https://en.wikipedia.org/wiki/Rank_(differential_topology)"
+     - "https://ncatlab.org/nlab/show/rank"
+     - "https://www.encyclopediaofmath.org/index.php/Rank"
+  
+  - concept: real-bipolar
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: real bipolar of $a1
+    property: msup
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><msup intent='real-bipolar($a1)'><mi arg='a1'>A</mi><mo>∘</mo></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Polar_set"
+     - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)"
+     - "https://www.encyclopediaofmath.org/index.php/Polar_set"
+  
+  - concept: real-part
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: real part of $a1
+    property: function
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mrow intent='real-part($a1)'><mi>ℜ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='real-part($a1)'><mi>Re</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='real-part($a1)'><mi>ℛℯ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RealPart.html"
+     - "https://dlmf.nist.gov/1.9#E2"
+     - "https://en.wikipedia.org/wiki/Complex_number#Notation"
+  
+  - concept: real-prepolar
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: real prepolar of $a1
+    property: prescript
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><mmultiscripts intent='real-prepolar($a1)'><mi arg='a1'>B</mi><mprescripts/><mrow/><mo>∘</mo></mmultiscripts></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Polar_set"
+     - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)"
+     - "https://www.encyclopediaofmath.org/index.php/Polar_set"
+  
+  - concept: real-polar
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: real polar of $a1
+    property: msup
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><msup intent='real-polar($a1)'><mi arg='a1'>X</mi><mi>r</mi></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Polar_set"
+     - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)"
+     - "https://www.encyclopediaofmath.org/index.php/Polar_set"
+  
+  - concept: recession-cone
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: recession cone of $a1
+    property: function
+    subject-area: "convex analysis"
+    mathml:
+     - "<math><mrow intent='recession-cone($a1)'><mi>recc</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Recession_cone"
+  
+  - concept: reciprocal-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: reciprocal polynomial of $a1
+    property: msup
+    subject-area: "algebra"
+    mathml:
+     - "<math><msup intent='reciprocal-polynomial($a1)'><mi arg='a1'>X</mi><mo>*</mo></msup></math>"
+     - "<math><msup intent='reciprocal-polynomial($a1)'><mi arg='a1'>X</mi><mi>R</mi></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ReciprocalPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Reciprocal_polynomial"
+    alias:
+     - reflected-polynomial
+  
+  - concept: rectification
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: rectification of $a1
+    property: function
+    subject-area: "euclidean geometry"
+    mathml:
+     - "<math><mrow intent='rectification($a1)'><mi>r</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Rectification.html"
+     - "https://en.wikipedia.org/wiki/Rectification_(geometry)"
+     - "https://ncatlab.org/nlab/show/rectification"
+  
+  - concept: reduced-suspension
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: reduced suspension of $a1
+    property: function
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='reduced-suspension($a1)'><mi>Σ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Suspension_(topology)"
+  
+  - concept: relative-homology
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: relative homology of $a1
+    property: "indexed function"
+    subject-area: "algebraic topology"
+    mathml:
+     - "<math><mrow intent='relative-homology($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Relative_homology"
+     - "https://ncatlab.org/nlab/show/relative+homology"
+     - "https://www.encyclopediaofmath.org/index.php/Relative_homology"
+  
+  - concept: repunit
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: repunit of $a1
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='repunit($a1)'><mi>R</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Repunit.html"
+     - "https://en.wikipedia.org/wiki/Repunit"
+     - "https://en.wikipedia.org/wiki/Repunit_prime"
+  
+  - concept: residue
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: residue of $a1
+    property: function
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mrow intent='residue($a1)'><mi>Res</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='residue($a1)'><mi>res</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Residue.html"
+     - "https://en.wikipedia.org/wiki/Residue_(complex_analysis)"
+     - "https://dlmf.nist.gov/1.10#SS3.p5"
+  
+  - concept: resolvent
+    arity: 1
+    arguments: [$a1]
+    speech:
       en: resolvent
-      property: "indexed function"
-      area: "galois theory"
-      mathml:
-       - "<math><msub intent='resolvent($a1)'><mi>R</mi><mi arg='a1'>G</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Resolvent.html"
-       - "https://en.wikipedia.org/wiki/Resolvent_(Galois_theory)"
-       - "https://www.encyclopediaofmath.org/index.php/Resolvent"
-    
-    - concept: resolvent-set
-      arity: 1
-      en: resolvent set of $1
-      property: function
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='resolvent-set($a1)'><mi>ρ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Resolvent_set"
-       - "https://www.encyclopediaofmath.org/index.php/Resolvent_set"
-    
-    - concept: restricted-quantifier
-      arity: 2
-      en: restricted quantifier $1 $2
-      property: mixfix
-      area: "formal logic"
-      mathml:
-       - "<math><mrow intent='restricted-quantifier($a1,$a2)'><msub><mrow><mo>(</mo><mo>∀</mo><mi arg='a1'>x</mi><mo>)</mo></mrow><mi arg='a2'>R</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='restricted-quantifier($a1,$a2)'><msub><mrow><mo>(</mo><mo>∃</mo><mi arg='a1'>x</mi><mo>)</mo></mrow><mi arg='a2'>R</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://www.encyclopediaofmath.org/index.php/Restricted_quantifier"
-       - "https://human.libretexts.org/Bookshelves/Philosophy/Book%3A_A_Modern_Formal_Logic_Primer_(Teller)/Volume_II%3A_Predicate_Logic/4%3A_Transcription/4.1%3A_Restricted_Quantifiers"
-    
-    - concept: restricted-wreath-product
-      arity: 2
-      en: $1 restricted wreath product $2
-      property: infix
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='restricted-wreath-product($a1,$a2)'><mi arg='a1'>X</mi><mi>wr</mi><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='restricted-wreath-product($a1,$a2)'><mi arg='a1'>X</mi><msub><mi>wr</mi><mi>&#x03a9;</mi></msub><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WreathProduct.html"
-       - "https://en.wikipedia.org/wiki/Wreath_product"
-       - "https://ncatlab.org/nlab/show/wreath+product"
-       - "https://www.encyclopediaofmath.org/index.php/Wreath_product"
-    
-    - concept: restriction
-      arity: 2
+    property: "indexed function"
+    subject-area: "galois theory"
+    mathml:
+     - "<math><msub intent='resolvent($a1)'><mi>R</mi><mi arg='a1'>G</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Resolvent.html"
+     - "https://en.wikipedia.org/wiki/Resolvent_(Galois_theory)"
+     - "https://www.encyclopediaofmath.org/index.php/Resolvent"
+  
+  - concept: resolvent-set
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: resolvent set of $a1
+    property: function
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='resolvent-set($a1)'><mi>ρ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Resolvent_set"
+     - "https://www.encyclopediaofmath.org/index.php/Resolvent_set"
+  
+  - concept: restricted-quantifier
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: restricted quantifier $a1 $a2
+    property: mixfix
+    subject-area: "formal logic"
+    mathml:
+     - "<math><mrow intent='restricted-quantifier($a1,$a2)'><msub><mrow><mo>(</mo><mo>∀</mo><mi arg='a1'>x</mi><mo>)</mo></mrow><mi arg='a2'>R</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='restricted-quantifier($a1,$a2)'><msub><mrow><mo>(</mo><mo>∃</mo><mi arg='a1'>x</mi><mo>)</mo></mrow><mi arg='a2'>R</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://www.encyclopediaofmath.org/index.php/Restricted_quantifier"
+     - "https://human.libretexts.org/Bookshelves/Philosophy/Book%3A_A_Modern_Formal_Logic_Primer_(Teller)/Volume_II%3A_Predicate_Logic/4%3A_Transcription/4.1%3A_Restricted_Quantifiers"
+  
+  - concept: restricted-wreath-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 restricted wreath product $a2
+    property: infix
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='restricted-wreath-product($a1,$a2)'><mi arg='a1'>X</mi><mi>wr</mi><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='restricted-wreath-product($a1,$a2)'><mi arg='a1'>X</mi><msub><mi>wr</mi><mi>&#x03a9;</mi></msub><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WreathProduct.html"
+     - "https://en.wikipedia.org/wiki/Wreath_product"
+     - "https://ncatlab.org/nlab/show/wreath+product"
+     - "https://www.encyclopediaofmath.org/index.php/Wreath_product"
+  
+  - concept: restriction
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: restriction
-      property: indexed postfix
-      area: "elementary mathematics"
-      mathml:
-        - "<math><mrow intent='restriction($a1,$a2)'><mi arg='a1'>f</mi><msub><mo>↾</mo><mi arg='a2'>A</mi></msub></mrow></math>"
-        - "<math><mrow intent='restriction($a1,$a2)'><mi arg='a1'>f</mi><msub><mo>|</mo><mi arg='a2'>A</mi></msub></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Restricted_representation"
-       - "https://en.wikipedia.org/wiki/Restriction_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Selection_(relational_algebra)"
-       - "https://ncatlab.org/nlab/show/restriction"
-    
-    - concept: resultant
-      arity: 1
-      en: resultant of $1
-      property: function
-      area: "polynomials"
-      mathml:
-       - "<math><mrow intent='resultant($a1)'><mi>res</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='resultant($a1)'><mi>Res</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Resultant.html"
-       - "https://en.wikipedia.org/wiki/Resultant"
-       - "https://ncatlab.org/nlab/show/resultant"
-       - "https://www.encyclopediaofmath.org/index.php/Resultant"
-      alias:
-       - eliminant
-    
-    - concept: rewrite-rule
-      arity: 2
-      en: $1 rewrite rule $2
-      property: infix
-      area: "logic"
-      mathml:
-       - "<math><mrow intent='rewrite-rule($a1,$a2)'><mi arg='a1'>X</mi><mo>→</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Semi-Thue_system"
-      alias:
-       - rewrite-relation
-    
-    - concept: reynolds-number
-      arity: 0
+    property: indexed postfix
+    subject-area: "elementary mathematics"
+    mathml:
+      - "<math><mrow intent='restriction($a1,$a2)'><mi arg='a1'>f</mi><msub><mo>↾</mo><mi arg='a2'>A</mi></msub></mrow></math>"
+      - "<math><mrow intent='restriction($a1,$a2)'><mi arg='a1'>f</mi><msub><mo>|</mo><mi arg='a2'>A</mi></msub></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Restricted_representation"
+     - "https://en.wikipedia.org/wiki/Restriction_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Selection_(relational_algebra)"
+     - "https://ncatlab.org/nlab/show/restriction"
+  
+  - concept: resultant
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: resultant of $a1
+    property: function
+    subject-area: "polynomials"
+    mathml:
+     - "<math><mrow intent='resultant($a1)'><mi>res</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='resultant($a1)'><mi>Res</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Resultant.html"
+     - "https://en.wikipedia.org/wiki/Resultant"
+     - "https://ncatlab.org/nlab/show/resultant"
+     - "https://www.encyclopediaofmath.org/index.php/Resultant"
+    alias:
+     - eliminant
+  
+  - concept: rewrite-rule
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 rewrite rule $a2
+    property: infix
+    subject-area: "logic"
+    mathml:
+     - "<math><mrow intent='rewrite-rule($a1,$a2)'><mi arg='a1'>X</mi><mo>→</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Semi-Thue_system"
+    alias:
+     - rewrite-relation
+  
+  - concept: reynolds-number
+    arity: 0
+    arguments: []
+    speech:
       en: reynolds number
-      property: symbol
-      area: "fluid dynamics"
-      mathml:
-       - "<math><mi intent='reynolds-number'>Re</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Reynolds_number"
-    
-    - concept: ricci-scalar
-      arity: 0
+    property: symbol
+    subject-area: "fluid dynamics"
+    mathml:
+     - "<math><mi intent='reynolds-number'>Re</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Reynolds_number"
+  
+  - concept: ricci-scalar
+    arity: 0
+    arguments: []
+    speech:
       en: ricci scalar
-      property: symbol
-      area: "riemannian geometry"
-      mathml:
-       - "<math><mi intent='ricci-scalar'>S</mi></math>"
-       - "<math><mi intent='ricci-scalar'>R</mi></math>"
-       - "<math><mi intent='ricci-scalar'>Sc</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RicciScalar.html"
-       - "https://en.wikipedia.org/wiki/Scalar_curvature"
-      alias:
-       - scalar-curvature
-    
-    - concept: ricci-tensor
-      arity: 1
-      en: ricci tensor of $1
-      property: "indexed symbol"
-      area: "riemannian geometry"
-      mathml:
-       - "<math><mrow intent='ricci-tensor($a1)'><mi>R</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RicciTensor.html"
-       - "https://www.encyclopediaofmath.org/index.php/Ricci_tensor"
-    
-    - concept: riemann-integral
-      arity: 1
-      en: riemann integral of $1
-      property: indexed
-      area: "calculus"
-      mathml:
-       - "<math><mrow intent='riemann-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RiemannIntegral.html"
-       - "https://en.wikipedia.org/wiki/Lebesgue_integrability_condition"
-       - "https://en.wikipedia.org/wiki/Riemann_integral"
-       - "https://www.encyclopediaofmath.org/index.php/Riemann_integral"
-    
-    
-    - concept: riemann-sphere
-      arity: 0
+    property: symbol
+    subject-area: "riemannian geometry"
+    mathml:
+     - "<math><mi intent='ricci-scalar'>S</mi></math>"
+     - "<math><mi intent='ricci-scalar'>R</mi></math>"
+     - "<math><mi intent='ricci-scalar'>Sc</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RicciScalar.html"
+     - "https://en.wikipedia.org/wiki/Scalar_curvature"
+    alias:
+     - scalar-curvature
+  
+  - concept: ricci-tensor
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: ricci tensor of $a1
+    property: "indexed symbol"
+    subject-area: "riemannian geometry"
+    mathml:
+     - "<math><mrow intent='ricci-tensor($a1)'><mi>R</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RicciTensor.html"
+     - "https://www.encyclopediaofmath.org/index.php/Ricci_tensor"
+  
+  - concept: riemann-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: riemann integral of $a1
+    property: indexed
+    subject-area: "calculus"
+    mathml:
+     - "<math><mrow intent='riemann-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RiemannIntegral.html"
+     - "https://en.wikipedia.org/wiki/Lebesgue_integrability_condition"
+     - "https://en.wikipedia.org/wiki/Riemann_integral"
+     - "https://www.encyclopediaofmath.org/index.php/Riemann_integral"
+  
+  
+  - concept: riemann-sphere
+    arity: 0
+    arguments: []
+    speech:
       en: riemann sphere
-      property: scripted symbol
-      area: "projective geometry"
-      mathml:
-       - "<math><mover intent='riemann-sphere'><mi>ℂ</mi><mo>^</mo></mover></math>"
-       - "<math><mover intent='riemann-sphere'><mi>ℂ</mi><mo>¯</mo></mover></math>"
-       - "<math><msub intent='riemann-sphere'><mi>ℂ</mi><mo>∞</mo></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RiemannSphere.html"
-       - "https://en.wikipedia.org/wiki/Riemann_sphere"
-       - "https://ncatlab.org/nlab/show/Riemann+sphere"
-       - "https://www.encyclopediaofmath.org/index.php/Riemann_sphere"
-      alias:
-       - extended-complex-numbers
-       - extended-complex-plane
-    
-    - concept: riemann-theta-function
-      arity: 1
-      en: riemann theta function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='riemann-theta-function($a1)'><mi>θ⁡</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RiemannThetaFunction.html"
-       - "https://dlmf.nist.gov/21.2#i"
-       - "https://dlmf.nist.gov/21.2#E1"
-    
-    - concept: riemann-zeta-function
-      arity: 1
-      en: riemann zeta function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='riemann-zeta-function($a1)'><mi>ζ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RiemannZetaFunction.html"
-       - "https://en.wikipedia.org/wiki/%CE%96(x)"
-       - "https://en.wikipedia.org/wiki/Riemann_zeta_function"
-       - "https://dlmf.nist.gov/25.1"
-       - "https://dlmf.nist.gov/25.2#E1"
-      alias:
-       - euler-riemann-zeta-function
-    
-    - concept: riemann-christoffel-tensor
-      arity: 1
-      en: riemann christoffel tensor of $1
-      property: "indexed function"
-      area: "riemannian geometry"
-      mathml:
-       - "<math><mrow intent='riemann-christoffel-tensor($a1)'><mi>R</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Riemann-ChristoffelTensor.html"
-       - "https://en.wikipedia.org/wiki/Riemann_curvature_tensor"
-       - "https://www.encyclopediaofmath.org/index.php/Riemann-Christoffel_tensor"
-       - "https://www.encyclopediaofmath.org/index.php/RiemannâXXXXChristoffel_tensor"
-      alias:
-       - riemann-curvature-tensor
-    
-    - concept: riemann-stieltje-integral
-      arity: 1
-      en: riemann stieltje integral of $1
-      property: indexed
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='riemann-stieltje-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Riemann-StieltjesIntegral.html"
-       - "https://en.wikipedia.org/wiki/%E2%88%AB_f_d%CE%B1"
-       - "https://en.wikipedia.org/wiki/%E2%88%ABfd%CE%B1"
-       - "https://en.wikipedia.org/wiki/Riemann%E2%80%93Stieltjes_integral"
-       - "https://www.encyclopediaofmath.org/index.php/Riemann-Stieltjes_integral"
-       - "https://www.encyclopediaofmath.org/index.php/RiemannâXXXXStieltjes_integral"
-      alias:
-       - stieltje-integral
-    
-    - concept: right-angle
-      arity: 1
-      en: right angle of $1
-      property: prefix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='right-angle($a1)'><mo>∟</mo><mi arg='a1'>x</mi></mrow></math>"
-       - "<math><mrow intent='right-angle($a1)'><mo>⊾</mo><mi arg='a1'>x</mi></mrow></math>"
-       - "<math><mrow intent='right-angle($a1)'><mo>⦜</mo><mi arg='a1'>x</mi></mrow></math>"
-       - "<math><mrow intent='right-angle($a1)'><mo>⦝</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RightAngle.html"
-       - "https://en.wikipedia.org/wiki/Right_angle"
-    
-    - concept: right-derivative
-      arity: 1
-      en: right derivative of $1
-      property: operator
-      area: "calculus"
-      mathml:
-       - "<math><msub intent='right-derivative($a1)'><mo>∂</mo><mo>+</mo></msub><mi arg='a1'>f</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Left_and_right_derivative"
-    
-    - concept: right-quotient
-      arity: 2
-      en: $1 right quotient $2
-      property: infix
-      area: "formal languages"
-      mathml:
-       - "<math><mrow intent='right-quotient($a1,$a2)'><mi arg='a1'>X</mi><mo>\\</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Quotient_of_a_formal_language"
-    
-    - concept: ring-of-formal-power-series
-      arity: 2
-      en: ring of formal power series $1 $2
-      property: mixfix
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='ring-of-formal-power-series($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>⟦</mo><mi arg='a2'>x</mi><mo>⟧</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Formal_power_series#The_ring_of_formal_power_series"
-    
-    - concept: rising-factorial
-      arity: 2
-      en: $2<i>th</i> rising factorial of  $1
-      property: mixfix
-      area: "combinatorics"
-      mathml:
-        - "<math><msup intent='rising-factorial($a1,$a2)'><mi arg='a1'>x</mi><mrow><mo>(</mo><mi arg='a2'>n</mi><mo>)</mo></mrow></msup></math>"
-        - "<math><msup intent='rising-factorial($a1,$a2)'><mi arg='a1'>x</mi><mover><mi arg='a2'>n</mi><mo>¯</mo></mover></msup></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Falling_and_rising_factorials"
-       - "https://mathworld.wolfram.com/RisingFactorial.html"
-       - "https://dlmf.nist.gov/26.1#P1.p1"
-      alias:
-       - pochhammer-function
-       - pochhammer-polynomial
-       - ascending-factorial
-       - rising-sequential-product
-       - upper-factorial
-    
-    - concept: roman-numeral
-      arity: 0
+    property: scripted symbol
+    subject-area: "projective geometry"
+    mathml:
+     - "<math><mover intent='riemann-sphere'><mi>ℂ</mi><mo>^</mo></mover></math>"
+     - "<math><mover intent='riemann-sphere'><mi>ℂ</mi><mo>¯</mo></mover></math>"
+     - "<math><msub intent='riemann-sphere'><mi>ℂ</mi><mo>∞</mo></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RiemannSphere.html"
+     - "https://en.wikipedia.org/wiki/Riemann_sphere"
+     - "https://ncatlab.org/nlab/show/Riemann+sphere"
+     - "https://www.encyclopediaofmath.org/index.php/Riemann_sphere"
+    alias:
+     - extended-complex-numbers
+     - extended-complex-plane
+  
+  - concept: riemann-theta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: riemann theta function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='riemann-theta-function($a1)'><mi>θ⁡</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RiemannThetaFunction.html"
+     - "https://dlmf.nist.gov/21.2#i"
+     - "https://dlmf.nist.gov/21.2#E1"
+  
+  - concept: riemann-zeta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: riemann zeta function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='riemann-zeta-function($a1)'><mi>ζ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RiemannZetaFunction.html"
+     - "https://en.wikipedia.org/wiki/%CE%96(x)"
+     - "https://en.wikipedia.org/wiki/Riemann_zeta_function"
+     - "https://dlmf.nist.gov/25.1"
+     - "https://dlmf.nist.gov/25.2#E1"
+    alias:
+     - euler-riemann-zeta-function
+  
+  - concept: riemann-christoffel-tensor
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: riemann christoffel tensor of $a1
+    property: "indexed function"
+    subject-area: "riemannian geometry"
+    mathml:
+     - "<math><mrow intent='riemann-christoffel-tensor($a1)'><mi>R</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Riemann-ChristoffelTensor.html"
+     - "https://en.wikipedia.org/wiki/Riemann_curvature_tensor"
+     - "https://www.encyclopediaofmath.org/index.php/Riemann-Christoffel_tensor"
+     - "https://www.encyclopediaofmath.org/index.php/RiemannâXXXXChristoffel_tensor"
+    alias:
+     - riemann-curvature-tensor
+  
+  - concept: riemann-stieltje-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: riemann stieltje integral of $a1
+    property: indexed
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='riemann-stieltje-integral($a1)'><mo>∫</mo><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Riemann-StieltjesIntegral.html"
+     - "https://en.wikipedia.org/wiki/%E2%88%AB_f_d%CE%B1"
+     - "https://en.wikipedia.org/wiki/%E2%88%ABfd%CE%B1"
+     - "https://en.wikipedia.org/wiki/Riemann%E2%80%93Stieltjes_integral"
+     - "https://www.encyclopediaofmath.org/index.php/Riemann-Stieltjes_integral"
+     - "https://www.encyclopediaofmath.org/index.php/RiemannâXXXXStieltjes_integral"
+    alias:
+     - stieltje-integral
+  
+  - concept: right-angle
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: right angle of $a1
+    property: prefix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='right-angle($a1)'><mo>∟</mo><mi arg='a1'>x</mi></mrow></math>"
+     - "<math><mrow intent='right-angle($a1)'><mo>⊾</mo><mi arg='a1'>x</mi></mrow></math>"
+     - "<math><mrow intent='right-angle($a1)'><mo>⦜</mo><mi arg='a1'>x</mi></mrow></math>"
+     - "<math><mrow intent='right-angle($a1)'><mo>⦝</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RightAngle.html"
+     - "https://en.wikipedia.org/wiki/Right_angle"
+  
+  - concept: right-derivative
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: right derivative of $a1
+    property: operator
+    subject-area: "calculus"
+    mathml:
+     - "<math><msub intent='right-derivative($a1)'><mo>∂</mo><mo>+</mo></msub><mi arg='a1'>f</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Left_and_right_derivative"
+  
+  - concept: right-quotient
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 right quotient $a2
+    property: infix
+    subject-area: "formal languages"
+    mathml:
+     - "<math><mrow intent='right-quotient($a1,$a2)'><mi arg='a1'>X</mi><mo>\\</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Quotient_of_a_formal_language"
+  
+  - concept: ring-of-formal-power-series
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: ring of formal power series $a1 $a2
+    property: mixfix
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='ring-of-formal-power-series($a1,$a2)'><mi arg='a1'>R</mi><mrow><mo>⟦</mo><mi arg='a2'>x</mi><mo>⟧</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Formal_power_series#The_ring_of_formal_power_series"
+  
+  - concept: rising-factorial
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a2<i>th</i> rising factorial of  $a1
+    property: mixfix
+    subject-area: "combinatorics"
+    mathml:
+      - "<math><msup intent='rising-factorial($a1,$a2)'><mi arg='a1'>x</mi><mrow><mo>(</mo><mi arg='a2'>n</mi><mo>)</mo></mrow></msup></math>"
+      - "<math><msup intent='rising-factorial($a1,$a2)'><mi arg='a1'>x</mi><mover><mi arg='a2'>n</mi><mo>¯</mo></mover></msup></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Falling_and_rising_factorials"
+     - "https://mathworld.wolfram.com/RisingFactorial.html"
+     - "https://dlmf.nist.gov/26.1#P1.p1"
+    alias:
+     - pochhammer-function
+     - pochhammer-polynomial
+     - ascending-factorial
+     - rising-sequential-product
+     - upper-factorial
+  
+  - concept: roman-numeral
+    arity: 0
+    arguments: []
+    speech:
       en: roman numeral
-      property: symbol
-      area: "number theory"
-      mathml:
-       - "<math><mi intent='roman-numeral' mathvariant='normal'>i</mi></math>"
-       - "<math><mi intent='roman-numeral'>ii</mi></math>"
-       - "<math><mi intent='roman-numeral'>iii</mi></math>"
-       - "<math><mi intent='roman-numeral'>iv</mi></math>"
-       - "<math><mi intent='roman-numeral'>v</mi></math>"
-       - "<math><mi intent='roman-numeral'>vi</mi></math>"
-       - "<math><mi intent='roman-numeral'>vii</mi></math>"
-       - "<math><mi intent='roman-numeral'>viii</mi></math>"
-       - "<math><mi intent='roman-numeral'>ix</mi></math>"
-       - "<math><mi intent='roman-numeral'>x</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RomanNumerals.html"
-       - "https://en.wikipedia.org/wiki/Roman_numerals"
-       - "https://www.encyclopediaofmath.org/index.php/Roman_numerals"
-    
-    - concept: roof
-      arity: 3
-      en: roof of $1, $2 and $3
-      property: mixfix
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='roof($a1,$a2,$a3)'><mi arg='a1'>X</mi><mo>←</mo><mi arg='a2'>Y</mi><mo>→</mo><mi arg='a3'>Z</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Span_(category_theory)"
-       - "https://ncatlab.org/nlab/show/span"
-      alias:
-       - span
-       - correspondence
-    
-    - concept: root-of-unity
-      arity: 0
+    property: symbol
+    subject-area: "number theory"
+    mathml:
+     - "<math><mi intent='roman-numeral' mathvariant='normal'>i</mi></math>"
+     - "<math><mi intent='roman-numeral'>ii</mi></math>"
+     - "<math><mi intent='roman-numeral'>iii</mi></math>"
+     - "<math><mi intent='roman-numeral'>iv</mi></math>"
+     - "<math><mi intent='roman-numeral'>v</mi></math>"
+     - "<math><mi intent='roman-numeral'>vi</mi></math>"
+     - "<math><mi intent='roman-numeral'>vii</mi></math>"
+     - "<math><mi intent='roman-numeral'>viii</mi></math>"
+     - "<math><mi intent='roman-numeral'>ix</mi></math>"
+     - "<math><mi intent='roman-numeral'>x</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RomanNumerals.html"
+     - "https://en.wikipedia.org/wiki/Roman_numerals"
+     - "https://www.encyclopediaofmath.org/index.php/Roman_numerals"
+  
+  - concept: roof
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: roof of $a1, $a2 and $a3
+    property: mixfix
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='roof($a1,$a2,$a3)'><mi arg='a1'>X</mi><mo>←</mo><mi arg='a2'>Y</mi><mo>→</mo><mi arg='a3'>Z</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Span_(category_theory)"
+     - "https://ncatlab.org/nlab/show/span"
+    alias:
+     - span
+     - correspondence
+  
+  - concept: root-of-unity
+    arity: 0
+    arguments: []
+    speech:
       en: root of unity
-      property: symbol
-      area: "complex numbers"
-      mathml:
-       - "<math><mi intent='root-of-unity'>ω</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/RootofUnity.html"
-       - "https://en.wikipedia.org/wiki/Root_of_unity"
-       - "https://ncatlab.org/nlab/show/root+of+unity"
-    
-    - concept: root-mean-square
-      arity: 1
-      en: root mean square of $1
-      property: msub
-      area: "means"
-      mathml:
-       - "<math><msub intent='root-mean-square($a1)'><mi arg='a1'>G</mi><mi>RMS</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Root-Mean-Square.html"
-      alias:
-       - rms
-       - quadratic-mean
-    
-    - concept: rooted-product-of-graphs
-      arity: 2
-      en: $1 rooted product of graphs $2
-      property: infix
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='rooted-product-of-graphs($a1,$a2)'><mi arg='a1'>X</mi><mo>∘</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Rooted_product_of_graphs"
-    
-    - concept: ruark-number
-      arity: 0
+    property: symbol
+    subject-area: "complex numbers"
+    mathml:
+     - "<math><mi intent='root-of-unity'>ω</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/RootofUnity.html"
+     - "https://en.wikipedia.org/wiki/Root_of_unity"
+     - "https://ncatlab.org/nlab/show/root+of+unity"
+  
+  - concept: root-mean-square
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: root mean square of $a1
+    property: msub
+    subject-area: "means"
+    mathml:
+     - "<math><msub intent='root-mean-square($a1)'><mi arg='a1'>G</mi><mi>RMS</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Root-Mean-Square.html"
+    alias:
+     - rms
+     - quadratic-mean
+  
+  - concept: rooted-product-of-graphs
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 rooted product of graphs $a2
+    property: infix
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='rooted-product-of-graphs($a1,$a2)'><mi arg='a1'>X</mi><mo>∘</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Rooted_product_of_graphs"
+  
+  - concept: ruark-number
+    arity: 0
+    arguments: []
+    speech:
       en: ruark number
-      property: symbol
-      area: "physics"
-      mathml:
-       - "<math><mi intent='ruark-number'>Ru</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Euler_number_(physics)"
-    
-    - concept: s-set-theory
-      arity: 0
+    property: symbol
+    subject-area: "physics"
+    mathml:
+     - "<math><mi intent='ruark-number'>Ru</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Euler_number_(physics)"
+  
+  - concept: s-set-theory
+    arity: 0
+    arguments: []
+    speech:
       en: s set theory
-      property: constant
-      area: "set theory"
-      mathml:
-       - "<math><mi intent='s-set-theory'>S</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/S_(set_theory)"
-    
-    - concept: s5-modal-logic
-      arity: 0
+    property: constant
+    subject-area: "set theory"
+    mathml:
+     - "<math><mi intent='s-set-theory'>S</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/S_(set_theory)"
+  
+  - concept: s5-modal-logic
+    arity: 0
+    arguments: []
+    speech:
       en: s5 modal logic
-      property: constant
-      area: "logic"
-      mathml:
-       - "<math><mi intent='s5-modal-logic'>S5</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/S5_(modal_logic)"
-    
-    - concept: sample-space
-      arity: 0
+    property: constant
+    subject-area: "logic"
+    mathml:
+     - "<math><mi intent='s5-modal-logic'>S5</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/S5_(modal_logic)"
+  
+  - concept: sample-space
+    arity: 0
+    arguments: []
+    speech:
       en: sample space
-      property: symbol
-      area: "probability theory"
-      mathml:
-       - "<math><mi intent='sample-space'>S</mi></math>"
-       - "<math><mi intent='sample-space'>Ω</mi></math>"
-       - "<math><mi intent='sample-space'>U</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SampleSpace.html"
-       - "https://en.wikipedia.org/wiki/Sample_space"
-       - "https://www.encyclopediaofmath.org/index.php/Sample_space"
-    
-    - concept: sample-variance
-      arity: 1
-      en: sample variance of $1
-      property: embellished symbol
-      area: "probability theory"
-      mathml:
-       - "<math><msubsup intent='sample-variance($a1)'><mi>S</mi><mi arg='a1'>y</mi><mn>2</mn></msubsup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SampleVariance.html"
-       - "https://www.encyclopediaofmath.org/index.php/Sample_variance"
-       - "https://en.wikipedia.org/wiki/Variance#Sample_variance"
-    
-    - concept: scalar-triple-product
-      arity: 3
-      en: scalar triple product  of $1, $2 and $3
-      property: mixfix, fenced
-      area: "vector algebra"
-      mathml:
-       - "<math><mrow intent='scalar-triple-product($a1,$a2,$a3)'><mi arg='a1'>A</mi><mo>·</mo><mrow><mo>(</mo><mi arg='a2'>B</mi><mo>·</mo><mi arg='a3'>C</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='scalar-triple-product($a1,$a2,$a3)'><mo>[</mo><mi arg='a1'>A</mi><mo>,</mo><mi arg='a2'>B</mi><mo>,</mo><mi arg='a3'>C</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ScalarTripleProduct.html"
-       - "https://en.wikipedia.org/wiki/Triple_product"
-    
-    - concept: scaled-riemann-theta-function
-      arity: 1
-      en: scaled riemann theta function of $1
-      property: mover
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='scaled-riemann-theta-function($a1)'><mover><mi>θ</mi><mo>^</mo></mover><mrow><mo>(</mo><mi arg='a1'>𝐳</mi><mo>|</mo><mi>𝛀</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://dlmf.nist.gov/21.2#i"
-       - "https://dlmf.nist.gov/21.2#E1"
+    property: symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mi intent='sample-space'>S</mi></math>"
+     - "<math><mi intent='sample-space'>Ω</mi></math>"
+     - "<math><mi intent='sample-space'>U</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SampleSpace.html"
+     - "https://en.wikipedia.org/wiki/Sample_space"
+     - "https://www.encyclopediaofmath.org/index.php/Sample_space"
+  
+  - concept: sample-variance
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: sample variance of $a1
+    property: embellished symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><msubsup intent='sample-variance($a1)'><mi>S</mi><mi arg='a1'>y</mi><mn>2</mn></msubsup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SampleVariance.html"
+     - "https://www.encyclopediaofmath.org/index.php/Sample_variance"
+     - "https://en.wikipedia.org/wiki/Variance#Sample_variance"
+  
+  - concept: scalar-triple-product
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: scalar triple product  of $a1, $a2 and $a3
+    property: mixfix, fenced
+    subject-area: "vector algebra"
+    mathml:
+     - "<math><mrow intent='scalar-triple-product($a1,$a2,$a3)'><mi arg='a1'>A</mi><mo>·</mo><mrow><mo>(</mo><mi arg='a2'>B</mi><mo>·</mo><mi arg='a3'>C</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='scalar-triple-product($a1,$a2,$a3)'><mo>[</mo><mi arg='a1'>A</mi><mo>,</mo><mi arg='a2'>B</mi><mo>,</mo><mi arg='a3'>C</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ScalarTripleProduct.html"
+     - "https://en.wikipedia.org/wiki/Triple_product"
+  
+  - concept: scaled-riemann-theta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: scaled riemann theta function of $a1
+    property: mover
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='scaled-riemann-theta-function($a1)'><mover><mi>θ</mi><mo>^</mo></mover><mrow><mo>(</mo><mi arg='a1'>𝐳</mi><mo>|</mo><mi>𝛀</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://dlmf.nist.gov/21.2#i"
+     - "https://dlmf.nist.gov/21.2#E1"
 
-    - concept: schlaefli-symbol
-      arity: ">=0"
-      en: schlaefli symbol of $1, ...
-      property: fenced
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='schlaefli-symbol($a1,$a2,$a3)'><mo>{</mo><mi arg='a1'>p</mi><mo>,</mo><mi arg='a2'>q</mi><mo>,</mo><mi arg='a3'>r</mi><mo>}</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol"
-    
-    - concept: schroder-number
-      arity: 1
-      en: schroder number of $1
-      property: "indexed symbol"
-      area: "combinatorics"
-      mathml:
-       - "<math><msub intent='schroder-number($a1)'><mi>S</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SchroederNumber.html"
-       - "https://en.wikipedia.org/wiki/Schr%C3%B6der_number"
-       - "https://dlmf.nist.gov/26.6#E4"
-    
-    - concept: schur-multiplier
-      arity: 1
-      en: schur multiplier of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='schur-multiplier($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SchurMultiplier.html"
-       - "https://en.wikipedia.org/wiki/Schur_multiplier"
-       - "https://en.wikipedia.org/wiki/Schur_cover"
-      alias:
-       - schur-multiplicator
-    
-    - concept: schwartz-space
-      arity: 0
+  - concept: schlaefli-symbol
+    arity: ">=0"
+    speech:
+      en: schlaefli symbol of $a1, ...
+    property: fenced
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='schlaefli-symbol($a1,$a2,$a3)'><mo>{</mo><mi arg='a1'>p</mi><mo>,</mo><mi arg='a2'>q</mi><mo>,</mo><mi arg='a3'>r</mi><mo>}</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol"
+  
+  - concept: schroder-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: schroder number of $a1
+    property: "indexed symbol"
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><msub intent='schroder-number($a1)'><mi>S</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SchroederNumber.html"
+     - "https://en.wikipedia.org/wiki/Schr%C3%B6der_number"
+     - "https://dlmf.nist.gov/26.6#E4"
+  
+  - concept: schur-multiplier
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: schur multiplier of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='schur-multiplier($a1)'><mi>M</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SchurMultiplier.html"
+     - "https://en.wikipedia.org/wiki/Schur_multiplier"
+     - "https://en.wikipedia.org/wiki/Schur_cover"
+    alias:
+     - schur-multiplicator
+  
+  - concept: schwartz-space
+    arity: 0
+    arguments: []
+    speech:
       en: schwartz space
-      property: symbol
-      area: "topology"
-      mathml:
-       - "<math><mi intent='schwartz-space'>𝒮</mi></math>"
-       - "<math><mi intent='schwartz-space'>S</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SchwartzSpace.html"
-       - "https://en.wikipedia.org/wiki/Schwartz_space"
-       - "https://ncatlab.org/nlab/show/Schwartz+space"
-    
-    - concept: schwarzian-derivative
-      arity: 2
-      en: schwarzian derivative $1 $2
-      property: fenced, mixfix
-      area: "complex analysis"
-      mathml:
-       - "<math><mrow intent='schwarzian-derivative($a1,$a2)'><mo>{</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>}</mo></mrow></math>"
-      notationa: "mrow ( S $1 ) ($2"
-      urls: 
-       - "https://mathworld.wolfram.com/SchwarzianDerivative.html"
-       - "https://en.wikipedia.org/wiki/Schwarzian_derivative"
-       - "https://dlmf.nist.gov/1.13#E20"
-       - "https://www.encyclopediaofmath.org/index.php/Schwarzian_derivative"
-    
-    - concept: second-carmichael-function
-      arity: 1
-      en: second carmichael function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='second-carmichael-function($a1)'><msup><mi>λ</mi><mo>′</mo></msup><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/CarmichaelFunction.html"
-       - "https://en.wikipedia.org/wiki/Carmichael_function"
-    
-    - concept: sectional-curvature
-      arity: 1
-      en: sectional curvature of $1
-      property: function
-      area: "riemannian geometry"
-      mathml:
-       - "<math><mrow intent='sectional-curvature($a1)'><mi>K</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='sectional-curvature($a1)'><mi>κ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SectionalCurvature.html"
-       - "https://en.wikipedia.org/wiki/Sectional_curvature"
-       - "https://www.encyclopediaofmath.org/index.php/Sectional_curvature"
-    
-    - concept: sedenion
-      arity: 0
+    property: symbol
+    subject-area: "topology"
+    mathml:
+     - "<math><mi intent='schwartz-space'>𝒮</mi></math>"
+     - "<math><mi intent='schwartz-space'>S</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SchwartzSpace.html"
+     - "https://en.wikipedia.org/wiki/Schwartz_space"
+     - "https://ncatlab.org/nlab/show/Schwartz+space"
+  
+  - concept: schwarzian-derivative
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: schwarzian derivative $a1 $a2
+    property: fenced, mixfix
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mrow intent='schwarzian-derivative($a1,$a2)'><mo>{</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>}</mo></mrow></math>"
+    notationa: "mrow ( S $a1 ) ($a2"
+    urls: 
+     - "https://mathworld.wolfram.com/SchwarzianDerivative.html"
+     - "https://en.wikipedia.org/wiki/Schwarzian_derivative"
+     - "https://dlmf.nist.gov/1.13#E20"
+     - "https://www.encyclopediaofmath.org/index.php/Schwarzian_derivative"
+  
+  - concept: second-carmichael-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: second carmichael function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='second-carmichael-function($a1)'><msup><mi>λ</mi><mo>′</mo></msup><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/CarmichaelFunction.html"
+     - "https://en.wikipedia.org/wiki/Carmichael_function"
+  
+  - concept: sectional-curvature
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: sectional curvature of $a1
+    property: function
+    subject-area: "riemannian geometry"
+    mathml:
+     - "<math><mrow intent='sectional-curvature($a1)'><mi>K</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='sectional-curvature($a1)'><mi>κ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SectionalCurvature.html"
+     - "https://en.wikipedia.org/wiki/Sectional_curvature"
+     - "https://www.encyclopediaofmath.org/index.php/Sectional_curvature"
+  
+  - concept: sedenion
+    arity: 0
+    arguments: []
+    speech:
       en: sedenion
-      property: symbol
-      area: "abstract algebra"
-      mathml:
-       - "<math><mi intent='sedenion'>𝕊</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Sedenion"
-       - "https://ncatlab.org/nlab/show/sedenion"
-    
-    - concept: selection
-      arity: 3
+    property: symbol
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mi intent='sedenion'>𝕊</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Sedenion"
+     - "https://ncatlab.org/nlab/show/sedenion"
+  
+  - concept: selection
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
       en: selection
-      property: "indexed function"
-      area: "relational algebra"
-      mathml:
-       - "<math><msub intent='selection($a1,$a2,$a3)'><mi>&#x03c3;</mi><mrow><mi arg='a1'>a</mi><mi arg='a2'>&#x03b8;</mi><mi arg='a3'>b</mi></mrow></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Selection_(relational_algebra)"
-    
-    - concept: seminorm
-      arity: 1
-      en: seminorm of $1
-      property: fenced
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='seminorm($a1)'><mo>‖</mo><mi arg='a1'>X</mi><mo>‖</mo></mrow></math>"
-       - "<math><mrow intent='seminorm($a1)'><mo>|</mo><mi arg='a1'>X</mi><mo>|</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Seminorm.html"
-       - "https://en.wikipedia.org/wiki/Norm_(mathematics)"
-      alias:
-       - pseudonorm
-    
-    - concept: set-of-invertible-maps
-      arity: 1
-      en: set of invertible maps of $1
-      property: prefix
-      area: "commutative algebra"
-      mathml:
-       - "<math><mrow intent='set-of-invertible-maps($a1)'><mo>!</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://arxiv.org/abs/2009.015866"
-    
-    - concept: shannon-entropy
-      arity: 0
+    property: "indexed function"
+    subject-area: "relational algebra"
+    mathml:
+     - "<math><msub intent='selection($a1,$a2,$a3)'><mi>&#x03c3;</mi><mrow><mi arg='a1'>a</mi><mi arg='a2'>&#x03b8;</mi><mi arg='a3'>b</mi></mrow></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Selection_(relational_algebra)"
+  
+  - concept: seminorm
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: seminorm of $a1
+    property: fenced
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='seminorm($a1)'><mo>‖</mo><mi arg='a1'>X</mi><mo>‖</mo></mrow></math>"
+     - "<math><mrow intent='seminorm($a1)'><mo>|</mo><mi arg='a1'>X</mi><mo>|</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Seminorm.html"
+     - "https://en.wikipedia.org/wiki/Norm_(mathematics)"
+    alias:
+     - pseudonorm
+  
+  - concept: set-of-invertible-maps
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: set of invertible maps of $a1
+    property: prefix
+    subject-area: "commutative algebra"
+    mathml:
+     - "<math><mrow intent='set-of-invertible-maps($a1)'><mo>!</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://arxiv.org/abs/2009.015866"
+  
+  - concept: shannon-entropy
+    arity: 0
+    arguments: []
+    speech:
       en: shannon entropy
-      property: symbol
-      area: "information theory"
-      mathml:
-       - "<math><mi intent='shannon-entropy'>H</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ShannonEntropy.html"
-       - "https://en.wikipedia.org/wiki/Entropy_(information_theory)"
-       - "https://ncatlab.org/nlab/show/entropy"
-       - "https://www.encyclopediaofmath.org/index.php/Entropy"
-      alias:
-       - entropy
-    
-    - concept: shift-operator
-      arity: 1
-      en: shift operator of $1
-      property: operator
-      area: "functional analysis"
-      mathml:
-       - "<math><mrow intent='shift-operator($a1)'><msup><mi>T</mi><mo>t</mo></msup><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ShiftOperator.html"
-       - "https://en.wikipedia.org/wiki/Shift_operator"
-       - "https://www.encyclopediaofmath.org/index.php/Shift_operator"
-      alias:
-       - translation-operator
-       - lag-operator
-    
-    - concept: shimura-variety
-      arity: 1
-      en: shimura variety of $1
-      property: function
-      area: "algebraic geometry"
-      mathml:
-       - "<math><mrow intent='shimura-variety($a1)'><mi>Sh</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Shimura_variety"
-       - "https://ncatlab.org/nlab/show/Shimura+variety"
-       - "https://www.encyclopediaofmath.org/index.php/Shimura_variety"
-    
-    - concept: short-exact-sequence
-      arity: 3
-      en: short exact sequence $1 $2 $3
-      property: mixfix
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='short-exact-sequence($a1,$a2,$a3)'><mn>0</mn><mo>→</mo><mi arg='a1'>X</mi><mo>→</mo><mi arg='a2'>Y</mi><mo>→</mo><mi arg='a3'>Z</mi><mo>→</mo><mn>0</mn></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ShortExactSequence.html"
-       - "https://en.wikipedia.org/wiki/Exact_sequence"
-    
-    - concept: short-rate
-      arity: 0
+    property: symbol
+    subject-area: "information theory"
+    mathml:
+     - "<math><mi intent='shannon-entropy'>H</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ShannonEntropy.html"
+     - "https://en.wikipedia.org/wiki/Entropy_(information_theory)"
+     - "https://ncatlab.org/nlab/show/entropy"
+     - "https://www.encyclopediaofmath.org/index.php/Entropy"
+    alias:
+     - entropy
+  
+  - concept: shift-operator
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: shift operator of $a1
+    property: operator
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><mrow intent='shift-operator($a1)'><msup><mi>T</mi><mo>t</mo></msup><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ShiftOperator.html"
+     - "https://en.wikipedia.org/wiki/Shift_operator"
+     - "https://www.encyclopediaofmath.org/index.php/Shift_operator"
+    alias:
+     - translation-operator
+     - lag-operator
+  
+  - concept: shimura-variety
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: shimura variety of $a1
+    property: function
+    subject-area: "algebraic geometry"
+    mathml:
+     - "<math><mrow intent='shimura-variety($a1)'><mi>Sh</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Shimura_variety"
+     - "https://ncatlab.org/nlab/show/Shimura+variety"
+     - "https://www.encyclopediaofmath.org/index.php/Shimura_variety"
+  
+  - concept: short-exact-sequence
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: short exact sequence $a1 $a2 $a3
+    property: mixfix
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='short-exact-sequence($a1,$a2,$a3)'><mn>0</mn><mo>→</mo><mi arg='a1'>X</mi><mo>→</mo><mi arg='a2'>Y</mi><mo>→</mo><mi arg='a3'>Z</mi><mo>→</mo><mn>0</mn></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ShortExactSequence.html"
+     - "https://en.wikipedia.org/wiki/Exact_sequence"
+  
+  - concept: short-rate
+    arity: 0
+    arguments: []
+    speech:
       en: short rate
-      property: symbol
-      area: "mathematical finance"
-      mathml:
-       - "<math><msub intent='short-rate'><mi>r</mi><mi>t</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Short_rate"
-       - "https://en.wikipedia.org/wiki/Short-rate_model"
-       - "https://en.wikipedia.org/wiki/Kalotay%E2%80%93Williams%E2%80%93Fabozzi_model"
-       - "https://en.wikipedia.org/wiki/Longstaff%E2%80%93Schwartz_model"
-    
-    - concept: sidon-sequence
-      arity: 0
+    property: symbol
+    subject-area: "mathematical finance"
+    mathml:
+     - "<math><msub intent='short-rate'><mi>r</mi><mi>t</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Short_rate"
+     - "https://en.wikipedia.org/wiki/Short-rate_model"
+     - "https://en.wikipedia.org/wiki/Kalotay%E2%80%93Williams%E2%80%93Fabozzi_model"
+     - "https://en.wikipedia.org/wiki/Longstaff%E2%80%93Schwartz_model"
+  
+  - concept: sidon-sequence
+    arity: 0
+    arguments: []
+    speech:
       en: sidon sequence
-      property: symbol
-      area: "combinatorics"
-      mathml:
-       - "<math><mi intent='sidon-sequence'>A</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SidonSequence.html"
-       - "https://en.wikipedia.org/wiki/Sidon_sequence"
-      alias:
-       - sidon-set
-    
-    - concept: sign-function
-      arity: 1
-      en: sign function of $1
-      property: function
-      area: "special-functions"
-      mathml:
-       - "<math><mrow intent='sign-function($a1)'><mi>sgn</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Sign_function"
-      alias:
-       - signum-function
-    
-    - concept: signature-of-permutation
-      arity: 1
-      en: signature of permutation of $1
-      property: function
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='signature-of-permutation($a1)'><mi>sign</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/signature+of+a+permutation"
-      alias:
-       - sign-of-permutation
-    
-    - concept: silver-ratio
-      arity: 0
+    property: symbol
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mi intent='sidon-sequence'>A</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SidonSequence.html"
+     - "https://en.wikipedia.org/wiki/Sidon_sequence"
+    alias:
+     - sidon-set
+  
+  - concept: sign-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: sign function of $a1
+    property: function
+    subject-area: "special-functions"
+    mathml:
+     - "<math><mrow intent='sign-function($a1)'><mi>sgn</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Sign_function"
+    alias:
+     - signum-function
+  
+  - concept: signature-of-permutation
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: signature of permutation of $a1
+    property: function
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='signature-of-permutation($a1)'><mi>sign</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/signature+of+a+permutation"
+    alias:
+     - sign-of-permutation
+  
+  - concept: silver-ratio
+    arity: 0
+    arguments: []
+    speech:
       en: silver ratio
-      property: constant
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='silver-ratio'><mi>δ</mi><mi>S</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SilverRatio.html"
-       - "https://en.wikipedia.org/wiki/Silver_ratio"
-       - "https://en.wikipedia.org/wiki/Silver_rectangle"
-    
-    - concept: similar
-      arity: 2
-      en: $1 similar $2
-      property: infix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='similar($a1,$a2)'><mi arg='a1'>X</mi><mo>~</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Similar.html"
-       - "https://en.wikipedia.org/wiki/Matrix_similarity"
-       - "https://en.wikipedia.org/wiki/Similarity_(geometry)"
-    
-    - concept: simplex
-      arity: 1
-      en: $1 simplex 
-      property: "indexed symbol"
-      area: "geometry"
-      mathml:
-       - "<math><msup intent='simplex($a1)'><mo>Δ</mo><mi arg='a1'>n</mi></msup></math>"
-       - "<math><mrow intent='simplex($a1)'><mo>Δ</mo><mrow><mo>[</mo><mi arg='a1'>n</mi><mo>]</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Simplex.html"
-       - "https://en.wikipedia.org/wiki/Simplex"
-       - "https://ncatlab.org/nlab/show/simplex"
-       - "https://www.encyclopediaofmath.org/index.php/Simplex"
-    
-    - concept: sinc-function
-      arity: 1
-      en: sinc function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='sinc-function($a1)'><mi>S</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='sinc-function($a1)'><mi>sinc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SincFunction.html"
-       - "https://en.wikipedia.org/wiki/Sinc_function"
-       - "https://dlmf.nist.gov/3.3#SS6.p2"
-    
-    - concept: sine-integral
-      arity: 1
-      en: sine integral of $1
-      property: operator
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='sine-integral($a1)'><mi>Si</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SineIntegral.html"
-       - "https://dlmf.nist.gov/6.2#ii"
-       - "https://dlmf.nist.gov/6.2#E9"
-       - "https://dlmf.nist.gov/6.2#E10"
-    
-    - concept: size-of-test
-      arity: 0
+    property: constant
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='silver-ratio'><mi>δ</mi><mi>S</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SilverRatio.html"
+     - "https://en.wikipedia.org/wiki/Silver_ratio"
+     - "https://en.wikipedia.org/wiki/Silver_rectangle"
+  
+  - concept: similar
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 similar $a2
+    property: infix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='similar($a1,$a2)'><mi arg='a1'>X</mi><mo>~</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Similar.html"
+     - "https://en.wikipedia.org/wiki/Matrix_similarity"
+     - "https://en.wikipedia.org/wiki/Similarity_(geometry)"
+  
+  - concept: simplex
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1 simplex 
+    property: "indexed symbol"
+    subject-area: "geometry"
+    mathml:
+     - "<math><msup intent='simplex($a1)'><mo>Δ</mo><mi arg='a1'>n</mi></msup></math>"
+     - "<math><mrow intent='simplex($a1)'><mo>Δ</mo><mrow><mo>[</mo><mi arg='a1'>n</mi><mo>]</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Simplex.html"
+     - "https://en.wikipedia.org/wiki/Simplex"
+     - "https://ncatlab.org/nlab/show/simplex"
+     - "https://www.encyclopediaofmath.org/index.php/Simplex"
+  
+  - concept: sinc-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: sinc function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='sinc-function($a1)'><mi>S</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='sinc-function($a1)'><mi>sinc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SincFunction.html"
+     - "https://en.wikipedia.org/wiki/Sinc_function"
+     - "https://dlmf.nist.gov/3.3#SS6.p2"
+  
+  - concept: sine-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: sine integral of $a1
+    property: operator
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='sine-integral($a1)'><mi>Si</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SineIntegral.html"
+     - "https://dlmf.nist.gov/6.2#ii"
+     - "https://dlmf.nist.gov/6.2#E9"
+     - "https://dlmf.nist.gov/6.2#E10"
+  
+  - concept: size-of-test
+    arity: 0
+    arguments: []
+    speech:
       en: size of test
-      property: symbol
-      area: "statistics"
-      mathml:
-       - "<math><mi intent='size-of-test'>α</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Size_(statistics)"
-    
-    - concept: skewes-number
-      arity: 1
-      en: skewes number of $1
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='skewes-number($a1)'><mi>Sk</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SkewesNumber.html"
-       - "https://en.wikipedia.org/wiki/Skewes%27_number"
-    
-    - concept: small-o
-      arity: 1
-      en: small o of $1
-      property: prefix
-      area: "complexity"
-      mathml:
-       - "<math><mrow intent='small-o($a1)'><mi>o</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Big_O_notation"
-       - "https://mathworld.wolfram.com/o.html"
-    
-    - concept: smith-number
-      arity: 1
-      en: smith number of $1
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='smith-number($a1)'><mi>S</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SmithNumber.html"
-       - "https://en.wikipedia.org/wiki/Smith_number"
-    
-    - concept: sobolev-space
-      arity: 2
+    property: symbol
+    subject-area: "statistics"
+    mathml:
+     - "<math><mi intent='size-of-test'>α</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Size_(statistics)"
+  
+  - concept: skewes-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: skewes number of $a1
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='skewes-number($a1)'><mi>Sk</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SkewesNumber.html"
+     - "https://en.wikipedia.org/wiki/Skewes%27_number"
+  
+  - concept: small-o
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: small o of $a1
+    property: prefix
+    subject-area: "complexity"
+    mathml:
+     - "<math><mrow intent='small-o($a1)'><mi>o</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Big_O_notation"
+     - "https://mathworld.wolfram.com/o.html"
+  
+  - concept: smith-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: smith number of $a1
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='smith-number($a1)'><mi>S</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SmithNumber.html"
+     - "https://en.wikipedia.org/wiki/Smith_number"
+  
+  - concept: sobolev-space
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: sobolev space
-      property: "indexed symbol"
-      area: "fourier analysis"
-      mathml:
-       - "<math><mrow intent='sobolev-space($a1,$a2)'><msup><mi>W</mi><mrow><mi arg='a1'>k</mi><mi arg='a2'>p</mi></mrow></msup></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SobolevSpace.html"
-       - "https://en.wikipedia.org/wiki/Sobolev_space"
-       - "https://ncatlab.org/nlab/show/Sobolev+space"
-       - "https://www.encyclopediaofmath.org/index.php/Sobolev_space"
-    
-    - concept: socle
-      arity: 1
-      en: socle of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='socle($a1)'><mi>soc</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Socle.html"
-       - "https://en.wikipedia.org/wiki/Socle_(mathematics)"
-       - "https://ncatlab.org/nlab/show/socle"
-       - "https://www.encyclopediaofmath.org/index.php/Socle"
-    
-    - concept: soft-o
-      arity: 0
+    property: "indexed symbol"
+    subject-area: "fourier analysis"
+    mathml:
+     - "<math><mrow intent='sobolev-space($a1,$a2)'><msup><mi>W</mi><mrow><mi arg='a1'>k</mi><mi arg='a2'>p</mi></mrow></msup></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SobolevSpace.html"
+     - "https://en.wikipedia.org/wiki/Sobolev_space"
+     - "https://ncatlab.org/nlab/show/Sobolev+space"
+     - "https://www.encyclopediaofmath.org/index.php/Sobolev_space"
+  
+  - concept: socle
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: socle of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='socle($a1)'><mi>soc</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Socle.html"
+     - "https://en.wikipedia.org/wiki/Socle_(mathematics)"
+     - "https://ncatlab.org/nlab/show/socle"
+     - "https://www.encyclopediaofmath.org/index.php/Socle"
+  
+  - concept: soft-o
+    arity: 0
+    arguments: []
+    speech:
       en: soft o
-      property: symbol
-      area: "complexity theory"
-      mathml:
-       - "<math><mi intent='soft-o'>Õ</mi></math>"
-      urls: 
-      alias:
-       - Extensions_to_the_Bachmann–Landau_notations
-    
-    - concept: solid-angle
-      arity: 0
+    property: symbol
+    subject-area: "complexity theory"
+    mathml:
+     - "<math><mi intent='soft-o'>Õ</mi></math>"
+    urls: 
+    alias:
+     - Extensions_to_the_Bachmann–Landau_notations
+  
+  - concept: solid-angle
+    arity: 0
+    arguments: []
+    speech:
       en: solid angle
-      property: symbol
-      area: "geometry"
-      mathml:
-       - "<math><mi intent='solid-angle'>Ω</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SolidAngle.html"
-       - "https://en.wikipedia.org/wiki/Solid_angle"
-       - "https://www.encyclopediaofmath.org/index.php/Solid_angle"
-    
-    - concept: span
-      arity: 1
-      en: $1 span
-      property: unit
-      area: "imperial units"
-      mathml:
-       - "<math><mrow intent='span($a1)'><mi>span</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Span_(unit)"
-    
-    - concept: special-linear-group
-      arity: 1
-      en: special linear group of $1
-      property: "indexed function"
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='special-linear-group($a1)'><mi>SL</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SpecialLinearGroup.html"
-       - "https://en.wikipedia.org/wiki/Special_linear_group"
-       - "https://ncatlab.org/nlab/show/special+linear+group"
-       - "https://www.encyclopediaofmath.org/index.php/Special_linear_group"
-    
-    - concept: special-orthogonal-group
-      arity: 1
-      en: special orthogonal group of $1
-      property: "indexed function"
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='special-orthogonal-group($a1)'><mi>SO</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SpecialOrthogonalGroup.html"
-       - "https://ncatlab.org/nlab/show/special+orthogonal+group"
-    
-    - concept: special-unitary-group
-      arity: 1
-      en: special unitary group of $1
-      property: function
-      area: "lie groups"
-      mathml:
-       - "<math><mrow intent='special-unitary-group($a1)'><mi>SU</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SpecialUnitaryGroup.html"
-       - "https://en.wikipedia.org/wiki/Special_unitary_group"
-       - "https://ncatlab.org/nlab/show/special+unitary+group"
-    
-    - concept: spectral-radius
-      arity: 1
-      en: spectral radius of $1
-      property: function
-      area: "spectral theory"
-      mathml:
-       - "<math><mrow intent='spectral-radius($a1)'><mi>ρ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SpectralRadius.html"
-       - "https://en.wikipedia.org/wiki/Spectral_radius"
-       - "https://www.encyclopediaofmath.org/index.php/Spectral_radius"
-    
-    - concept: spectrum
-      arity: 1
-      en: spectrum of $1
-      property: function
-      area: "functional analysis"
-      mathml:
-       - "<math><mrow intent='spectrum($a1)'><mi>σ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Spectrum_(functional_analysis)"
-    
-    - concept: spectrum-category
-      arity: 0
+    property: symbol
+    subject-area: "geometry"
+    mathml:
+     - "<math><mi intent='solid-angle'>Ω</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SolidAngle.html"
+     - "https://en.wikipedia.org/wiki/Solid_angle"
+     - "https://www.encyclopediaofmath.org/index.php/Solid_angle"
+  
+  - concept: span
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1 span
+    property: unit
+    subject-area: "imperial units"
+    mathml:
+     - "<math><mrow intent='span($a1)'><mi>span</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Span_(unit)"
+  
+  - concept: special-linear-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: special linear group of $a1
+    property: "indexed function"
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='special-linear-group($a1)'><mi>SL</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SpecialLinearGroup.html"
+     - "https://en.wikipedia.org/wiki/Special_linear_group"
+     - "https://ncatlab.org/nlab/show/special+linear+group"
+     - "https://www.encyclopediaofmath.org/index.php/Special_linear_group"
+  
+  - concept: special-orthogonal-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: special orthogonal group of $a1
+    property: "indexed function"
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='special-orthogonal-group($a1)'><mi>SO</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SpecialOrthogonalGroup.html"
+     - "https://ncatlab.org/nlab/show/special+orthogonal+group"
+  
+  - concept: special-unitary-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: special unitary group of $a1
+    property: function
+    subject-area: "lie groups"
+    mathml:
+     - "<math><mrow intent='special-unitary-group($a1)'><mi>SU</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SpecialUnitaryGroup.html"
+     - "https://en.wikipedia.org/wiki/Special_unitary_group"
+     - "https://ncatlab.org/nlab/show/special+unitary+group"
+  
+  - concept: spectral-radius
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: spectral radius of $a1
+    property: function
+    subject-area: "spectral theory"
+    mathml:
+     - "<math><mrow intent='spectral-radius($a1)'><mi>ρ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SpectralRadius.html"
+     - "https://en.wikipedia.org/wiki/Spectral_radius"
+     - "https://www.encyclopediaofmath.org/index.php/Spectral_radius"
+  
+  - concept: spectrum
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: spectrum of $a1
+    property: function
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><mrow intent='spectrum($a1)'><mi>σ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Spectrum_(functional_analysis)"
+  
+  - concept: spectrum-category
+    arity: 0
+    arguments: []
+    speech:
       en: spectrum category
-      property: symbol
-      area: "category theory"
-      mathml:
-       - "<math><mi intent='spectrum-category'>Sp</mi></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/Spectrum"
-    
-    - concept: spectrum-of-matrix
-      arity: 1
-      en: spectrum of matrix of $1
-      property: msub
-      area: "linear algebra"
-      mathml:
-       - "<math><msub intent='spectrum-of-matrix($a1)'><mi>σ</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Spectrum_of_a_matrix"
-    
-    - concept: spectrum-of-algebra
-      arity: 1
-      en: spectrum of algebra of $1
-      property: mover
-      area: "algebra"
-      mathml:
-       - "<math><mover intent='spectrum-of-algebra($a1)'><mi arg='a1'>A</mi><mo>^</mo></mover></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Spectrum_of_a_C*-algebra"
-    
-    - concept: spectrum-of-ring
-      arity: 1
-      en: spectrum of ring of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='spectrum-of-ring($a1)'><mi>Spec</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Spectrum_of_a_ring"
-    
-    - concept: spherical-bessel-function-of-third-kind
-      arity: 2
+    property: symbol
+    subject-area: "category theory"
+    mathml:
+     - "<math><mi intent='spectrum-category'>Sp</mi></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/Spectrum"
+  
+  - concept: spectrum-of-matrix
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: spectrum of matrix of $a1
+    property: msub
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><msub intent='spectrum-of-matrix($a1)'><mi>σ</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Spectrum_of_a_matrix"
+  
+  - concept: spectrum-of-algebra
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: spectrum of algebra of $a1
+    property: mover
+    subject-area: "algebra"
+    mathml:
+     - "<math><mover intent='spectrum-of-algebra($a1)'><mi arg='a1'>A</mi><mo>^</mo></mover></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Spectrum_of_a_C*-algebra"
+  
+  - concept: spectrum-of-ring
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: spectrum of ring of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='spectrum-of-ring($a1)'><mi>Spec</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Spectrum_of_a_ring"
+  
+  - concept: spherical-bessel-function-of-third-kind
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
       en: spherical bessel function of third kind
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='spherical-bessel-function($a1)'><msubsup><mi>h</mi><mi>n</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mrow><mo>(</mo><mi arg='a1'>z</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='spherical-bessel-function($a1)'><msubsup><mi>h</mi><mi>n</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup><mrow><mo>(</mo><mi arg='a1'>z</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SphericalBesselFunctionoftheThirdKind.html"
-       - "https://dlmf.nist.gov/10.47#E5"
-       - "https://dlmf.nist.gov/10.47#E6"
-    
-    - concept: spherical-coordinate
-      arity: 3
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='spherical-bessel-function($a1)'><msubsup><mi>h</mi><mi>n</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mrow><mo>(</mo><mi arg='a1'>z</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='spherical-bessel-function($a1)'><msubsup><mi>h</mi><mi>n</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup><mrow><mo>(</mo><mi arg='a1'>z</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SphericalBesselFunctionoftheThirdKind.html"
+     - "https://dlmf.nist.gov/10.47#E5"
+     - "https://dlmf.nist.gov/10.47#E6"
+  
+  - concept: spherical-coordinate
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
       en: spherical coordinate
-      property: fenced
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='spherical-coordinate($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SphericalCoordinates.html"
-       - "https://www.encyclopediaofmath.org/index.php/Spherical_coordinates"
-    
-    - concept: spin-angular-momentum
-      arity: 0
+    property: fenced
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='spherical-coordinate($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SphericalCoordinates.html"
+     - "https://www.encyclopediaofmath.org/index.php/Spherical_coordinates"
+  
+  - concept: spin-angular-momentum
+    arity: 0
+    arguments: []
+    speech:
       en: spin angular momentum
-      property: symbol
-      area: "quantum mechanics"
-      mathml:
-       - "<math><mi intent='spin-angular-momentum'>S</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Spin_(physics)"
-    
-    - concept: spin-group
-      arity: 0
+    property: symbol
+    subject-area: "quantum mechanics"
+    mathml:
+     - "<math><mi intent='spin-angular-momentum'>S</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Spin_(physics)"
+  
+  - concept: spin-group
+    arity: 0
+    arguments: []
+    speech:
       en: spin group
-      property: symbol
-      area: "group theory"
-      mathml:
-       - "<math><mi intent='spin-group'>Spin</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SpinGroup.html"
-       - "https://en.wikipedia.org/wiki/Spin_group"
-       - "https://ncatlab.org/nlab/show/spin+group"
-       - "https://www.encyclopediaofmath.org/index.php/Spin_group"
-    
-    - concept: spin-quantum-number
-      arity: 0
+    property: symbol
+    subject-area: "group theory"
+    mathml:
+     - "<math><mi intent='spin-group'>Spin</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SpinGroup.html"
+     - "https://en.wikipedia.org/wiki/Spin_group"
+     - "https://ncatlab.org/nlab/show/spin+group"
+     - "https://www.encyclopediaofmath.org/index.php/Spin_group"
+  
+  - concept: spin-quantum-number
+    arity: 0
+    arguments: []
+    speech:
       en: spin quantum number
-      property: symbol
-      area: "quantum mechanics"
-      mathml:
-       - "<math><mi intent='spin-quantum-number'>s</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Spin_(physics)"
-    
-    - concept: square
-      arity: 4
-      en: "square $1 $2 $3 $4"
-      property: prefix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='square($a1,$a2,$a3,$a4)'><mo>□</mo><mrow><mi arg='a1'>A</mi><mo>&#x2009;</mo><mi arg='a2'>B</mi><mo>&#x2009;</mo><mi arg='a3'>C</mi><mo>&#x2009;</mo><mi arg='a4'>D</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Square.html"
-       - "https://en.wikipedia.org/wiki/Square"
-    
-    - concept: stable-distribution
-      arity: 0
+    property: symbol
+    subject-area: "quantum mechanics"
+    mathml:
+     - "<math><mi intent='spin-quantum-number'>s</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Spin_(physics)"
+  
+  - concept: square
+    arity: 4
+    arguments: [$a1, $a2, $a3, $a4]
+    speech:
+      en: "square $a1 $a2 $a3 $a4"
+    property: prefix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='square($a1,$a2,$a3,$a4)'><mo>□</mo><mrow><mi arg='a1'>A</mi><mo>&#x2009;</mo><mi arg='a2'>B</mi><mo>&#x2009;</mo><mi arg='a3'>C</mi><mo>&#x2009;</mo><mi arg='a4'>D</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Square.html"
+     - "https://en.wikipedia.org/wiki/Square"
+  
+  - concept: stable-distribution
+    arity: 0
+    arguments: []
+    speech:
       en: stable distribution
-      property: symbol
-      area: "probability theory"
-      mathml:
-       - "<math><msub intent='stable-distribution'><mi>S</mi><mn>1</mn></msub></math>"
-       - "<math><msub intent='stable-distribution'><mi>S</mi><mn>2</mn></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/StableDistribution.html"
-       - "https://en.wikipedia.org/wiki/Stable_distribution"
-       - "https://www.encyclopediaofmath.org/index.php/Stable_distribution"
-    
-    - concept: stalk
-      arity: 2
-      en: stalk of $1 at $2
-      property: msub
-      area: "sheaf theory"
-      mathml:
-       - "<math><msub intent='stalk($a1,$a2)'><mi arg='a1'>ℱ</mi><mi arg='a2'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Stalk_(sheaf)"
-    
-    - concept: standard-deviation
-      arity: 0
+    property: symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><msub intent='stable-distribution'><mi>S</mi><mn>1</mn></msub></math>"
+     - "<math><msub intent='stable-distribution'><mi>S</mi><mn>2</mn></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/StableDistribution.html"
+     - "https://en.wikipedia.org/wiki/Stable_distribution"
+     - "https://www.encyclopediaofmath.org/index.php/Stable_distribution"
+  
+  - concept: stalk
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: stalk of $a1 at $a2
+    property: msub
+    subject-area: "sheaf theory"
+    mathml:
+     - "<math><msub intent='stalk($a1,$a2)'><mi arg='a1'>ℱ</mi><mi arg='a2'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Stalk_(sheaf)"
+  
+  - concept: standard-deviation
+    arity: 0
+    arguments: []
+    speech:
       en: standard deviation
-      property: symbol
-      area: "probability theory"
-      mathml:
-       - "<math><mi intent='standard-deviation'>σ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/StandardDeviation.html"
-       - "https://en.wikipedia.org/wiki/Standard_deviation"
-       - "https://en.wikipedia.org/wiki/Sample_standard_deviation"
-       - "https://www.encyclopediaofmath.org/index.php/Standard_deviation"
-    
-    - concept: standard-flattening
-      arity: 1
-      en: standard flattening of $1
-      property: "indexed symbol"
-      area: "multilinear algebra"
-      mathml:
-       - "<math><msub intent='standard-flattening($a1)'><mi>𝐀</mi><mrow><mo>[</mo><mi arg='a1'>m</mi><mo>]</mo></mrow></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Matricization"
-      alias:
-       - matricization
-       - unfolding
-    
-    - concept: stanley-reisner-ring
-      arity: 2
-      en: stanley reisner ring $1 $2
-      property: mixfix
-      area: "commutative algebra"
-      mathml:
-       - "<math><mrow intent='stanley-reisner-ring($a1,$a2)'><mi arg='a1'>k</mi><mrow><mo>[</mo><mi arg='a2'>Δ</mi><mo>]</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Stanley%E2%80%93Reisner_ring"
-       - "https://www.encyclopediaofmath.org/index.php/Stanley-Reisner_ring"
-       - "https://www.encyclopediaofmath.org/index.php/StanleyâXXXXReisner_ring"
-      alias:
-       - face-ring
-    
-    - concept: stanley-reisner-ideal
-      arity: 1
-      en: stanley reisner ideal of $1
-      property: msub
-      area: "commutative algebra"
-      mathml:
-       - "<math><msub intent='stanley-reisner-ideal($a1)'><mi>I</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Stanley%E2%80%93Reisner_ring"
-       - "https://www.encyclopediaofmath.org/index.php/Stanley-Reisner_ring"
-       - "https://www.encyclopediaofmath.org/index.php/StanleyâXXXXReisner_ring"
-      alias:
-       - face-ideal
-    
-    - concept: star-game
-      arity: 0
+    property: symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><mi intent='standard-deviation'>σ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/StandardDeviation.html"
+     - "https://en.wikipedia.org/wiki/Standard_deviation"
+     - "https://en.wikipedia.org/wiki/Sample_standard_deviation"
+     - "https://www.encyclopediaofmath.org/index.php/Standard_deviation"
+  
+  - concept: standard-flattening
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: standard flattening of $a1
+    property: "indexed symbol"
+    subject-area: "multilinear algebra"
+    mathml:
+     - "<math><msub intent='standard-flattening($a1)'><mi>𝐀</mi><mrow><mo>[</mo><mi arg='a1'>m</mi><mo>]</mo></mrow></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Matricization"
+    alias:
+     - matricization
+     - unfolding
+  
+  - concept: stanley-reisner-ring
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: stanley reisner ring $a1 $a2
+    property: mixfix
+    subject-area: "commutative algebra"
+    mathml:
+     - "<math><mrow intent='stanley-reisner-ring($a1,$a2)'><mi arg='a1'>k</mi><mrow><mo>[</mo><mi arg='a2'>Δ</mi><mo>]</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Stanley%E2%80%93Reisner_ring"
+     - "https://www.encyclopediaofmath.org/index.php/Stanley-Reisner_ring"
+     - "https://www.encyclopediaofmath.org/index.php/StanleyâXXXXReisner_ring"
+    alias:
+     - face-ring
+  
+  - concept: stanley-reisner-ideal
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: stanley reisner ideal of $a1
+    property: msub
+    subject-area: "commutative algebra"
+    mathml:
+     - "<math><msub intent='stanley-reisner-ideal($a1)'><mi>I</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Stanley%E2%80%93Reisner_ring"
+     - "https://www.encyclopediaofmath.org/index.php/Stanley-Reisner_ring"
+     - "https://www.encyclopediaofmath.org/index.php/StanleyâXXXXReisner_ring"
+    alias:
+     - face-ideal
+  
+  - concept: star-game
+    arity: 0
+    arguments: []
+    speech:
       en: star
-      property: constant
-      area: "combinatorial game theory"
-      mathml:
-       - "<math><mo intent='star-game'>∗</mo></math>"
-       - "<math><mrow intent='star-game'><mo>{</mo><mn>0</mn><mo>|</mo><mn>0</mn><mo>}</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Star_(game_theory)"
-    
-    - concept: star-height
-      arity: 1
-      en: star height of $1
-      property: function
-      area: "formal languages"
-      mathml:
-       - "<math><mrow intent='star-height($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Star_height"
-    
-    - concept: steinberg-group
-      arity: 1
-      en: steinberg group of $1
-      property: function
-      area: "k-theory"
-      mathml:
-       - "<math><mrow intent='steinberg-group($a1)'><mi>St</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Group_of_Lie_type"
-       - "https://en.wikipedia.org/wiki/Steinberg_group_(K-theory)"
-       - "https://ncatlab.org/nlab/show/Steinberg+group"
-    
-    - concept: stiefel-manifold
-      arity: 2
-      en: $1<i>th</i> stiefel manifold over $2
-      property: mixfix
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='stiefel-manifold($a1,$a2)'><msub><mi>V</mi><mi arg='a1'>k</mi></msub><mrow><mo>(</mo><msup arg='a2'><mi>ℝ</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math>"
-      notation: "mrow msub V $1 /msub ( $2"
-      urls: 
-       - "https://mathworld.wolfram.com/StiefelManifold.html"
-       - "https://en.wikipedia.org/wiki/Stiefel_manifold"
-       - "https://www.encyclopediaofmath.org/index.php/Stiefel_manifold"
-    
-    - concept: stiefel-whitney-class
-      arity: 1
-      en: stiefel whitney class of $1
-      property: function
-      area: "algebraic topology"
-      mathml:
-       - "<math><mrow intent='stiefel-whitney-class($a1)'><mi>w</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Stiefel-WhitneyClass.html"
-       - "https://en.wikipedia.org/wiki/Stiefel%E2%80%93Whitney_class"
-       - "https://ncatlab.org/nlab/show/Stiefel-Whitney+class"
-       - "https://www.encyclopediaofmath.org/index.php/Stiefel-Whitney_class"
-       - "https://www.encyclopediaofmath.org/index.php/StiefelâXXXXWhitney_class"
-    
-    - concept: stieltjes-wigert-polynomial
-      arity: 1
-      en: stieltjes wigert polynomial of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='stieltjes-wigert-polynomial($a1)'><mi>S</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Stieltjes-WigertPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Stieltjes%E2%80%93Wigert_polynomials"
-       - "https://dlmf.nist.gov/18.27#E18"
-    
-    - concept: stirling-number-of-first-kind
-      arity: 1
-      en: stirling number of first kind of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='stirling-number-of-first-kind($a1)'><mi>s</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/StirlingNumberoftheFirstKind.html"
-       - "https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind"
-       - "https://dlmf.nist.gov/26.8#SS1.p1"
-    
-    - concept: stirling-number-of-second-kind
-      arity: 1
-      en: stirling number of second kind of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='stirling-number-of-second-kind($a1)'><mi>S</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html"
-       - "https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind"
-       - "https://dlmf.nist.gov/26.8#SS1.p3"
-    
-    - concept: strength-of-a-graph
-      arity: 1
-      en: strength of a graph of $1
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='strength-of-a-graph($a1)'><mi>σ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Strength_of_a_graph"
-      alias:
-       - strength
-    
-    - concept: string-concatenation
-      arity: 2
-      en: $1 string concatenation $2
-      property: infix
-      area: "computer science"
-      mathml:
-       - "<math><mrow intent='string-concatenation($a1,$a2)'><mi arg='a1'>ABC</mi><mo>*</mo><mi arg='a2'>XYZ</mi></mrow></math>"
-       - "<math><mrow intent='string-concatenation($a1,$a2)'><mi arg='a1'>ABC</mi><mo>⁢</mo><mi arg='a2'>XYZ</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Concatenation.html"
-       - "https://en.wikipedia.org/wiki/Concatenation_(mathematics)"
-    
-    - concept: strong-product
-      arity: 2
-      en: $1 strong product $2
-      property: infix
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='strong-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⊠</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/w/index.php?title=Graph_product"
-      alias:
-       - normal-product
-       - and-product
-    
-    - concept: struve-function
-      arity: 1
-      en: struve function of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='struve-function($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/StruveFunction.html"
-       - "https://en.wikipedia.org/wiki/Struve_function"
-       - "https://dlmf.nist.gov/11.2#E1"
-       - "https://dlmf.nist.gov/11.2#E5"
-       - "https://www.encyclopediaofmath.org/index.php/Struve_function"
-    
-    - concept: stufe
-      arity: 1
-      en: stufe of $1
-      property: function
-      area: "field theory"
-      mathml:
-       - "<math><mrow intent='stufe($a1)'><mi>s</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Stufe_(algebra)"
-    
-    - concept: subfactorial
-      arity: 1
-      en: subfactorial of $1
-      property: prefix
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='subfactorial($a1)'><mo>!</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Derangement"
-      alias:
-       - derangement-number
-       - de-montmort-number
-    
-    - concept: subgroup
-      arity: 2
-      en: $1 subgroup $2
-      property: infix
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='subgroup($a1,$a2)'><mi arg='a1'>X</mi><mo>≤</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Subgroup.html"
-       - "https://en.wikipedia.org/wiki/Subgroup"
-       - "https://ncatlab.org/nlab/show/subgroup"
-       - "https://www.encyclopediaofmath.org/index.php/Subgroup"
-    
-    - concept: succeeds
-      arity: 2
-      en: $1 succeeds $2
-      property: infix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='succeeds($a1,$a2)'><mi arg='a1'>X</mi><mo>≻</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Succeeds.html"
-       - "https://en.wikipedia.org/wiki/Ordered_set_operators"
-    
-    - concept: succeeds-or-equals
-      arity: 2
-      en: $1 succeeds or equals $2
-      property: infix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='succeeds-or-equals($a1,$a2)'><mi arg='a1'>X</mi><mo>≽</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Ordered_set_operators"
-    
-    - concept: successor
-      arity: 1
-      en: successor of $1
-      property: "function, msup"
-      area: "number theory"
-      mathml:
-       - "<math><msup intent='successor($a1)'><mi arg='a1'>X</mi><mo>+</mo></msup></math>"
-       - "<math><mrow intent='successor($a1)'><mi>s</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='successor($a1)'><mi>S</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Proclus"
-       - "https://en.wikipedia.org/wiki/Successor_cardinal"
-       - "https://en.wikipedia.org/wiki/Successor_ordinal"
-       - "https://ncatlab.org/nlab/show/successor"
-    
-    - concept: such-that
-      arity: 2
-      en: $1 such that $2
-      property: infix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='such-that($a1,$a2)'><mi arg='a1'>X</mi><mo>|</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='such-that($a1,$a2)'><mi arg='a1'>X</mi><mo>:</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Set_(mathematics)#Set-builder_notation"
-    
-    - concept: sumset
-      arity: 2
-      en: $1 sumset $2
-      property: infix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='sumset($a1,$a2)'><mi arg='a1'>X</mi><mo>+</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Sumset.html"
-       - "https://en.wikipedia.org/wiki/Sumset"
-    
-    - concept: superfluous-submodule
-      arity: 2
-      en: $1 superfluous submodule $2
-      property: infix
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='superfluous-submodule($a1,$a2)'><mi arg='a1'>X</mi><msub><mo>⊆</mo><mi>s</mi></msub><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='superfluous-submodule($a1,$a2)'><mi arg='a1'>X</mi><mo>≪</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Essential_extension"
-      alias:
-       - small-submodule
-    
-    - concept: support
-      arity: 1
-      en: support of $1
-      property: function
-      area: "analysis"
-      mathml:
-       - "<math><mrow intent='support($a1)'><mi>supp</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Support.html"
-       - "https://en.wikipedia.org/wiki/Support_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Support_of_a_module"
-       - "https://en.wikipedia.org/wiki/Support_(measure_theory)"
-       - "https://ncatlab.org/nlab/show/support"
-      alias:
-       - spectrum
-       - topological-support
-    
-    - concept: supremum
-      arity: 1
-      en: supremum of $1
-      property: "function, largeop"
-      area: "order theory, lattice theory"
-      mathml:
-       - "<math><mrow intent='supremum($a1)'><mi>sup</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='supremum($a1)'><mo>⋁</mo><mi arg='a1'>X</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Supremum.html"
-      alias:
-       - join
-       - least-upper-bound
-    
-    - concept: supremum-limit
-      arity: 1
-      en: supremum limit of $1
-      property: indexed
-      area: "limits"
-      mathml:
-       - "<math><mrow intent='supremum-limit($a1)'><mi>lim sup</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='supremum-limit($a1)'><mover><mi>lim</mi><mo>¯</mo></mover><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SupremumLimit.html"
-       - "https://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior"
-      alias:
-       - limit-superior
-       - limit-supremum
-       - limsup
-       - superior-limit
-       - upper-limit
-       - outer-limit
-    
-    - concept: surface-integral
-      arity: 1
-      en: surface integral of $1
-      property: indexed
-      area: "calculus"
-      mathml:
-       - "<math><mrow intent='surface-integral($a1)'><msub><mo>∬</mo><mi>S</mi></msub><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SurfaceIntegral.html"
-       - "https://en.wikipedia.org/wiki/Surface_integral"
-       - "https://www.encyclopediaofmath.org/index.php/Surface_integral"
-    
-    - concept: surjection
-      arity: 3
-      en: surjection  $1, from $2 to $3
-      property: mixfix, infix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='surjection($a1,$a2,$a3)'><mi arg='a1'>f</mi><mo>:</mo><mi arg='a2'>X</mi><mo>&#x21a0;</mo><mi arg='a3'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Bijection#Definition"
-       - "https://en.wikipedia.org/wiki/Surjective_function"
-    
-    - concept: suspension
-      arity: 1
-      en: suspension of $1
-      property: function
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='suspension($a1)'><mi>S</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Suspension.html"
-       - "https://en.wikipedia.org/wiki/Suspension_(topology)"
-       - "https://ncatlab.org/nlab/show/suspension"
-       - "https://www.encyclopediaofmath.org/index.php/Suspension"
-    
-    - concept: symmetric-algebra
-      arity: 1
-      en: symmetric algebra of $1
-      property: function
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='symmetric-algebra($a1)'><mi>S</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='symmetric-algebra($a1)'><mi>Sym</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Symmetric_algebra"
-       - "https://ncatlab.org/nlab/show/symmetric+algebra"
-       - "https://www.encyclopediaofmath.org/index.php/Symmetric_algebra"
-    
-    - concept: symmetric-difference
-      arity: 2
-      en: $1 symmetric difference $2
-      property: infix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='symmetric-difference($a1,$a2)'><mi arg='a1'>X</mi><mo>△</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='symmetric-difference($a1,$a2)'><mi arg='a1'>X</mi><mo>⊕</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='symmetric-difference($a1,$a2)'><mi arg='a1'>X</mi><mo>⊖</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SymmetricDifference.html"
-       - "https://en.wikipedia.org/wiki/Symmetric_difference"
-       - "https://ncatlab.org/nlab/show/symmetric+difference"
-    
-    - concept: symmetric-group
-      arity: 1
-      en: symmetric group of $1
-      property: "msub, function, postfix"
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='symmetric-group($a1)'><mi>S</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='symmetric-group($a1)'><mi>𝔖</mi><mi arg='a1'>x</mi></msub></math>"
-       - "<math><msub intent='symmetric-group($a1)'><mi>Σ</mi><mi arg='a1'>x</mi></msub></math>"
-      notationd: "mrow Σ ( $1 )"
-      notationc: "mrow Sym ( $1 )"
-      notationb: "mrow $1 !"
-      notationa: ""
-      urls: 
-       - "https://mathworld.wolfram.com/SymmetricGroup.html"
-       - "https://en.wikipedia.org/wiki/Symmetric_group"
-       - "https://www.encyclopediaofmath.org/index.php/Symmetric_group"
-    
-    - concept: symmetric-space
-      arity: 0
+    property: constant
+    subject-area: "combinatorial game theory"
+    mathml:
+     - "<math><mo intent='star-game'>∗</mo></math>"
+     - "<math><mrow intent='star-game'><mo>{</mo><mn>0</mn><mo>|</mo><mn>0</mn><mo>}</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Star_(game_theory)"
+  
+  - concept: star-height
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: star height of $a1
+    property: function
+    subject-area: "formal languages"
+    mathml:
+     - "<math><mrow intent='star-height($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Star_height"
+  
+  - concept: steinberg-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: steinberg group of $a1
+    property: function
+    subject-area: "k-theory"
+    mathml:
+     - "<math><mrow intent='steinberg-group($a1)'><mi>St</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Group_of_Lie_type"
+     - "https://en.wikipedia.org/wiki/Steinberg_group_(K-theory)"
+     - "https://ncatlab.org/nlab/show/Steinberg+group"
+  
+  - concept: stiefel-manifold
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1<i>th</i> stiefel manifold over $a2
+    property: mixfix
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='stiefel-manifold($a1,$a2)'><msub><mi>V</mi><mi arg='a1'>k</mi></msub><mrow><mo>(</mo><msup arg='a2'><mi>ℝ</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math>"
+    notation: "mrow msub V $a1 /msub ( $a2"
+    urls: 
+     - "https://mathworld.wolfram.com/StiefelManifold.html"
+     - "https://en.wikipedia.org/wiki/Stiefel_manifold"
+     - "https://www.encyclopediaofmath.org/index.php/Stiefel_manifold"
+  
+  - concept: stiefel-whitney-class
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: stiefel whitney class of $a1
+    property: function
+    subject-area: "algebraic topology"
+    mathml:
+     - "<math><mrow intent='stiefel-whitney-class($a1)'><mi>w</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Stiefel-WhitneyClass.html"
+     - "https://en.wikipedia.org/wiki/Stiefel%E2%80%93Whitney_class"
+     - "https://ncatlab.org/nlab/show/Stiefel-Whitney+class"
+     - "https://www.encyclopediaofmath.org/index.php/Stiefel-Whitney_class"
+     - "https://www.encyclopediaofmath.org/index.php/StiefelâXXXXWhitney_class"
+  
+  - concept: stieltjes-wigert-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: stieltjes wigert polynomial of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='stieltjes-wigert-polynomial($a1)'><mi>S</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Stieltjes-WigertPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Stieltjes%E2%80%93Wigert_polynomials"
+     - "https://dlmf.nist.gov/18.27#E18"
+  
+  - concept: stirling-number-of-first-kind
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: stirling number of first kind of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='stirling-number-of-first-kind($a1)'><mi>s</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/StirlingNumberoftheFirstKind.html"
+     - "https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind"
+     - "https://dlmf.nist.gov/26.8#SS1.p1"
+  
+  - concept: stirling-number-of-second-kind
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: stirling number of second kind of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='stirling-number-of-second-kind($a1)'><mi>S</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html"
+     - "https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind"
+     - "https://dlmf.nist.gov/26.8#SS1.p3"
+  
+  - concept: strength-of-a-graph
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: strength of a graph of $a1
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='strength-of-a-graph($a1)'><mi>σ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Strength_of_a_graph"
+    alias:
+     - strength
+  
+  - concept: string-concatenation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 string concatenation $a2
+    property: infix
+    subject-area: "computer science"
+    mathml:
+     - "<math><mrow intent='string-concatenation($a1,$a2)'><mi arg='a1'>ABC</mi><mo>*</mo><mi arg='a2'>XYZ</mi></mrow></math>"
+     - "<math><mrow intent='string-concatenation($a1,$a2)'><mi arg='a1'>ABC</mi><mo>⁢</mo><mi arg='a2'>XYZ</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Concatenation.html"
+     - "https://en.wikipedia.org/wiki/Concatenation_(mathematics)"
+  
+  - concept: strong-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 strong product $a2
+    property: infix
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='strong-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⊠</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/w/index.php?title=Graph_product"
+    alias:
+     - normal-product
+     - and-product
+  
+  - concept: struve-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: struve function of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='struve-function($a1)'><mi>H</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/StruveFunction.html"
+     - "https://en.wikipedia.org/wiki/Struve_function"
+     - "https://dlmf.nist.gov/11.2#E1"
+     - "https://dlmf.nist.gov/11.2#E5"
+     - "https://www.encyclopediaofmath.org/index.php/Struve_function"
+  
+  - concept: stufe
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: stufe of $a1
+    property: function
+    subject-area: "field theory"
+    mathml:
+     - "<math><mrow intent='stufe($a1)'><mi>s</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Stufe_(algebra)"
+  
+  - concept: subfactorial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: subfactorial of $a1
+    property: prefix
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='subfactorial($a1)'><mo>!</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Derangement"
+    alias:
+     - derangement-number
+     - de-montmort-number
+  
+  - concept: subgroup
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 subgroup $a2
+    property: infix
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='subgroup($a1,$a2)'><mi arg='a1'>X</mi><mo>≤</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Subgroup.html"
+     - "https://en.wikipedia.org/wiki/Subgroup"
+     - "https://ncatlab.org/nlab/show/subgroup"
+     - "https://www.encyclopediaofmath.org/index.php/Subgroup"
+  
+  - concept: succeeds
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 succeeds $a2
+    property: infix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='succeeds($a1,$a2)'><mi arg='a1'>X</mi><mo>≻</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Succeeds.html"
+     - "https://en.wikipedia.org/wiki/Ordered_set_operators"
+  
+  - concept: succeeds-or-equals
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 succeeds or equals $a2
+    property: infix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='succeeds-or-equals($a1,$a2)'><mi arg='a1'>X</mi><mo>≽</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Ordered_set_operators"
+  
+  - concept: successor
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: successor of $a1
+    property: "function, msup"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msup intent='successor($a1)'><mi arg='a1'>X</mi><mo>+</mo></msup></math>"
+     - "<math><mrow intent='successor($a1)'><mi>s</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='successor($a1)'><mi>S</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Proclus"
+     - "https://en.wikipedia.org/wiki/Successor_cardinal"
+     - "https://en.wikipedia.org/wiki/Successor_ordinal"
+     - "https://ncatlab.org/nlab/show/successor"
+  
+  - concept: such-that
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 such that $a2
+    property: infix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='such-that($a1,$a2)'><mi arg='a1'>X</mi><mo>|</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='such-that($a1,$a2)'><mi arg='a1'>X</mi><mo>:</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Set_(mathematics)#Set-builder_notation"
+  
+  - concept: sumset
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 sumset $a2
+    property: infix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='sumset($a1,$a2)'><mi arg='a1'>X</mi><mo>+</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Sumset.html"
+     - "https://en.wikipedia.org/wiki/Sumset"
+  
+  - concept: superfluous-submodule
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 superfluous submodule $a2
+    property: infix
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='superfluous-submodule($a1,$a2)'><mi arg='a1'>X</mi><msub><mo>⊆</mo><mi>s</mi></msub><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='superfluous-submodule($a1,$a2)'><mi arg='a1'>X</mi><mo>≪</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Essential_extension"
+    alias:
+     - small-submodule
+  
+  - concept: support
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: support of $a1
+    property: function
+    subject-area: "analysis"
+    mathml:
+     - "<math><mrow intent='support($a1)'><mi>supp</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Support.html"
+     - "https://en.wikipedia.org/wiki/Support_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Support_of_a_module"
+     - "https://en.wikipedia.org/wiki/Support_(measure_theory)"
+     - "https://ncatlab.org/nlab/show/support"
+    alias:
+     - spectrum
+     - topological-support
+  
+  - concept: supremum
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: supremum of $a1
+    property: "function, largeop"
+    subject-area: "order theory, lattice theory"
+    mathml:
+     - "<math><mrow intent='supremum($a1)'><mi>sup</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='supremum($a1)'><mo>⋁</mo><mi arg='a1'>X</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Supremum.html"
+    alias:
+     - join
+     - least-upper-bound
+  
+  - concept: supremum-limit
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: supremum limit of $a1
+    property: indexed
+    subject-area: "limits"
+    mathml:
+     - "<math><mrow intent='supremum-limit($a1)'><mi>lim sup</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='supremum-limit($a1)'><mover><mi>lim</mi><mo>¯</mo></mover><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SupremumLimit.html"
+     - "https://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior"
+    alias:
+     - limit-superior
+     - limit-supremum
+     - limsup
+     - superior-limit
+     - upper-limit
+     - outer-limit
+  
+  - concept: surface-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: surface integral of $a1
+    property: indexed
+    subject-area: "calculus"
+    mathml:
+     - "<math><mrow intent='surface-integral($a1)'><msub><mo>∬</mo><mi>S</mi></msub><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SurfaceIntegral.html"
+     - "https://en.wikipedia.org/wiki/Surface_integral"
+     - "https://www.encyclopediaofmath.org/index.php/Surface_integral"
+  
+  - concept: surjection
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: surjection  $a1, from $a2 to $a3
+    property: mixfix, infix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='surjection($a1,$a2,$a3)'><mi arg='a1'>f</mi><mo>:</mo><mi arg='a2'>X</mi><mo>&#x21a0;</mo><mi arg='a3'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Bijection#Definition"
+     - "https://en.wikipedia.org/wiki/Surjective_function"
+  
+  - concept: suspension
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: suspension of $a1
+    property: function
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='suspension($a1)'><mi>S</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Suspension.html"
+     - "https://en.wikipedia.org/wiki/Suspension_(topology)"
+     - "https://ncatlab.org/nlab/show/suspension"
+     - "https://www.encyclopediaofmath.org/index.php/Suspension"
+  
+  - concept: symmetric-algebra
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: symmetric algebra of $a1
+    property: function
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='symmetric-algebra($a1)'><mi>S</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='symmetric-algebra($a1)'><mi>Sym</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Symmetric_algebra"
+     - "https://ncatlab.org/nlab/show/symmetric+algebra"
+     - "https://www.encyclopediaofmath.org/index.php/Symmetric_algebra"
+  
+  - concept: symmetric-difference
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 symmetric difference $a2
+    property: infix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='symmetric-difference($a1,$a2)'><mi arg='a1'>X</mi><mo>△</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='symmetric-difference($a1,$a2)'><mi arg='a1'>X</mi><mo>⊕</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='symmetric-difference($a1,$a2)'><mi arg='a1'>X</mi><mo>⊖</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SymmetricDifference.html"
+     - "https://en.wikipedia.org/wiki/Symmetric_difference"
+     - "https://ncatlab.org/nlab/show/symmetric+difference"
+  
+  - concept: symmetric-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: symmetric group of $a1
+    property: "msub, function, postfix"
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='symmetric-group($a1)'><mi>S</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='symmetric-group($a1)'><mi>𝔖</mi><mi arg='a1'>x</mi></msub></math>"
+     - "<math><msub intent='symmetric-group($a1)'><mi>Σ</mi><mi arg='a1'>x</mi></msub></math>"
+    notationd: "mrow Σ ( $a1 )"
+    notationc: "mrow Sym ( $a1 )"
+    notationb: "mrow $a1 !"
+    notationa: ""
+    urls: 
+     - "https://mathworld.wolfram.com/SymmetricGroup.html"
+     - "https://en.wikipedia.org/wiki/Symmetric_group"
+     - "https://www.encyclopediaofmath.org/index.php/Symmetric_group"
+  
+  - concept: symmetric-space
+    arity: 0
+    arguments: []
+    speech:
       en: symmetric space
-      property: constant
-      area: "topology"
-      mathml:
-       - "<math><msub intent='symmetric-space'><mi>R</mi><mn>0</mn></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions)s"
-    
-    - concept: symplectic-group
-      arity: 1
-      en: symplectic group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='symplectic-group($a1)'><mi>Sp</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/SymplecticGroup.html"
-       - "https://en.wikipedia.org/wiki/Symplectic_group"
-       - "https://en.wikipedia.org/wiki/Symplectic_Lie_algebra"
-       - "https://ncatlab.org/nlab/show/symplectic+group"
-       - "https://www.encyclopediaofmath.org/index.php/Symplectic_group"
-    
-    - concept: szego-polynomial
-      arity: 1
-      en: szego polynomial of $1
-      property: "indexed function"
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><msub intent='szego-polynomial($a1)'><mi>ϕ</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Szeg%C5%91_polynomial"
-       - "https://www.encyclopediaofmath.org/index.php/Szego_polynomial"
-       - "https://www.encyclopediaofmath.org/index.php/Szegö_polynomial"
-    
-    - concept: tangent-bundle
-      arity: 1
-      en: tangent bundle of $1
-      property: function
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='tangent-bundle($a1)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TangentBundle.html"
-       - "https://en.wikipedia.org/wiki/Tangent_bundle"
-       - "https://ncatlab.org/nlab/show/tangent+bundle"
-       - "https://www.encyclopediaofmath.org/index.php/Tangent_bundle"
-    
-    - concept: tangent-space
-      arity: 1
-      en: tangent space of $1
-      property: "indexed function"
-      area: "topology"
-      mathml:
-       - "<math><msub intent='tangent-space($a1)'><mi>T</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TangentSpace.html"
-       - "https://en.wikipedia.org/wiki/Tangent_space"
-       - "https://www.encyclopediaofmath.org/index.php/Tangent_space"
-    
-    - concept: tate-algebra
-      arity: 0
+    property: constant
+    subject-area: "topology"
+    mathml:
+     - "<math><msub intent='symmetric-space'><mi>R</mi><mn>0</mn></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions)s"
+  
+  - concept: symplectic-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: symplectic group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='symplectic-group($a1)'><mi>Sp</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/SymplecticGroup.html"
+     - "https://en.wikipedia.org/wiki/Symplectic_group"
+     - "https://en.wikipedia.org/wiki/Symplectic_Lie_algebra"
+     - "https://ncatlab.org/nlab/show/symplectic+group"
+     - "https://www.encyclopediaofmath.org/index.php/Symplectic_group"
+  
+  - concept: szego-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: szego polynomial of $a1
+    property: "indexed function"
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><msub intent='szego-polynomial($a1)'><mi>ϕ</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Szeg%C5%91_polynomial"
+     - "https://www.encyclopediaofmath.org/index.php/Szego_polynomial"
+     - "https://www.encyclopediaofmath.org/index.php/Szegö_polynomial"
+  
+  - concept: tangent-bundle
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: tangent bundle of $a1
+    property: function
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='tangent-bundle($a1)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TangentBundle.html"
+     - "https://en.wikipedia.org/wiki/Tangent_bundle"
+     - "https://ncatlab.org/nlab/show/tangent+bundle"
+     - "https://www.encyclopediaofmath.org/index.php/Tangent_bundle"
+  
+  - concept: tangent-space
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: tangent space of $a1
+    property: "indexed function"
+    subject-area: "topology"
+    mathml:
+     - "<math><msub intent='tangent-space($a1)'><mi>T</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TangentSpace.html"
+     - "https://en.wikipedia.org/wiki/Tangent_space"
+     - "https://www.encyclopediaofmath.org/index.php/Tangent_space"
+  
+  - concept: tate-algebra
+    arity: 0
+    arguments: []
+    speech:
       en: tate algebra
-      property: symbol
-      area: "analytic geometry"
-      mathml:
-       - "<math><msub intent='tate-algebra'><mi>T</mi><mi>n</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Tate_algebra"
-       - "https://ncatlab.org/nlab/show/Tate+algebra"
-       - "https://www.encyclopediaofmath.org/index.php/Tate_algebra"
-    
-    - concept: tate-module
-      arity: 1
-      en: tate module of $1
-      property: "indexed function"
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='tate-module($a1)'><mi>T</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Tate_module"
-       - "https://ncatlab.org/nlab/show/Tate+module"
-       - "https://www.encyclopediaofmath.org/index.php/Tate_module"
-    
-    - concept: tau-particle
-      arity: 0
+    property: symbol
+    subject-area: "analytic geometry"
+    mathml:
+     - "<math><msub intent='tate-algebra'><mi>T</mi><mi>n</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Tate_algebra"
+     - "https://ncatlab.org/nlab/show/Tate+algebra"
+     - "https://www.encyclopediaofmath.org/index.php/Tate_algebra"
+  
+  - concept: tate-module
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: tate module of $a1
+    property: "indexed function"
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='tate-module($a1)'><mi>T</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Tate_module"
+     - "https://ncatlab.org/nlab/show/Tate+module"
+     - "https://www.encyclopediaofmath.org/index.php/Tate_module"
+  
+  - concept: tau-particle
+    arity: 0
+    arguments: []
+    speech:
       en: tau particle
-      property: symbol
-      area: "particle physics"
-      mathml:
-       - "<math><mi intent='tau-particle'>τ</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Tau_(particle)"
-    
-    - concept: taxicab-number
-      arity: 1
-      en: taxicab number of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='taxicab-number($a1)'><mi>Ta</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TaxicabNumber.html"
-       - "https://en.wikipedia.org/wiki/Taxicab_number"
-    
-    - concept: taylor-polynomial
-      arity: 1
-      en: taylor polynomial of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='taylor-polynomial($a1)'><mi>Ta</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TaylorPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Taylor%27s_theorem"
-       - "https://www.encyclopediaofmath.org/index.php/Taylor_polynomial"
-    
-    - concept: teichmuller-space
-      arity: 1
-      en: teichmuller space of $1
-      property: function
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='teichmuller-space($a1)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TeichmuellerSpace.html"
-       - "https://en.wikipedia.org/wiki/Teichm%C3%BCller_space"
-       - "https://www.encyclopediaofmath.org/index.php/Teichmüller_space"
-    
-    - concept: temperature
-      arity: 0
+    property: symbol
+    subject-area: "particle physics"
+    mathml:
+     - "<math><mi intent='tau-particle'>τ</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Tau_(particle)"
+  
+  - concept: taxicab-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: taxicab number of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='taxicab-number($a1)'><mi>Ta</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TaxicabNumber.html"
+     - "https://en.wikipedia.org/wiki/Taxicab_number"
+  
+  - concept: taylor-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: taylor polynomial of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='taylor-polynomial($a1)'><mi>Ta</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TaylorPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Taylor%27s_theorem"
+     - "https://www.encyclopediaofmath.org/index.php/Taylor_polynomial"
+  
+  - concept: teichmuller-space
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: teichmuller space of $a1
+    property: function
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='teichmuller-space($a1)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TeichmuellerSpace.html"
+     - "https://en.wikipedia.org/wiki/Teichm%C3%BCller_space"
+     - "https://www.encyclopediaofmath.org/index.php/Teichmüller_space"
+  
+  - concept: temperature
+    arity: 0
+    arguments: []
+    speech:
       en: temperature
-      property: symbol
-      area: "physics"
-      mathml:
-       - "<math><mi intent='temperature'>T</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Temperature.html"
-       - "https://en.wikipedia.org/wiki/Temperature"
-       - "https://ncatlab.org/nlab/show/temperature"
-    
-    - concept: tensor-algebra
-      arity: 1
-      en: tensor algebra of $1
-      property: function
-      area: "multilinear algebra"
-      mathml:
-       - "<math><mrow intent='tensor-algebra($a1)'><mi>T</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='tensor-algebra($a1)'><msup><mi>T</mi><mo>•</mo></msup><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Tensor_algebra"
-    
-    - concept: tensor-product
-      arity: 2
-      en: $1 tensor product $2
-      property: infix
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='tensor-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⊗</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TensorProduct.html"
-       - "https://en.wikipedia.org/wiki/Tensor_product"
-       - "https://en.wikipedia.org/wiki/Tensor_product_of_graphs"
-       - "https://ncatlab.org/nlab/show/tensor+product"
-       - "https://www.encyclopediaofmath.org/index.php/Tensor_product"
-    
-    - concept: tensor-product-of-graphs
-      arity: 2
-      en: $1 tensor product of graphs $2
-      property: infix
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='tensor-product-of-graphs($a1,$a2)'><mi arg='a1'>X</mi><mo>×</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Tensor_product_of_graphs"
-      alias:
-       - kronecker-product-of-graphs
-       - categorical-product
-    
-    - concept: therefore-sign
-      arity: 1
-      en: therefore $1
-      property: prefix
-      area: "logic"
-      mathml:
-       - "<math><mrow intent='therefore-sign($a1)'><mo>∴</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Therefore_sign"
-       - "https://en.wikipedia.org/wiki/.%C2%B7."
-       - "https://en.wikipedia.org/wiki/%E2%88%B4"
-    
-    - concept: theta-function
-      arity: 1
-      en: theta function of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><msub intent='theta-function($a1)'><mi>θ</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ThetaFunction.html"
-       - "https://en.wikipedia.org/wiki/Theta_function"
-       - "https://dlmf.nist.gov/20.2#i"
-       - "https://dlmf.nist.gov/20.2#i"
-       - "https://dlmf.nist.gov/20.2#i"
-       - "https://ncatlab.org/nlab/show/theta+function"
-    
-    - concept: thom-space
-      arity: 1
-      en: thom space of $1
-      property: function
-      area: "algebraic topology"
-      mathml:
-       - "<math><mrow intent='thom-space($a1)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Thom_space"
-       - "https://ncatlab.org/nlab/show/Thom+space"
-       - "https://www.encyclopediaofmath.org/index.php/Thom_space"
-    
-    - concept: thompson-group
-      arity: 0
+    property: symbol
+    subject-area: "physics"
+    mathml:
+     - "<math><mi intent='temperature'>T</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Temperature.html"
+     - "https://en.wikipedia.org/wiki/Temperature"
+     - "https://ncatlab.org/nlab/show/temperature"
+  
+  - concept: tensor-algebra
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: tensor algebra of $a1
+    property: function
+    subject-area: "multilinear algebra"
+    mathml:
+     - "<math><mrow intent='tensor-algebra($a1)'><mi>T</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='tensor-algebra($a1)'><msup><mi>T</mi><mo>•</mo></msup><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Tensor_algebra"
+  
+  - concept: tensor-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 tensor product $a2
+    property: infix
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='tensor-product($a1,$a2)'><mi arg='a1'>X</mi><mo>⊗</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TensorProduct.html"
+     - "https://en.wikipedia.org/wiki/Tensor_product"
+     - "https://en.wikipedia.org/wiki/Tensor_product_of_graphs"
+     - "https://ncatlab.org/nlab/show/tensor+product"
+     - "https://www.encyclopediaofmath.org/index.php/Tensor_product"
+  
+  - concept: tensor-product-of-graphs
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 tensor product of graphs $a2
+    property: infix
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='tensor-product-of-graphs($a1,$a2)'><mi arg='a1'>X</mi><mo>×</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Tensor_product_of_graphs"
+    alias:
+     - kronecker-product-of-graphs
+     - categorical-product
+  
+  - concept: therefore-sign
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: therefore $a1
+    property: prefix
+    subject-area: "logic"
+    mathml:
+     - "<math><mrow intent='therefore-sign($a1)'><mo>∴</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Therefore_sign"
+     - "https://en.wikipedia.org/wiki/.%C2%B7."
+     - "https://en.wikipedia.org/wiki/%E2%88%B4"
+  
+  - concept: theta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: theta function of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><msub intent='theta-function($a1)'><mi>θ</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ThetaFunction.html"
+     - "https://en.wikipedia.org/wiki/Theta_function"
+     - "https://dlmf.nist.gov/20.2#i"
+     - "https://dlmf.nist.gov/20.2#i"
+     - "https://dlmf.nist.gov/20.2#i"
+     - "https://ncatlab.org/nlab/show/theta+function"
+  
+  - concept: thom-space
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: thom space of $a1
+    property: function
+    subject-area: "algebraic topology"
+    mathml:
+     - "<math><mrow intent='thom-space($a1)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Thom_space"
+     - "https://ncatlab.org/nlab/show/Thom+space"
+     - "https://www.encyclopediaofmath.org/index.php/Thom_space"
+  
+  - concept: thompson-group
+    arity: 0
+    arguments: []
+    speech:
       en: thompson group
-      property: symbol
-      area: "group theory"
-      mathml:
-       - "<math><mi intent='thompson-group'>Th</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ThompsonGroup.html"
-       - "https://en.wikipedia.org/wiki/Thompson_groups"
-       - "https://en.wikipedia.org/wiki/Thompson_sporadic_group"
-    
-    - concept: to
-      arity: 2
-      en: $1 to $2
-      property: infix
-      area: "arithmetic"
-      mathml:
-       - "<math><mrow intent='to($a1,$a2)'><mi arg='a1'>X</mi><mo>:</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/One-to-One.html"
-    
-    - concept: todd-class
-      arity: 1
-      en: todd class of $1
-      property: function
-      area: "characteristic classes"
-      mathml:
-       - "<math><mrow intent='todd-class($a1)'><mi>td</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='todd-class($a1)'><mi>Td</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Todd_class"
-       - "https://ncatlab.org/nlab/show/Todd+class"
-       - "https://www.encyclopediaofmath.org/index.php/Todd_class"
-    
-    - concept: topological-entropy
-      arity: 1
-      en: topological entropy of $1
-      property: function
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='topological-entropy($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TopologicalEntropy.html"
-       - "https://en.wikipedia.org/wiki/Topological_entropy"
-       - "https://www.encyclopediaofmath.org/index.php/Topological_entropy"
-    
-    - concept: toroidal-coordinate
-      arity: 3
-      en: toroidal coordinates $1 $2 $3
-      property: fenced
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='toroidal-coordinate($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>σ</mi><mo>,</mo><mi arg='a2'>τ</mi><mo>,</mo><mi arg='a3'>ϕ</mi><mo>)</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ToroidalCoordinates.html"
-       - "https://en.wikipedia.org/wiki/Toroidal_coordinates"
-       - "https://www.encyclopediaofmath.org/index.php/Toroidal_coordinates"
-    
-    - concept: torque
-      arity: 0
+    property: symbol
+    subject-area: "group theory"
+    mathml:
+     - "<math><mi intent='thompson-group'>Th</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ThompsonGroup.html"
+     - "https://en.wikipedia.org/wiki/Thompson_groups"
+     - "https://en.wikipedia.org/wiki/Thompson_sporadic_group"
+  
+  - concept: to
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 to $a2
+    property: infix
+    subject-area: "arithmetic"
+    mathml:
+     - "<math><mrow intent='to($a1,$a2)'><mi arg='a1'>X</mi><mo>:</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/One-to-One.html"
+  
+  - concept: todd-class
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: todd class of $a1
+    property: function
+    subject-area: "characteristic classes"
+    mathml:
+     - "<math><mrow intent='todd-class($a1)'><mi>td</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='todd-class($a1)'><mi>Td</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Todd_class"
+     - "https://ncatlab.org/nlab/show/Todd+class"
+     - "https://www.encyclopediaofmath.org/index.php/Todd_class"
+  
+  - concept: topological-entropy
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: topological entropy of $a1
+    property: function
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='topological-entropy($a1)'><mi>h</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TopologicalEntropy.html"
+     - "https://en.wikipedia.org/wiki/Topological_entropy"
+     - "https://www.encyclopediaofmath.org/index.php/Topological_entropy"
+  
+  - concept: toroidal-coordinate
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: toroidal coordinates $a1 $a2 $a3
+    property: fenced
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='toroidal-coordinate($a1,$a2,$a3)'><mo>(</mo><mi arg='a1'>σ</mi><mo>,</mo><mi arg='a2'>τ</mi><mo>,</mo><mi arg='a3'>ϕ</mi><mo>)</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ToroidalCoordinates.html"
+     - "https://en.wikipedia.org/wiki/Toroidal_coordinates"
+     - "https://www.encyclopediaofmath.org/index.php/Toroidal_coordinates"
+  
+  - concept: torque
+    arity: 0
+    arguments: []
+    speech:
       en: torque
-      property: symbol
-      area: "mechanics"
-      mathml:
-       - "<math><mi intent='torque'>τ</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Torque"
-    
-    - concept: torsion
-      arity: 0
+    property: symbol
+    subject-area: "mechanics"
+    mathml:
+     - "<math><mi intent='torque'>τ</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Torque"
+  
+  - concept: torsion
+    arity: 0
+    arguments: []
+    speech:
       en: torsion
-      property: symbol
-      area: "differential geometry"
-      mathml:
-       - "<math><mi intent='torsion'>τ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Torsion.html"
-       - "https://en.wikipedia.org/wiki/Torsion_of_a_curve"
-       - "https://ncatlab.org/nlab/show/torsion"
-       - "https://www.encyclopediaofmath.org/index.php/Torsion"
-    
-    - concept: torsion-submodule
-      arity: 1
-      en: torsion submodule of $1
-      property: function
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='torsion-submodule($a1)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Torsion_(algebra)"
-    
-    - concept: torsion-subgroup
-      arity: 1
-      en: torsion subgroup of $1
-      property: msub
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='torsion-subgroup($a1)'><mi arg='a1'>G</mi><mi>T</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Torsion_subgroup"
-       - "https://ncatlab.org/nlab/show/torsion+subgroup"
-    
-    - concept: torsion-tensor
-      arity: 1
-      en: torsion tensor of $1
-      property: function
-      area: "differential geometry"
-      mathml:
-       - "<math><mrow intent='torsion-tensor($a1)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Torsion_tensor"
-    
-    - concept: total-derivative
-      arity: 2
-      en: total derivative of $1 at $2
-      property: mixfix
-      area: "differential calculus"
-      mathml:
-       - "<math><mrow intent='total-derivative($a1,$a2)'><msub><mi>D</mi><mi arg='a2'>a</mi></msub><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TotalDerivative.html"
-       - "https://en.wikipedia.org/wiki/Total_derivative"
-       - "https://www.encyclopediaofmath.org/index.php/Total_derivative"
-      alias:
-       - total-differential
-    
-    - concept: total-variation
-      arity: 1
-      en: total variation of $1
-      property: fenced
-      area: "measure theory"
-      mathml:
-       - "<math><mrow intent='total-variation($a1)'><mo>|</mo><mi arg='a1'>x</mi><mo>|</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TotalVariation.html"
-       - "https://en.wikipedia.org/wiki/Total_variation"
-       - "https://dlmf.nist.gov/1.4#E33"
-    
-    - concept: trace
-      arity: 1
-      en: trace of $1
-      property: function
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='trace($a1)'><mi>tr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Trace_(linear_algebra)"
-    
-    - concept: transitive-closure
-      arity: 1
-      en: transitive closure of $1
-      property: msup
-      area: "set theory"
-      mathml:
-       - "<math><msup intent='transitive-closure($a1)'><mi arg='a1'>X</mi><mo>+</mo></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TransitiveClosure.html"
-       - "https://en.wikipedia.org/wiki/Transitive_closure"
-       - "https://ncatlab.org/nlab/show/transitive+closure"
-    
-    - concept: triangle
-      arity: 3
+    property: symbol
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mi intent='torsion'>τ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Torsion.html"
+     - "https://en.wikipedia.org/wiki/Torsion_of_a_curve"
+     - "https://ncatlab.org/nlab/show/torsion"
+     - "https://www.encyclopediaofmath.org/index.php/Torsion"
+  
+  - concept: torsion-submodule
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: torsion submodule of $a1
+    property: function
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='torsion-submodule($a1)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Torsion_(algebra)"
+  
+  - concept: torsion-subgroup
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: torsion subgroup of $a1
+    property: msub
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='torsion-subgroup($a1)'><mi arg='a1'>G</mi><mi>T</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Torsion_subgroup"
+     - "https://ncatlab.org/nlab/show/torsion+subgroup"
+  
+  - concept: torsion-tensor
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: torsion tensor of $a1
+    property: function
+    subject-area: "differential geometry"
+    mathml:
+     - "<math><mrow intent='torsion-tensor($a1)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Torsion_tensor"
+  
+  - concept: total-derivative
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: total derivative of $a1 at $a2
+    property: mixfix
+    subject-area: "differential calculus"
+    mathml:
+     - "<math><mrow intent='total-derivative($a1,$a2)'><msub><mi>D</mi><mi arg='a2'>a</mi></msub><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TotalDerivative.html"
+     - "https://en.wikipedia.org/wiki/Total_derivative"
+     - "https://www.encyclopediaofmath.org/index.php/Total_derivative"
+    alias:
+     - total-differential
+  
+  - concept: total-variation
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: total variation of $a1
+    property: fenced
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mrow intent='total-variation($a1)'><mo>|</mo><mi arg='a1'>x</mi><mo>|</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TotalVariation.html"
+     - "https://en.wikipedia.org/wiki/Total_variation"
+     - "https://dlmf.nist.gov/1.4#E33"
+  
+  - concept: trace
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: trace of $a1
+    property: function
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='trace($a1)'><mi>tr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Trace_(linear_algebra)"
+  
+  - concept: transitive-closure
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: transitive closure of $a1
+    property: msup
+    subject-area: "set theory"
+    mathml:
+     - "<math><msup intent='transitive-closure($a1)'><mi arg='a1'>X</mi><mo>+</mo></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TransitiveClosure.html"
+     - "https://en.wikipedia.org/wiki/Transitive_closure"
+     - "https://ncatlab.org/nlab/show/transitive+closure"
+  
+  - concept: triangle
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
       en: triangle
-      property: prefix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='triangle($a1,$a2,$a3)'><mo>△</mo><mrow><mi arg='a1'>A</mi><mo>&#x2009;</mo><mi arg='a2'>B</mi><mo>&#x2009;</mo><mi arg='a3'>C</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Triangle.html"
-       - "https://en.wikipedia.org/wiki/Triangle"
-       - "https://ncatlab.org/nlab/show/triangle"
-       - "https://www.encyclopediaofmath.org/index.php/Triangle"
-    
-    - concept: triangle-function
-      arity: 1
-      en: triangle function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='triangle-function($a1)'><mi>Λ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='triangle-function($a1)'><mi>tri</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TriangleFunction.html"
-       - "https://en.wikipedia.org/wiki/Triangular_function"
-      alias:
-       - hat-function
-       - tent-function
-    
-    - concept: triangular-number
-      arity: 1
-      en: triangular number $1
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='triangular-number($a1)'><mi>T</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TriangularNumber.html"
-       - "https://en.wikipedia.org/wiki/Triangular_number"
-       - "https://en.wikipedia.org/wiki/Centered_triangular_number"
-       - "https://www.encyclopediaofmath.org/index.php/Triangular_number"
-    
-    - concept: trilinear-coordinates
-      arity: 3
-      en: trilinear coordinates $1, $2, $3
-      property: infix
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='trilinear-coordinates($a1,$a2,$a3)'><mi arg='a1'>x</mi><mo>:</mo><mi arg='a2'>y</mi><mo>:</mo><mi arg='a3'>z</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Trilinear_coordinates"
-    
-    - concept: trimean
-      arity: 1
-      en: trimean of $1
-      property: function
-      area: "statistics"
-      mathml:
-       - "<math><mrow intent='trimean($a1)'><mi>TM</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Trimean"
-      alias:
-       - tukey-trimean
-    
-    - concept: triple-bond
-      arity: 2
-      en: $1 triple bond $2
-      property: infix
-      area: "chemistry"
-      mathml:
-       - "<math><mrow intent='triple-bond($a1,$a2)'><mi arg='a1'>X</mi><mo>≡</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Triple_bond"
-    
-    - concept: triple-scalar-product
-      arity: 3
-      en: triple scalar product of $1, $2 and $3
-      property: fenced
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='triple-scalar-product($a1,$a2,$a3)'><mo>[</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TripleScalarProduct.html"
-      alias:
-       - scalar-triple-product
-    
-    - concept: triple-torus
-      arity: 0
+    property: prefix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='triangle($a1,$a2,$a3)'><mo>△</mo><mrow><mi arg='a1'>A</mi><mo>&#x2009;</mo><mi arg='a2'>B</mi><mo>&#x2009;</mo><mi arg='a3'>C</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Triangle.html"
+     - "https://en.wikipedia.org/wiki/Triangle"
+     - "https://ncatlab.org/nlab/show/triangle"
+     - "https://www.encyclopediaofmath.org/index.php/Triangle"
+  
+  - concept: triangle-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: triangle function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='triangle-function($a1)'><mi>Λ</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='triangle-function($a1)'><mi>tri</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TriangleFunction.html"
+     - "https://en.wikipedia.org/wiki/Triangular_function"
+    alias:
+     - hat-function
+     - tent-function
+  
+  - concept: triangular-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: triangular number $a1
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='triangular-number($a1)'><mi>T</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TriangularNumber.html"
+     - "https://en.wikipedia.org/wiki/Triangular_number"
+     - "https://en.wikipedia.org/wiki/Centered_triangular_number"
+     - "https://www.encyclopediaofmath.org/index.php/Triangular_number"
+  
+  - concept: trilinear-coordinates
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: trilinear coordinates $a1, $a2, $a3
+    property: infix
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='trilinear-coordinates($a1,$a2,$a3)'><mi arg='a1'>x</mi><mo>:</mo><mi arg='a2'>y</mi><mo>:</mo><mi arg='a3'>z</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Trilinear_coordinates"
+  
+  - concept: trimean
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: trimean of $a1
+    property: function
+    subject-area: "statistics"
+    mathml:
+     - "<math><mrow intent='trimean($a1)'><mi>TM</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Trimean"
+    alias:
+     - tukey-trimean
+  
+  - concept: triple-bond
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 triple bond $a2
+    property: infix
+    subject-area: "chemistry"
+    mathml:
+     - "<math><mrow intent='triple-bond($a1,$a2)'><mi arg='a1'>X</mi><mo>≡</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Triple_bond"
+  
+  - concept: triple-scalar-product
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: triple scalar product of $a1, $a2 and $a3
+    property: fenced
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='triple-scalar-product($a1,$a2,$a3)'><mo>[</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TripleScalarProduct.html"
+    alias:
+     - scalar-triple-product
+  
+  - concept: triple-torus
+    arity: 0
+    arguments: []
+    speech:
       en: triple torus
-      property: "indexed symbol"
-      area: "topology"
-      mathml:
-       - "<math><msup intent='triple-torus'><mi>𝕋</mi><mn>3</mn></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TripleTorus.html"
-       - "https://en.wikipedia.org/wiki/Three-torus"
-       - "https://en.wikipedia.org/wiki/Triple_torus"
-    
-    - concept: truncation
-      arity: 1
-      en: truncation of $1
-      property: function
-      area: "numerical analysis"
-      mathml:
-       - "<math><mrow intent='truncation($a1)'><mi>trunc</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Truncation.html"
-       - "https://en.wikipedia.org/wiki/Truncation"
-    
-    - concept: tube-domain
-      arity: 1
-      en: tube domain of $1
-      property: msub
-      area: "complex analysis"
-      mathml:
-       - "<math><msub intent='tube-domain($a1)'><mi>T</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Tube_domain"
-       - "https://www.encyclopediaofmath.org/index.php/Tube_domain"
-    
-    - concept: turan-graph
-      arity: 2
-      en: turan graph $1 $2
-      property: "function, indexed function"
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='turan-graph($a1,$a2)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>,</mo><mi arg='a2'>r</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TuranGraph.html"
-       - "https://en.wikipedia.org/wiki/Tur%C3%A1n_graph"
-       - "https://en.wikipedia.org/wiki/Cocktail_party_graph"
-    
-    - concept: turan-number
-      arity: 3
-      en: turan number of $1, $2 and $3
-      property: function
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='turan-number($a1,$a2,$a3)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Tur%C3%A1n_number"
-       - "https://www.encyclopediaofmath.org/index.php/Turan_number"
-       - "https://www.encyclopediaofmath.org/index.php/Turán_number"
-    
-    - concept: turn
-      arity: 1
-      en: turn of $1
-      property: unit
-      area: "geometry"
-      mathml:
-       - "<math><mrow intent='turn($a1)'><mi>cyc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='turn($a1)'><mi>rev</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='turn($a1)'><mi>tr</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-       - "<math><mrow intent='turn($a1)'><mi>pla</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Turn_(geometry)"
-      alias:
-       - cycle
-       - revolution
-       - plenus angulus
-    
-    - concept: twisted-tensor-product
-      arity: 2
-      en: $1 twisted tensor product $2
-      property: infix
-      area: "topology"
-      mathml:
-       - "<math><mrow intent='twisted-tensor-product($a1,$a2)'><mi arg='a1'>X</mi><msub><mo>⊗</mo><mi>τ</mi></msub><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/twisted+tensor+product"
-    
-    - concept: tychonoff-space
-      arity: 0
+    property: "indexed symbol"
+    subject-area: "topology"
+    mathml:
+     - "<math><msup intent='triple-torus'><mi>𝕋</mi><mn>3</mn></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TripleTorus.html"
+     - "https://en.wikipedia.org/wiki/Three-torus"
+     - "https://en.wikipedia.org/wiki/Triple_torus"
+  
+  - concept: truncation
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: truncation of $a1
+    property: function
+    subject-area: "numerical analysis"
+    mathml:
+     - "<math><mrow intent='truncation($a1)'><mi>trunc</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Truncation.html"
+     - "https://en.wikipedia.org/wiki/Truncation"
+  
+  - concept: tube-domain
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: tube domain of $a1
+    property: msub
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><msub intent='tube-domain($a1)'><mi>T</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Tube_domain"
+     - "https://www.encyclopediaofmath.org/index.php/Tube_domain"
+  
+  - concept: turan-graph
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: turan graph $a1 $a2
+    property: "function, indexed function"
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='turan-graph($a1,$a2)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>n</mi><mo>,</mo><mi arg='a2'>r</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TuranGraph.html"
+     - "https://en.wikipedia.org/wiki/Tur%C3%A1n_graph"
+     - "https://en.wikipedia.org/wiki/Cocktail_party_graph"
+  
+  - concept: turan-number
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: turan number of $a1, $a2 and $a3
+    property: function
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='turan-number($a1,$a2,$a3)'><mi>T</mi><mrow><mo>(</mo><mi arg='a1'>a</mi><mo>,</mo><mi arg='a2'>b</mi><mo>,</mo><mi arg='a3'>c</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Tur%C3%A1n_number"
+     - "https://www.encyclopediaofmath.org/index.php/Turan_number"
+     - "https://www.encyclopediaofmath.org/index.php/Turán_number"
+  
+  - concept: turn
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: turn of $a1
+    property: unit
+    subject-area: "geometry"
+    mathml:
+     - "<math><mrow intent='turn($a1)'><mi>cyc</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='turn($a1)'><mi>rev</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='turn($a1)'><mi>tr</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+     - "<math><mrow intent='turn($a1)'><mi>pla</mi><mrow><mi arg='a1'>X</mi></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Turn_(geometry)"
+    alias:
+     - cycle
+     - revolution
+     - plenus angulus
+  
+  - concept: twisted-tensor-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 twisted tensor product $a2
+    property: infix
+    subject-area: "topology"
+    mathml:
+     - "<math><mrow intent='twisted-tensor-product($a1,$a2)'><mi arg='a1'>X</mi><msub><mo>⊗</mo><mi>τ</mi></msub><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/twisted+tensor+product"
+  
+  - concept: tychonoff-space
+    arity: 0
+    arguments: []
+    speech:
       en: tychonoff space
-      property: symbol
-      area: "topology"
-      mathml:
-       - "<math><msub intent='tychonoff-space'><mi>T</mi><mn>3</mn></msub></math>"
-       - "<math><msub intent='tychonoff-space'><mi>T</mi><mn>π</mn></msub></math>"
-       - "<math><msub intent='tychonoff-space'><mi>T</mi><mn>3½</mn></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/TychonoffSpace.html"
-       - "https://en.wikipedia.org/wiki/Tychonoff_space"
-       - "https://ncatlab.org/nlab/show/Tychonoff+space"
-    
-    - concept: typing-judgement
-      arity: 2
-      en: $1 typing judgement $2
-      property: infix
-      area: "type theory"
-      mathml:
-       - "<math><mrow intent='typing-judgement($a1,$a2)'><mi arg='a1'>X</mi><mo>:</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/judgment"
-    
-    - concept: ulam-number
-      arity: 1
-      en: $1<i>th</i> ulam number
-      property: "indexed symbol"
-      area: "integer sequences"
-      mathml:
-       - "<math><msub intent='ulam-number($a1)'><mi>U</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/UlamNumber.html"
-       - "https://en.wikipedia.org/wiki/Ulam_number"
-    
-    - concept: ultrapower
-      arity: 2
-      en: ultrapower $1 $2
-      property: mixfix
-      area: "abstract algebra"
-      mathml:
-       - "<math><mrow intent='ultrapower($a1,$a2)'><mo>∏</mo><mi arg='a1'>x</mi><mo>/</mo><mi arg='a2'>y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Ultrapower.html"
-       - "https://en.wikipedia.org/wiki/Ultraproduct"
-       - "https://ncatlab.org/nlab/show/ultrapower"
-    
-    - concept: ultraproduct
-      arity: 3
-      en: ultraproduct of $1, $2 modulo $3
-      property: mixfix
-      area: "abstract algebra"
-      mathml:
-      - "<math><mrow intent='ultraproduct($a1,$a2,$a3)'><msub><mo>∏</mo><mrow><mi>i</mi><mo>∈</mo><mi arg='a2'>I</mi></mrow></msub><mi arg='a1'>M</mi><mo>/</mo><mi arg='a3'>𝒰</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Ultraproduct.html"
-       - "https://en.wikipedia.org/wiki/Ultraproduct"
-       - "https://ncatlab.org/nlab/show/ultraproduct"
-    
-    - concept: uniformly-convergent
-      arity: 2
-      en: $1 uniformly convergs to $2
-      property: infix, indexed, postfix
-      area: "convergence"
-      mathml:
-       - "<math><mrow intent='uniformly-convergent($a1,$2)'><mi arg='a1'>f</mi><mo>⇉</mo><mi arg='a2'>g</mi></mrow></math>"
-       - "<math><mrow intent='uniformly-convergent($a1,$2)'><mi arg='a1'>f</mi><mover><mo>⟶</mo><mi>unif</mi></mover><mi arg='a2'>g</mi></mrow></math>"
-       - "<math><mrow intent='uniformly-convergent($a1,$2)'><mi>unif lim</mi><mi arg='a1'>f</mi><mo>=</mo><mi arg='a2'>g</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Uniform_convergence"
-    
-    - concept: unit-part
-      arity: 1
-      en: unit part of $1
-      property: fenced
-      area: "SI units"
-      mathml:
-       - "<math><mrow intent='unit-part($a1)'><mo>[</mo><mi arg='a1'>x</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values"
-       - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions"
-    
-    - concept: unit-vector
-      arity: 1
-      en: unit vector of $1
-      property: mover
-      area: "linear algebra"
-      mathml:
-       - "<math><mover intent='unit-vector($a1)'><mi arg='a1'>v</mi><mo>^</mo></mover></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/UnitVector.html"
-       - "https://en.wikipedia.org/wiki/Unit_vector"
-       - "https://www.encyclopediaofmath.org/index.php/Unit_vector"
-    
-    - concept: unitary-group
-      arity: 1
-      en: $1<i>th</i> unitary group
-      property: "indexed symbol"
-      area: "group theory"
-      mathml:
-       - "<math><msub intent='unitary-group($a1)'><mi>U</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/UnitaryGroup.html"
-       - "https://en.wikipedia.org/wiki/Unitary_group"
-       - "https://ncatlab.org/nlab/show/unitary+group"
-       - "https://www.encyclopediaofmath.org/index.php/Unitary_group"
-    
-    - concept: universal-gas-constant
-      arity: 0
+    property: symbol
+    subject-area: "topology"
+    mathml:
+     - "<math><msub intent='tychonoff-space'><mi>T</mi><mn>3</mn></msub></math>"
+     - "<math><msub intent='tychonoff-space'><mi>T</mi><mn>π</mn></msub></math>"
+     - "<math><msub intent='tychonoff-space'><mi>T</mi><mn>3½</mn></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/TychonoffSpace.html"
+     - "https://en.wikipedia.org/wiki/Tychonoff_space"
+     - "https://ncatlab.org/nlab/show/Tychonoff+space"
+  
+  - concept: typing-judgement
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 typing judgement $a2
+    property: infix
+    subject-area: "type theory"
+    mathml:
+     - "<math><mrow intent='typing-judgement($a1,$a2)'><mi arg='a1'>X</mi><mo>:</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/judgment"
+  
+  - concept: ulam-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> ulam number
+    property: "indexed symbol"
+    subject-area: "integer sequences"
+    mathml:
+     - "<math><msub intent='ulam-number($a1)'><mi>U</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/UlamNumber.html"
+     - "https://en.wikipedia.org/wiki/Ulam_number"
+  
+  - concept: ultrapower
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: ultrapower $a1 $a2
+    property: mixfix
+    subject-area: "abstract algebra"
+    mathml:
+     - "<math><mrow intent='ultrapower($a1,$a2)'><mo>∏</mo><mi arg='a1'>x</mi><mo>/</mo><mi arg='a2'>y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Ultrapower.html"
+     - "https://en.wikipedia.org/wiki/Ultraproduct"
+     - "https://ncatlab.org/nlab/show/ultrapower"
+  
+  - concept: ultraproduct
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: ultraproduct of $a1, $a2 modulo $a3
+    property: mixfix
+    subject-area: "abstract algebra"
+    mathml:
+    - "<math><mrow intent='ultraproduct($a1,$a2,$a3)'><msub><mo>∏</mo><mrow><mi>i</mi><mo>∈</mo><mi arg='a2'>I</mi></mrow></msub><mi arg='a1'>M</mi><mo>/</mo><mi arg='a3'>𝒰</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Ultraproduct.html"
+     - "https://en.wikipedia.org/wiki/Ultraproduct"
+     - "https://ncatlab.org/nlab/show/ultraproduct"
+  
+  - concept: uniformly-convergent
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 uniformly convergs to $a2
+    property: infix, indexed, postfix
+    subject-area: "convergence"
+    mathml:
+     - "<math><mrow intent='uniformly-convergent($a1,$a2)'><mi arg='a1'>f</mi><mo>⇉</mo><mi arg='a2'>g</mi></mrow></math>"
+     - "<math><mrow intent='uniformly-convergent($a1,$a2)'><mi arg='a1'>f</mi><mover><mo>⟶</mo><mi>unif</mi></mover><mi arg='a2'>g</mi></mrow></math>"
+     - "<math><mrow intent='uniformly-convergent($a1,$a2)'><mi>unif lim</mi><mi arg='a1'>f</mi><mo>=</mo><mi arg='a2'>g</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Uniform_convergence"
+  
+  - concept: unit-part
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: unit part of $a1
+    property: fenced
+    subject-area: "SI units"
+    mathml:
+     - "<math><mrow intent='unit-part($a1)'><mo>[</mo><mi arg='a1'>x</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values"
+     - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions"
+  
+  - concept: unit-vector
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: unit vector of $a1
+    property: mover
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mover intent='unit-vector($a1)'><mi arg='a1'>v</mi><mo>^</mo></mover></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/UnitVector.html"
+     - "https://en.wikipedia.org/wiki/Unit_vector"
+     - "https://www.encyclopediaofmath.org/index.php/Unit_vector"
+  
+  - concept: unitary-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> unitary group
+    property: "indexed symbol"
+    subject-area: "group theory"
+    mathml:
+     - "<math><msub intent='unitary-group($a1)'><mi>U</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/UnitaryGroup.html"
+     - "https://en.wikipedia.org/wiki/Unitary_group"
+     - "https://ncatlab.org/nlab/show/unitary+group"
+     - "https://www.encyclopediaofmath.org/index.php/Unitary_group"
+  
+  - concept: universal-gas-constant
+    arity: 0
+    arguments: []
+    speech:
       en: universal gas constant
-      property: constant
-      area: "physics"
-      mathml:
-       - "<math><mi intent='universal-gas-constant'>R</mi></math>"
-      notationa: "mover R -"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Gas_constant"
-      alias:
-       - gas-constant
-       - molar-gas-constant
-       - ideal-gas-constant
-    
-    - concept: universal-parabolic-constant
-      arity: 0
+    property: constant
+    subject-area: "physics"
+    mathml:
+     - "<math><mi intent='universal-gas-constant'>R</mi></math>"
+    notationa: "mover R -"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Gas_constant"
+    alias:
+     - gas-constant
+     - molar-gas-constant
+     - ideal-gas-constant
+  
+  - concept: universal-parabolic-constant
+    arity: 0
+    arguments: []
+    speech:
       en: universal parabolic constant
-      property: constant
-      area: "geometry"
-      mathml:
-       - "<math><mi intent='universal-parabolic-constant'>P</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/UniversalParabolicConstant.html"
-       - "https://en.wikipedia.org/wiki/Universal_parabolic_constant"
-    
-    - concept: universal-set
-      arity: 0
+    property: constant
+    subject-area: "geometry"
+    mathml:
+     - "<math><mi intent='universal-parabolic-constant'>P</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/UniversalParabolicConstant.html"
+     - "https://en.wikipedia.org/wiki/Universal_parabolic_constant"
+  
+  - concept: universal-set
+    arity: 0
+    arguments: []
+    speech:
       en: universal set
-      property: symbol
-      area: "set theory"
-      mathml:
-       - "<math><mi intent='universal-set'>V</mi></math>"
-       - "<math><mi intent='universal-set'>U</mi></math>"
-       - "<math><mi intent='universal-set'>ξ</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/UniversalSet.html"
-       - "https://en.wikipedia.org/wiki/Universal_set"
-       - "https://www.encyclopediaofmath.org/index.php/Universal_set"
-      alias:
-       - universe
-    
-    - concept: unique-existential
-      arity: 3
-      en: There exists unique $1
-      property: prefix
-      area: "logic"
-      mathml:
-       - "<math><mrow intent='unique-existential($a1)'><mo>∃!</mo><mi arg='a1'>n</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Uniqueness_quantification"
-       - "https://arxiv.org/pdf/1902.03852.pdf"
-    
-    - concept: unnatural-isomorphism
-      arity: 2
-      en: $1 unnatural isomorphism $2
-      property: infix
-      area: "set theory"
-      mathml:
-       - "<math><mrow intent='unnatural-isomorphism($a1,$a2)'><mi arg='a1'>X</mi><mo>≈</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Isomorphism#Relation_with_equality"
-    
-    - concept: unrestricted-wreath-product
-      arity: 2
-      en: $1 unrestricted wreath product $2
-      property: infix
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='unrestricted-wreath-product($a1,$a2)'><mi arg='a1'>X</mi><mo>≀</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='unrestricted-wreath-product($a1,$a2)'><mi arg='a1'>X</mi><mo>Wr</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='unrestricted-wreath-product($a1,$a2)'><mi arg='a1'>X</mi><msub><mo>Wr</mo><mi>&#x03a9;</mi></msub><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WreathProduct.html"
-       - "https://en.wikipedia.org/wiki/Wreath_product"
-       - "https://ncatlab.org/nlab/show/wreath+product"
-       - "https://www.encyclopediaofmath.org/index.php/Wreath_product"
-    
-    - concept: upper-closure-poset
-      arity: 1
-      en: upper closure poset of $1
-      property: prefix
-      area: "order theory"
-      mathml:
-       - "<math><mrow intent='upper-closure-poset($a1)'><mo>↑</mo><mi arg='a1'>x</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Upper_set#Upper_closure_and_lower_closure"
-    
-    - concept: upper-darboux-integral
-      arity: 1
-      en: upper darboux integral of $1
-      property: indexed
-      area: "real analysis"
-      mathml:
-       - "<math><mrow intent='upper-darboux-integral($a1)'><mover><munderover><mo>∫</mo><mi>a</mi><mi>b</mi></munderover><mo>¯</mo></mover><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Darboux_integral"
-       - "https://www.encyclopediaofmath.org/index.php/Darboux_integral"
-    
-    - concept: upper-dini-derivative
-      arity: 1
-      en: upper dini derivative of $1
-      property: decorated function
-      area: "analysis"
-      mathml:
-       - "<math><mrow intent='upper-dini-derivative($a1)'><msub><msup><mi arg='a1'>f</mi><mo>′</mo></msup><mo>+</mo></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/DiniDerivative.html"
-       - "https://en.wikipedia.org/wiki/Dini_derivative"
-       - "https://www.encyclopediaofmath.org/index.php/Dini_derivative"
-    
-    - concept: upper-half-plane
-      arity: 0
+    property: symbol
+    subject-area: "set theory"
+    mathml:
+     - "<math><mi intent='universal-set'>V</mi></math>"
+     - "<math><mi intent='universal-set'>U</mi></math>"
+     - "<math><mi intent='universal-set'>ξ</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/UniversalSet.html"
+     - "https://en.wikipedia.org/wiki/Universal_set"
+     - "https://www.encyclopediaofmath.org/index.php/Universal_set"
+    alias:
+     - universe
+  
+  - concept: unique-existential
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: There exists unique $a1
+    property: prefix
+    subject-area: "logic"
+    mathml:
+     - "<math><mrow intent='unique-existential($a1)'><mo>∃!</mo><mi arg='a1'>n</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Uniqueness_quantification"
+     - "https://arxiv.org/pdf/1902.03852.pdf"
+  
+  - concept: unnatural-isomorphism
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 unnatural isomorphism $a2
+    property: infix
+    subject-area: "set theory"
+    mathml:
+     - "<math><mrow intent='unnatural-isomorphism($a1,$a2)'><mi arg='a1'>X</mi><mo>≈</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Isomorphism#Relation_with_equality"
+  
+  - concept: unrestricted-wreath-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 unrestricted wreath product $a2
+    property: infix
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='unrestricted-wreath-product($a1,$a2)'><mi arg='a1'>X</mi><mo>≀</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='unrestricted-wreath-product($a1,$a2)'><mi arg='a1'>X</mi><mo>Wr</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='unrestricted-wreath-product($a1,$a2)'><mi arg='a1'>X</mi><msub><mo>Wr</mo><mi>&#x03a9;</mi></msub><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WreathProduct.html"
+     - "https://en.wikipedia.org/wiki/Wreath_product"
+     - "https://ncatlab.org/nlab/show/wreath+product"
+     - "https://www.encyclopediaofmath.org/index.php/Wreath_product"
+  
+  - concept: upper-closure-poset
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: upper closure poset of $a1
+    property: prefix
+    subject-area: "order theory"
+    mathml:
+     - "<math><mrow intent='upper-closure-poset($a1)'><mo>↑</mo><mi arg='a1'>x</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Upper_set#Upper_closure_and_lower_closure"
+  
+  - concept: upper-darboux-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: upper darboux integral of $a1
+    property: indexed
+    subject-area: "real analysis"
+    mathml:
+     - "<math><mrow intent='upper-darboux-integral($a1)'><mover><munderover><mo>∫</mo><mi>a</mi><mi>b</mi></munderover><mo>¯</mo></mover><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Darboux_integral"
+     - "https://www.encyclopediaofmath.org/index.php/Darboux_integral"
+  
+  - concept: upper-dini-derivative
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: upper dini derivative of $a1
+    property: decorated function
+    subject-area: "analysis"
+    mathml:
+     - "<math><mrow intent='upper-dini-derivative($a1)'><msub><msup><mi arg='a1'>f</mi><mo>′</mo></msup><mo>+</mo></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/DiniDerivative.html"
+     - "https://en.wikipedia.org/wiki/Dini_derivative"
+     - "https://www.encyclopediaofmath.org/index.php/Dini_derivative"
+  
+  - concept: upper-half-plane
+    arity: 0
+    arguments: []
+    speech:
       en: upper half plane
-      property: symbol
-      area: "complex analysis"
-      mathml:
-       - "<math><mi intent='upper-half-plane'>ℍ</mi></math>"
-       - "<math><msup intent='upper-half-plane'><mi>ℍ</mi><mo>+</mo></msup></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/UpperHalf-Plane.html"
-       - "https://en.wikipedia.org/wiki/Upper_half-plane"
-       - "https://ncatlab.org/nlab/show/upper+half-plane"
-    
-    - concept: upper-shadow
-      arity: 1
-      en: upper shadow of $1
-      property: function
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='upper-shadow($a1)'><msup><mi>𝜕</mi><mo>+</mo></msup><mi arg='a1'>A</mi></mrow></math>"
-      urls: 
-       - "http://qk206.user.srcf.net/notes/combinatorics.pdf"
-    
-    - concept: variance
-      arity: 1
-      en: variance of $1
-      property: function
-      area: "statistics"
-      mathml:
-       - "<math><mrow intent='variance($a1)'><mi>Var</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Variance"
-      alias:
-       - dispersion
-    
-    - concept: vect
-      arity: 1
-      en: vect of $1
-      property: "indexed symbol"
-      area: "category theory"
-      mathml:
-       - "<math><msub intent='vect($a1)'><mi>Vect</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/Vect"
-    
-    - concept: vector-concatenation
-      arity: 2
-      en: $1 vector concatenation $2
-      property: infix
-      area: "machine learning"
-      mathml:
-       - "<math><mrow intent='vector-concatenation($a1,$a2)'><mi arg='a1'>X</mi><mo>◦</mo><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='vector-concatenation($a1,$a2)'><mi arg='a1'>X</mi><mo>⊕</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://arxiv.org/pdf/1903.00172v1.pdf"
-       - "https://arxiv.org/abs/1901.10879"
-    
-    - concept: vector-projection
-      arity: 1
-      en: vector projection of $1
-      property: function
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='vector-projection($a1)'><mi>proj</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Vector_projection"
-      alias:
-       - vector-component
-       - vector-resolution
-    
-    - concept: vectorization
-      arity: 1
-      en: vectorization of $1
-      property: function
-      area: "linear algebra"
-      mathml:
-       - "<math><mrow intent='vectorization($a1)'><mi>vec</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Vectorization_(mathematics)"
-       - "https://en.wikipedia.org/wiki/Vectorization_(parallel_computing)"
-       - "https://en.wikipedia.org/wiki/Vectorization_(image_tracing)"
-    
-    - concept: versor
-      arity: 1
-      en: versor of $1
-      property: function
-      area: "quaternions"
-      mathml:
-       - "<math><mrow intent='versor($a1)'><mi>U</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Versor_(physics)"
-       - "https://en.wikipedia.org/wiki/Versor"
-       - "https://www.encyclopediaofmath.org/index.php/Versor"
-    
-    - concept: vertical
-      arity: 0
+    property: symbol
+    subject-area: "complex analysis"
+    mathml:
+     - "<math><mi intent='upper-half-plane'>ℍ</mi></math>"
+     - "<math><msup intent='upper-half-plane'><mi>ℍ</mi><mo>+</mo></msup></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/UpperHalf-Plane.html"
+     - "https://en.wikipedia.org/wiki/Upper_half-plane"
+     - "https://ncatlab.org/nlab/show/upper+half-plane"
+  
+  - concept: upper-shadow
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: upper shadow of $a1
+    property: function
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='upper-shadow($a1)'><msup><mi>𝜕</mi><mo>+</mo></msup><mi arg='a1'>A</mi></mrow></math>"
+    urls: 
+     - "http://qk206.user.srcf.net/notes/combinatorics.pdf"
+  
+  - concept: variance
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: variance of $a1
+    property: function
+    subject-area: "statistics"
+    mathml:
+     - "<math><mrow intent='variance($a1)'><mi>Var</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Variance"
+    alias:
+     - dispersion
+  
+  - concept: vect
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: vect of $a1
+    property: "indexed symbol"
+    subject-area: "category theory"
+    mathml:
+     - "<math><msub intent='vect($a1)'><mi>Vect</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/Vect"
+  
+  - concept: vector-concatenation
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 vector concatenation $a2
+    property: infix
+    subject-area: "machine learning"
+    mathml:
+     - "<math><mrow intent='vector-concatenation($a1,$a2)'><mi arg='a1'>X</mi><mo>◦</mo><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='vector-concatenation($a1,$a2)'><mi arg='a1'>X</mi><mo>⊕</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://arxiv.org/pdf/1903.00172v1.pdf"
+     - "https://arxiv.org/abs/1901.10879"
+  
+  - concept: vector-projection
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: vector projection of $a1
+    property: function
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='vector-projection($a1)'><mi>proj</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Vector_projection"
+    alias:
+     - vector-component
+     - vector-resolution
+  
+  - concept: vectorization
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: vectorization of $a1
+    property: function
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mrow intent='vectorization($a1)'><mi>vec</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Vectorization_(mathematics)"
+     - "https://en.wikipedia.org/wiki/Vectorization_(parallel_computing)"
+     - "https://en.wikipedia.org/wiki/Vectorization_(image_tracing)"
+  
+  - concept: versor
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: versor of $a1
+    property: function
+    subject-area: "quaternions"
+    mathml:
+     - "<math><mrow intent='versor($a1)'><mi>U</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Versor_(physics)"
+     - "https://en.wikipedia.org/wiki/Versor"
+     - "https://www.encyclopediaofmath.org/index.php/Versor"
+  
+  - concept: vertical
+    arity: 0
+    arguments: []
+    speech:
       en: vertical
-      property: 
-      area: 
-      mathml:
-       - "<math><mi intent='vertical'>vertical</mi></math>"
-      notation: 
-      urls: 
-       - "https://mathworld.wolfram.com/Vertical.html"
-       - "https://en.wikipedia.org/wiki/Horizontal_and_vertical"
-       - "https://en.wikipedia.org/wiki/Vertical_direction"
-    
-    - concept: vertical-composition
-      arity: 2
-      en: $1 vertical composition $2
-      property: infix
-      area: "category theory"
-      mathml:
-       - "<math><mrow intent='vertical-composition($a1,$a2)'><mi arg='a1'>X</mi><mo>∘</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://ncatlab.org/nlab/show/vertical+composition"
-       - "https://proofwiki.org/wiki/Definition: Vertical_Composition_of_Natural_Transformations"
-    
-    - concept: volterra-integral
-      arity: 1
-      en: volterra integral of $1
-      property: indexed
-      area: "calculus"
-      mathml:
-       - "<math><mrow intent='volterra-integral($a1)'><mo>Π</mo><mi arg='a1'>f</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Product_integral"
-    
-    - concept: volume
-      arity: 0
+    property: 
+    subject-area: 
+    mathml:
+     - "<math><mi intent='vertical'>vertical</mi></math>"
+    notation: 
+    urls: 
+     - "https://mathworld.wolfram.com/Vertical.html"
+     - "https://en.wikipedia.org/wiki/Horizontal_and_vertical"
+     - "https://en.wikipedia.org/wiki/Vertical_direction"
+  
+  - concept: vertical-composition
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 vertical composition $a2
+    property: infix
+    subject-area: "category theory"
+    mathml:
+     - "<math><mrow intent='vertical-composition($a1,$a2)'><mi arg='a1'>X</mi><mo>∘</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://ncatlab.org/nlab/show/vertical+composition"
+     - "https://proofwiki.org/wiki/Definition: Vertical_Composition_of_Natural_Transformations"
+  
+  - concept: volterra-integral
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: volterra integral of $a1
+    property: indexed
+    subject-area: "calculus"
+    mathml:
+     - "<math><mrow intent='volterra-integral($a1)'><mo>Π</mo><mi arg='a1'>f</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Product_integral"
+  
+  - concept: volume
+    arity: 0
+    arguments: []
+    speech:
       en: volume
-      property: symbol
-      area: "physics"
-      mathml:
-       - "<math><mi intent='volume'>V</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Volume.html"
-       - "https://en.wikipedia.org/wiki/Volume_(compression)"
-       - "https://en.wikipedia.org/wiki/Lebesgue_measure"
-       - "https://en.wikipedia.org/wiki/Volume_(thermodynamics)"
-       - "https://en.wikipedia.org/wiki/Volume"
-       - "https://ncatlab.org/nlab/show/volume"
-       - "https://www.encyclopediaofmath.org/index.php/Volume"
-    
-    - concept: volume-element
-      arity: 0
+    property: symbol
+    subject-area: "physics"
+    mathml:
+     - "<math><mi intent='volume'>V</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Volume.html"
+     - "https://en.wikipedia.org/wiki/Volume_(compression)"
+     - "https://en.wikipedia.org/wiki/Lebesgue_measure"
+     - "https://en.wikipedia.org/wiki/Volume_(thermodynamics)"
+     - "https://en.wikipedia.org/wiki/Volume"
+     - "https://ncatlab.org/nlab/show/volume"
+     - "https://www.encyclopediaofmath.org/index.php/Volume"
+  
+  - concept: volume-element
+    arity: 0
+    arguments: []
+    speech:
       en: volume element
-      property: symbol
-      area: "measure theory"
-      mathml:
-       - "<math><mi intent='volume-element'>d</mi><mi>V</mi></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/VolumeElement.html"
-       - "https://en.wikipedia.org/wiki/Volume_element"
-    
-    - concept: walsh-function
-      arity: 1
-      en: walsh function of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='walsh-function($a1)'><mi>W</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WalshFunction.html"
-       - "https://en.wikipedia.org/wiki/Walsh_function"
-       - "https://www.encyclopediaofmath.org/index.php/Walsh_functions"
-    
-    - concept: wavelet-transform
-      arity: 2
-      en: wavelet transform $1 $2
-      property: "embellished function"
-      area: "functional analysis"
-      mathml:
-       - "<math><mrow intent='wavelet-transform($a1,$a2)'><msub><mi>W</mi><mi arg='a1'>ψ</mi></msub><mi arg='a2'>y</mi></mrow></math>"
-      notation: "mrow [ msub W $1 /msub $2 ]"
-      urls: 
-       - "https://mathworld.wolfram.com/WaveletTransform.html"
-       - "https://en.wikipedia.org/wiki/Wavelet_transform"
-       - "https://en.wikipedia.org/wiki/Embedded_Zerotrees_of_Wavelet_transforms"
-      alias:
-       - integral-wavelet-transform
-    
-    - concept: way-below
-      arity: 2
-      en: $1 way below $2
-      property: infix
-      area: "domain theory"
-      mathml:
-       - "<math><mrow intent='way-below($a1,$a2)'><mi arg='a1'>X</mi><mo>≪</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "http://mizar.org/fm/1997-6/pdf6-1/waybel_3.pdf"
-       - "https://en.wikipedia.org/wiki/Domain_theory"
-      alias:
-       - way-inside
-       - order-of-approximation
-    
-    - concept: weak-convergence
-      arity: 2
-      en: $1 weak convergence $2
-      property: infix
-      area: "analysis"
-      mathml:
-       - "<math><mrow intent='weak-convergence($a1,$a2)'><mi arg='a1'>X</mi><mover><mo>→</mo><mi>w</mi></mover><mi arg='a2'>Y</mi></mrow></math>"
-       - "<math><mrow intent='weak-convergence($a1,$a2)'><mi arg='a1'>X</mi><mo>⇀</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WeakConvergence.html"
-       - "https://en.wikipedia.org/wiki/Weak_convergence_(Hilbert_space)"
-    
-    - concept: weber-function
-      arity: 1
-      en: weber function of $1
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='weber-function($a1)'><msub><mi>𝐄</mi><mi arg='a1'>ν</mi></msub><mrow><mo>(</mo><mi arg='a2'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WeberFunctions.html"
-       - "https://dlmf.nist.gov/11.10#E2"
-       - "https://www.encyclopediaofmath.org/index.php/Weber_function"
-    
-    - concept: weierstrass-elliptic-function
-      arity: 1
-      en: weierstrass elliptic function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='weierstrass-elliptic-function($a1)'><mi>℘</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WeierstrassEllipticFunction.html"
-       - "https://en.wikipedia.org/wiki/Weierstrass%27s_elliptic_functions"
-       - "https://dlmf.nist.gov/23.2#ii"
-       - "https://ncatlab.org/nlab/show/Weierstrass+elliptic+function"
-       - "https://www.encyclopediaofmath.org/index.php/Weierstrass_elliptic_functions"
-    
-    - concept: weierstrass-sigma-function
-      arity: 1
-      en: weierstrass sigma function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='weierstrass-sigma-function($a1)'><mi>σ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WeierstrassSigmaFunction.html"
-       - "https://dlmf.nist.gov/23.1"
-       - "https://dlmf.nist.gov/23.2#E6"
-       - "https://dlmf.nist.gov/23.3#SS1.p3"
-    
-    - concept: weierstrass-zeta-function
-      arity: 1
-      en: weierstrass zeta function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='weierstrass-zeta-function($a1)'><mi>ζ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WeierstrassZetaFunction.html"
-       - "https://dlmf.nist.gov/23.1"
-       - "https://dlmf.nist.gov/23.2#E5"
-       - "https://dlmf.nist.gov/23.3#SS1.p3"
-    
-    - concept: weight
-      arity: 1
-      en: weight of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='weight($a1)'><mi>wt</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Weight_(strings)"
-       - "https://ncatlab.org/nlab/show/weight"
-       - "https://www.encyclopediaofmath.org/index.php/Weight"
-    
-    - concept: weighted-lehmer-mean
-      arity: ">=0"
-      en: weighted lehmer mean of $1 $2 ...
-      property: "indexed function"
-      area: "means"
-      mathml:
-       - "<math><mrow intent='weighted-lehmer-mean($a1,$a2,$a3)'><msub><mi>L</mi><mi>p</mi></msub><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>,</mo><mi arg='a3'>z</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/LehmerMean.html"
-       - "https://en.wikipedia.org/wiki/Lehmer_mean"
-    
-    - concept: weighted-mean
-      arity: 1
-      en: weighted mean of $1
-      property: fenced
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='weighted-mean($a1)'><mo>⟨</mo><mi arg='a1'>x</mi><mo>⟩</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WeightedMean.html"
-       - "https://en.wikipedia.org/wiki/Weighted_arithmetic_mean"
-      alias:
-       - weighted-arithmetic-mean
-       - weighted-average
-    
-    - concept: wheel-graph
-      arity: 1
-      en: wheel graph of $1
-      property: "indexed symbol"
-      area: "graph theory"
-      mathml:
-       - "<math><msub intent='wheel-graph($a1)'><mi>W</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WheelGraph.html"
-       - "https://en.wikipedia.org/wiki/Wheel_graph"
-    
-    - concept: whitehead-group
-      arity: 1
-      en: whitehead group of $1
-      property: function
-      area: "group theory"
-      mathml:
-       - "<math><mrow intent='whitehead-group($a1)'><mi>Wh</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WhiteheadGroup.html"
-       - "https://en.wikipedia.org/wiki/Whitehead_torsion"
-       - "https://www.encyclopediaofmath.org/index.php/Whitehead_group"
-    
-    - concept: whitehead-bracket
-      arity: 2
-      en: whitehead bracket $1 $2
-      property: fenced
-      area: "lie algebra"
-      mathml:
-       - "<math><mrow intent='whitehead-bracket($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Whitehead_product"
-       - "https://ncatlab.org/nlab/show/Whitehead+product"
-       - "https://www.encyclopediaofmath.org/index.php/Whitehead_product"
-    
-    - concept: whitehead-torsion
-      arity: 1
-      en: whitehead torsion of $1
-      property: function
-      area: "geometric topology"
-      mathml:
-       - "<math><mrow intent='whitehead-torsion($a1)'><mi>τ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WhiteheadTorsion.html"
-       - "https://en.wikipedia.org/wiki/Whitehead_torsion"
-       - "https://www.encyclopediaofmath.org/index.php/Whitehead_torsion"
-    
-    - concept: whittaker-function
-      arity: 2
-      en: whittaker function $1 $2
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow><msub intent='whittaker-function($a1,$a2)'><mi>M</mi><mrow><mi arg='a1'>κ</mi><mo>,</mo><mi arg='a2'>μ</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow><msub intent='whittaker-function($a1,$a2)'><mi>W</mi><mrow><mi arg='a1'>κ</mi><mo>,</mo><mi arg='a2'>μ</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WhittakerFunction.html"
-       - "https://en.wikipedia.org/wiki/Whittaker_function"
-       - "https://dlmf.nist.gov/13#PT3"
-       - "https://www.encyclopediaofmath.org/index.php/Whittaker_functions"
+    property: symbol
+    subject-area: "measure theory"
+    mathml:
+     - "<math><mi intent='volume-element'>d</mi><mi>V</mi></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/VolumeElement.html"
+     - "https://en.wikipedia.org/wiki/Volume_element"
+  
+  - concept: walsh-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: walsh function of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='walsh-function($a1)'><mi>W</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WalshFunction.html"
+     - "https://en.wikipedia.org/wiki/Walsh_function"
+     - "https://www.encyclopediaofmath.org/index.php/Walsh_functions"
+  
+  - concept: wavelet-transform
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: wavelet transform $a1 $a2
+    property: "embellished function"
+    subject-area: "functional analysis"
+    mathml:
+     - "<math><mrow intent='wavelet-transform($a1,$a2)'><msub><mi>W</mi><mi arg='a1'>ψ</mi></msub><mi arg='a2'>y</mi></mrow></math>"
+    notation: "mrow [ msub W $a1 /msub $a2 ]"
+    urls: 
+     - "https://mathworld.wolfram.com/WaveletTransform.html"
+     - "https://en.wikipedia.org/wiki/Wavelet_transform"
+     - "https://en.wikipedia.org/wiki/Embedded_Zerotrees_of_Wavelet_transforms"
+    alias:
+     - integral-wavelet-transform
+  
+  - concept: way-below
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 way below $a2
+    property: infix
+    subject-area: "domain theory"
+    mathml:
+     - "<math><mrow intent='way-below($a1,$a2)'><mi arg='a1'>X</mi><mo>≪</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "http://mizar.org/fm/1997-6/pdf6-1/waybel_3.pdf"
+     - "https://en.wikipedia.org/wiki/Domain_theory"
+    alias:
+     - way-inside
+     - order-of-approximation
+  
+  - concept: weak-convergence
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 weak convergence $a2
+    property: infix
+    subject-area: "analysis"
+    mathml:
+     - "<math><mrow intent='weak-convergence($a1,$a2)'><mi arg='a1'>X</mi><mover><mo>→</mo><mi>w</mi></mover><mi arg='a2'>Y</mi></mrow></math>"
+     - "<math><mrow intent='weak-convergence($a1,$a2)'><mi arg='a1'>X</mi><mo>⇀</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WeakConvergence.html"
+     - "https://en.wikipedia.org/wiki/Weak_convergence_(Hilbert_space)"
+  
+  - concept: weber-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: weber function of $a1
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='weber-function($a1)'><msub><mi>𝐄</mi><mi arg='a1'>ν</mi></msub><mrow><mo>(</mo><mi arg='a2'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WeberFunctions.html"
+     - "https://dlmf.nist.gov/11.10#E2"
+     - "https://www.encyclopediaofmath.org/index.php/Weber_function"
+  
+  - concept: weierstrass-elliptic-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: weierstrass elliptic function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='weierstrass-elliptic-function($a1)'><mi>℘</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WeierstrassEllipticFunction.html"
+     - "https://en.wikipedia.org/wiki/Weierstrass%27s_elliptic_functions"
+     - "https://dlmf.nist.gov/23.2#ii"
+     - "https://ncatlab.org/nlab/show/Weierstrass+elliptic+function"
+     - "https://www.encyclopediaofmath.org/index.php/Weierstrass_elliptic_functions"
+  
+  - concept: weierstrass-sigma-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: weierstrass sigma function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='weierstrass-sigma-function($a1)'><mi>σ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WeierstrassSigmaFunction.html"
+     - "https://dlmf.nist.gov/23.1"
+     - "https://dlmf.nist.gov/23.2#E6"
+     - "https://dlmf.nist.gov/23.3#SS1.p3"
+  
+  - concept: weierstrass-zeta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: weierstrass zeta function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='weierstrass-zeta-function($a1)'><mi>ζ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WeierstrassZetaFunction.html"
+     - "https://dlmf.nist.gov/23.1"
+     - "https://dlmf.nist.gov/23.2#E5"
+     - "https://dlmf.nist.gov/23.3#SS1.p3"
+  
+  - concept: weight
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: weight of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='weight($a1)'><mi>wt</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Weight_(strings)"
+     - "https://ncatlab.org/nlab/show/weight"
+     - "https://www.encyclopediaofmath.org/index.php/Weight"
+  
+  - concept: weighted-lehmer-mean
+    arity: ">=0"
+    speech:
+      en: weighted lehmer mean of $a1 $a2 ...
+    property: "indexed function"
+    subject-area: "means"
+    mathml:
+     - "<math><mrow intent='weighted-lehmer-mean($a1,$a2,$a3)'><msub><mi>L</mi><mi>p</mi></msub><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>,</mo><mi arg='a3'>z</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/LehmerMean.html"
+     - "https://en.wikipedia.org/wiki/Lehmer_mean"
+  
+  - concept: weighted-mean
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: weighted mean of $a1
+    property: fenced
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='weighted-mean($a1)'><mo>⟨</mo><mi arg='a1'>x</mi><mo>⟩</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WeightedMean.html"
+     - "https://en.wikipedia.org/wiki/Weighted_arithmetic_mean"
+    alias:
+     - weighted-arithmetic-mean
+     - weighted-average
+  
+  - concept: wheel-graph
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: wheel graph of $a1
+    property: "indexed symbol"
+    subject-area: "graph theory"
+    mathml:
+     - "<math><msub intent='wheel-graph($a1)'><mi>W</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WheelGraph.html"
+     - "https://en.wikipedia.org/wiki/Wheel_graph"
+  
+  - concept: whitehead-group
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: whitehead group of $a1
+    property: function
+    subject-area: "group theory"
+    mathml:
+     - "<math><mrow intent='whitehead-group($a1)'><mi>Wh</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WhiteheadGroup.html"
+     - "https://en.wikipedia.org/wiki/Whitehead_torsion"
+     - "https://www.encyclopediaofmath.org/index.php/Whitehead_group"
+  
+  - concept: whitehead-bracket
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: whitehead bracket $a1 $a2
+    property: fenced
+    subject-area: "lie algebra"
+    mathml:
+     - "<math><mrow intent='whitehead-bracket($a1,$a2)'><mo>[</mo><mi arg='a1'>x</mi><mo>,</mo><mi arg='a2'>y</mi><mo>]</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Whitehead_product"
+     - "https://ncatlab.org/nlab/show/Whitehead+product"
+     - "https://www.encyclopediaofmath.org/index.php/Whitehead_product"
+  
+  - concept: whitehead-torsion
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: whitehead torsion of $a1
+    property: function
+    subject-area: "geometric topology"
+    mathml:
+     - "<math><mrow intent='whitehead-torsion($a1)'><mi>τ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WhiteheadTorsion.html"
+     - "https://en.wikipedia.org/wiki/Whitehead_torsion"
+     - "https://www.encyclopediaofmath.org/index.php/Whitehead_torsion"
+  
+  - concept: whittaker-function
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: whittaker function $a1 $a2
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow><msub intent='whittaker-function($a1,$a2)'><mi>M</mi><mrow><mi arg='a1'>κ</mi><mo>,</mo><mi arg='a2'>μ</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow><msub intent='whittaker-function($a1,$a2)'><mi>W</mi><mrow><mi arg='a1'>κ</mi><mo>,</mo><mi arg='a2'>μ</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WhittakerFunction.html"
+     - "https://en.wikipedia.org/wiki/Whittaker_function"
+     - "https://dlmf.nist.gov/13#PT3"
+     - "https://www.encyclopediaofmath.org/index.php/Whittaker_functions"
 
-    - concept: whittaker-function
-      arity: 3
-      en: whittaker function $1 $2 of $3
-      property: "indexed function"
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='whittaker-function($a1,$a2,$a3)'><msub><mi>M</mi><mrow><mi arg='a1'>κ</mi><mo>,</mo><mi arg='a2'>μ</mi></mrow></msub><mrow><mo>(</mo><mi arg='a3'>z</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='whittaker-function($a1,$a2,$a3)'><msub><mi>W</mi><mrow><mi arg='a1'>κ</mi><mo>,</mo><mi arg='a2'>μ</mi></mrow></msub><mrow><mo>(</mo><mi arg='a3'>z</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WhittakerFunction.html"
-       - "https://en.wikipedia.org/wiki/Whittaker_function"
-       - "https://dlmf.nist.gov/13#PT3"
-       - "https://www.encyclopediaofmath.org/index.php/Whittaker_functions"
-    
-    - concept: wiener-algebra
-      arity: 0
+  - concept: whittaker-function
+    arity: 3
+    arguments: [$a1, $a2, $a3]
+    speech:
+      en: whittaker function $a1 $a2 of $a3
+    property: "indexed function"
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='whittaker-function($a1,$a2,$a3)'><msub><mi>M</mi><mrow><mi arg='a1'>κ</mi><mo>,</mo><mi arg='a2'>μ</mi></mrow></msub><mrow><mo>(</mo><mi arg='a3'>z</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='whittaker-function($a1,$a2,$a3)'><msub><mi>W</mi><mrow><mi arg='a1'>κ</mi><mo>,</mo><mi arg='a2'>μ</mi></mrow></msub><mrow><mo>(</mo><mi arg='a3'>z</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WhittakerFunction.html"
+     - "https://en.wikipedia.org/wiki/Whittaker_function"
+     - "https://dlmf.nist.gov/13#PT3"
+     - "https://www.encyclopediaofmath.org/index.php/Whittaker_functions"
+  
+  - concept: wiener-algebra
+    arity: 0
+    arguments: []
+    speech:
       en: wiener algebra
-      property: symbol
-      area: "Fourier analysis"
-      mathml:
-      - "<math><mrow intent='wiener-algebra'><mi>A</mi><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WienerAlgebra.html"
-       - "https://en.wikipedia.org/wiki/Wiener_algebra"
-    
-    - concept: wiener-process
-      arity: 1
-      en: wiener process of $1
-      property: "indexed symbol"
-      area: "martingale theory"
-      mathml:
-       - "<math><msub intent='wiener-process($a1)'><mi>W</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WienerProcess.html"
-       - "https://en.wikipedia.org/wiki/Wiener_process"
-       - "https://www.encyclopediaofmath.org/index.php/Wiener_process"
-    
-    - concept: wiener-sausage
-      arity: 2
-      en: wiener sausage of radius $1 and length $2
-      property: "indexed symbol"
-      area: "mathematical physics"
-      mathml:
-       - "<math><mrow intent='wiener-sausage($a1,$a2)'><msub><mi>W</mi><mi arg='a1'>&#x03b4;</mi></msub><mrow><mo>(</mo><mi arg='a2'>t</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WienerSausage.html"
-       - "https://en.wikipedia.org/wiki/Wiener_sausage"
-       - "https://www.encyclopediaofmath.org/index.php/Wiener_sausage"
-    
-    - concept: wilson-polynomial
-      arity: 1
-      en: $1<i>th</i> wilson polynomial 
-      property: "indexed function"
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><msub intent='wilson-polynomial($a1)'><mi>W</mi><mi arg='a1'>n</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WilsonPolynomial.html"
-       - "https://en.wikipedia.org/wiki/Wilson_polynomials"
-       - "https://dlmf.nist.gov/18.25#T1.t1.r2"
-       - "https://www.encyclopediaofmath.org/index.php/Wilson_polynomials"
-    
-    - concept: wilson-quotient
-      arity: 1
-      en: wilson quotient of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='wilson-quotient($a1)'><mi>W</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WilsonQuotient.html"
-       - "https://en.wikipedia.org/wiki/Wilson_quotient"
-    
-    - concept: winding-number
-      arity: 1
-      en: winding number of $1
-      property: "function, symbol"
-      area: "algebraic topology"
-      mathml:
-       - "<math><mrow intent='winding-number($a1)'><mi>𝒩</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='winding-number($a1)'><mi>w</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Winding_number"
-       - "https://dlmf.nist.gov/1.9#E32"
-       - "https://ncatlab.org/nlab/show/winding+number"
-       - "https://planetmath.org/windingnumber"
-       - "https://www.encyclopediaofmath.org/index.php/Winding_number"
-    
-    - concept: window-function
-      arity: 1
-      en: window function of $1
-      property: function
-      area: "fourier analysis"
-      mathml:
-       - "<math><mrow intent='window-function($a1)'><mi>w</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WindowFunction.html"
-       - "https://en.wikipedia.org/wiki/Window_function"
-       - "https://www.encyclopediaofmath.org/index.php/Window_function"
-    
-    - concept: wishart-distribution
-      arity: 0
+    property: symbol
+    subject-area: "Fourier analysis"
+    mathml:
+    - "<math><mrow intent='wiener-algebra'><mi>A</mi><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WienerAlgebra.html"
+     - "https://en.wikipedia.org/wiki/Wiener_algebra"
+  
+  - concept: wiener-process
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: wiener process of $a1
+    property: "indexed symbol"
+    subject-area: "martingale theory"
+    mathml:
+     - "<math><msub intent='wiener-process($a1)'><mi>W</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WienerProcess.html"
+     - "https://en.wikipedia.org/wiki/Wiener_process"
+     - "https://www.encyclopediaofmath.org/index.php/Wiener_process"
+  
+  - concept: wiener-sausage
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: wiener sausage of radius $a1 and length $a2
+    property: "indexed symbol"
+    subject-area: "mathematical physics"
+    mathml:
+     - "<math><mrow intent='wiener-sausage($a1,$a2)'><msub><mi>W</mi><mi arg='a1'>&#x03b4;</mi></msub><mrow><mo>(</mo><mi arg='a2'>t</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WienerSausage.html"
+     - "https://en.wikipedia.org/wiki/Wiener_sausage"
+     - "https://www.encyclopediaofmath.org/index.php/Wiener_sausage"
+  
+  - concept: wilson-polynomial
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: $a1<i>th</i> wilson polynomial 
+    property: "indexed function"
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><msub intent='wilson-polynomial($a1)'><mi>W</mi><mi arg='a1'>n</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WilsonPolynomial.html"
+     - "https://en.wikipedia.org/wiki/Wilson_polynomials"
+     - "https://dlmf.nist.gov/18.25#T1.t1.r2"
+     - "https://www.encyclopediaofmath.org/index.php/Wilson_polynomials"
+  
+  - concept: wilson-quotient
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: wilson quotient of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='wilson-quotient($a1)'><mi>W</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WilsonQuotient.html"
+     - "https://en.wikipedia.org/wiki/Wilson_quotient"
+  
+  - concept: winding-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: winding number of $a1
+    property: "function, symbol"
+    subject-area: "algebraic topology"
+    mathml:
+     - "<math><mrow intent='winding-number($a1)'><mi>𝒩</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='winding-number($a1)'><mi>w</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Winding_number"
+     - "https://dlmf.nist.gov/1.9#E32"
+     - "https://ncatlab.org/nlab/show/winding+number"
+     - "https://planetmath.org/windingnumber"
+     - "https://www.encyclopediaofmath.org/index.php/Winding_number"
+  
+  - concept: window-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: window function of $a1
+    property: function
+    subject-area: "fourier analysis"
+    mathml:
+     - "<math><mrow intent='window-function($a1)'><mi>w</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WindowFunction.html"
+     - "https://en.wikipedia.org/wiki/Window_function"
+     - "https://www.encyclopediaofmath.org/index.php/Window_function"
+  
+  - concept: wishart-distribution
+    arity: 0
+    arguments: []
+    speech:
       en: wishart distribution
-      property: symbol
-      area: "probability theory"
-      mathml:
-       - "<math><msub intent='wishart-distribution'><mi>W</mi><mi>p</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WishartDistribution.html"
-       - "https://en.wikipedia.org/wiki/Wishart_distribution"
-       - "https://www.encyclopediaofmath.org/index.php/Wishart_distribution"
-    
-    - concept: witt-polynomials
-      arity: 1
-      en: witt polynomials of $1
-      property: "indexed function"
-      area: "ring theory"
-      mathml:
-       - "<math><msub intent='witt-polynomials($a1)'><mi>W</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Witt_vector"
-       - "https://www.encyclopediaofmath.org/index.php/Witt_vector"
-    
-    - concept: witt-vector
-      arity: ">=0"
-      en: witt vector of $1
-      property: fenced
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='witt-vector($a1)'><mi>W</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Witt_vector"
-       - "https://www.encyclopediaofmath.org/index.php/Witt_vector"
-    
-    - concept: woodall-number
-      arity: 1
-      en: woodall number of $1
-      property: "indexed symbol"
-      area: "number theory"
-      mathml:
-       - "<math><msub intent='woodall-number($a1)'><mi>W</mi><mi arg='a1'>x</mi></msub></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WoodallNumber.html"
-       - "https://en.wikipedia.org/wiki/Woodall_number"
-       - "https://en.wikipedia.org/wiki/Woodall_prime"
-    
-    - concept: wright-function
-      arity: 1
-      en: wright function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='wright-function($a1)'><mi>ϕ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/WrightFunction.html"
-    
-    - concept: wright-omega-function
-      arity: 1
-      en: wright omega function of $1
-      property: function
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='wright-omega-function($a1)'><mi>ω</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Wright_Omega_function"
-      alias:
-       - wright-function
-    
-    - concept: writhe
-      arity: 1
-      en: writhe of $1
-      property: function
-      area: "knot theory"
-      mathml:
-       - "<math><mrow intent='writhe($a1)'><mi>Wr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Writhe.html"
-       - "https://en.wikipedia.org/wiki/Writhe"
-       - "https://ncatlab.org/nlab/show/writhe"
-    
-    - concept: wronskian
-      arity: 2
-      en: wronskian of $1, $2
-      property: operator
-      area: "special functions"
-      mathml:
-       - "<math><mrow intent='wronskian($a1,$a2)'><mi>𝒲</mi><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>,</mo><mi arg='a2'>g</mi><mo>)</mo></mrow></mrow></math>"
-       - "<math><mrow intent='wronskian($a1,$a2)'><mi>W</mi><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>,</mo><mi arg='a2'>g</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Wronskian.html"
-       - "https://en.wikipedia.org/wiki/Wronskian"
-       - "https://dlmf.nist.gov/1.13#E4"
-       - "https://ncatlab.org/nlab/show/Wronskian"
-       - "https://www.encyclopediaofmath.org/index.php/Wronskian"
-    
-    - concept: yang-mill-functional
-      arity: 1
-      en: yang mill functional of $1
-      property: function
-      area: "gauge theory"
-      mathml:
-       - "<math><mrow intent='yang-mill-functional($a1)'><mi>ℒ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/Yang-MillsFunctional.html"
-       - "https://www.encyclopediaofmath.org/index.php/Yang-Mills_functional"
-       - "https://www.encyclopediaofmath.org/index.php/YangâXXXXMills_functional"
-    
-    - concept: z-matrix
-      arity: 0
+    property: symbol
+    subject-area: "probability theory"
+    mathml:
+     - "<math><msub intent='wishart-distribution'><mi>W</mi><mi>p</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WishartDistribution.html"
+     - "https://en.wikipedia.org/wiki/Wishart_distribution"
+     - "https://www.encyclopediaofmath.org/index.php/Wishart_distribution"
+  
+  - concept: witt-polynomials
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: witt polynomials of $a1
+    property: "indexed function"
+    subject-area: "ring theory"
+    mathml:
+     - "<math><msub intent='witt-polynomials($a1)'><mi>W</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Witt_vector"
+     - "https://www.encyclopediaofmath.org/index.php/Witt_vector"
+  
+  - concept: witt-vector
+    arity: ">=0"
+    speech:
+      en: witt vector of $a1
+    property: fenced
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='witt-vector($a1)'><mi>W</mi><mrow><mo>(</mo><mi arg='a1'>X</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Witt_vector"
+     - "https://www.encyclopediaofmath.org/index.php/Witt_vector"
+  
+  - concept: woodall-number
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: woodall number of $a1
+    property: "indexed symbol"
+    subject-area: "number theory"
+    mathml:
+     - "<math><msub intent='woodall-number($a1)'><mi>W</mi><mi arg='a1'>x</mi></msub></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WoodallNumber.html"
+     - "https://en.wikipedia.org/wiki/Woodall_number"
+     - "https://en.wikipedia.org/wiki/Woodall_prime"
+  
+  - concept: wright-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: wright function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='wright-function($a1)'><mi>ϕ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/WrightFunction.html"
+  
+  - concept: wright-omega-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: wright omega function of $a1
+    property: function
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='wright-omega-function($a1)'><mi>ω</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Wright_Omega_function"
+    alias:
+     - wright-function
+  
+  - concept: writhe
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: writhe of $a1
+    property: function
+    subject-area: "knot theory"
+    mathml:
+     - "<math><mrow intent='writhe($a1)'><mi>Wr</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Writhe.html"
+     - "https://en.wikipedia.org/wiki/Writhe"
+     - "https://ncatlab.org/nlab/show/writhe"
+  
+  - concept: wronskian
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: wronskian of $a1, $a2
+    property: operator
+    subject-area: "special functions"
+    mathml:
+     - "<math><mrow intent='wronskian($a1,$a2)'><mi>𝒲</mi><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>,</mo><mi arg='a2'>g</mi><mo>)</mo></mrow></mrow></math>"
+     - "<math><mrow intent='wronskian($a1,$a2)'><mi>W</mi><mrow><mo>(</mo><mi arg='a1'>f</mi><mo>,</mo><mi arg='a2'>g</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Wronskian.html"
+     - "https://en.wikipedia.org/wiki/Wronskian"
+     - "https://dlmf.nist.gov/1.13#E4"
+     - "https://ncatlab.org/nlab/show/Wronskian"
+     - "https://www.encyclopediaofmath.org/index.php/Wronskian"
+  
+  - concept: yang-mill-functional
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: yang mill functional of $a1
+    property: function
+    subject-area: "gauge theory"
+    mathml:
+     - "<math><mrow intent='yang-mill-functional($a1)'><mi>ℒ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/Yang-MillsFunctional.html"
+     - "https://www.encyclopediaofmath.org/index.php/Yang-Mills_functional"
+     - "https://www.encyclopediaofmath.org/index.php/YangâXXXXMills_functional"
+  
+  - concept: z-matrix
+    arity: 0
+    arguments: []
+    speech:
       en: z matrix
-      property: symbol
-      area: "linear algebra"
-      mathml:
-       - "<math><mi intent='z-matrix'>Z</mi></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Z-matrix_(mathematics)"
-    
-    - concept: z-matrix-molecule
-      arity: 1
-      en: z matrix molecule of $1
-      property: mtable
-      area: "chemistry"
-      mathml:
-       - "<math><mrow intent='z-matrix-molecule($a1)'><mtable arg='a1'><mtr><mtd><mtext>...</mtext></mtd></mtr><mtr><mtd><mtext>...</mtext></mtd></mtr></mtable></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Z-matrix_(chemistry)"
-    
-    - concept: z-transform
-      arity: 1
-      en: z transform of $1
-      property: function
-      area: "combinatorics"
-      mathml:
-       - "<math><mrow intent='z-transform($a1)'><mi>Z</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/z-Transform.html"
-       - "https://mathworld.wolfram.com/Z-Transform.html"
-       - "https://en.wikipedia.org/wiki/Z-transform"
-       - "https://www.encyclopediaofmath.org/index.php/Z-transform"
-    
-    - concept: zernike-polynomial
-      arity: 4
-      en: $1 $2 zernike polynomial of $3, $4
-      property: "indexed function"
-      area: "orthogonal polynomials"
-      mathml:
-       - "<math><mrow intent='zernike-polynomial($a1,$a2,$a3,$a4)'><msubsup><mi>Z</mi><mi arg='a1'>n</mi><mi arg='a2'>m</mi></msubsup><mrow><mo>(</mo><mi arg='a3'>ρ</mi><mo>,</mo><mi arg='a4'>φ</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ZernikePolynomial.html"
-       - "https://en.wikipedia.org/wiki/Zernike_polynomials"
-       - "https://www.encyclopediaofmath.org/index.php/Zernike_polynomials"
-    
-    - concept: zero-ideal
-      arity: 0
+    property: symbol
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mi intent='z-matrix'>Z</mi></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Z-matrix_(mathematics)"
+  
+  - concept: z-matrix-molecule
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: z matrix molecule of $a1
+    property: mtable
+    subject-area: "chemistry"
+    mathml:
+     - "<math><mrow intent='z-matrix-molecule($a1)'><mtable arg='a1'><mtr><mtd><mtext>...</mtext></mtd></mtr><mtr><mtd><mtext>...</mtext></mtd></mtr></mtable></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Z-matrix_(chemistry)"
+  
+  - concept: z-transform
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: z transform of $a1
+    property: function
+    subject-area: "combinatorics"
+    mathml:
+     - "<math><mrow intent='z-transform($a1)'><mi>Z</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/z-Transform.html"
+     - "https://mathworld.wolfram.com/Z-Transform.html"
+     - "https://en.wikipedia.org/wiki/Z-transform"
+     - "https://www.encyclopediaofmath.org/index.php/Z-transform"
+  
+  - concept: zernike-polynomial
+    arity: 4
+    arguments: [$a1, $a2, $a3, $a4]
+    speech:
+      en: $a1 $a2 zernike polynomial of $a3, $a4
+    property: "indexed function"
+    subject-area: "orthogonal polynomials"
+    mathml:
+     - "<math><mrow intent='zernike-polynomial($a1,$a2,$a3,$a4)'><msubsup><mi>Z</mi><mi arg='a1'>n</mi><mi arg='a2'>m</mi></msubsup><mrow><mo>(</mo><mi arg='a3'>ρ</mi><mo>,</mo><mi arg='a4'>φ</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ZernikePolynomial.html"
+     - "https://en.wikipedia.org/wiki/Zernike_polynomials"
+     - "https://www.encyclopediaofmath.org/index.php/Zernike_polynomials"
+  
+  - concept: zero-ideal
+    arity: 0
+    arguments: []
+    speech:
       en: zero ideal
-      property: symbol
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='zero-ideal'><mo>{</mo><mn>0</mn><mo>}</mo></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ZeroIdeal.html"
-       - "https://ncatlab.org/nlab/show/zero+ideal"
-    
-    - concept: zero-matrix
-      arity: 2
-      en: $1 $2 zero matrix
-      property: "indexed symbol"
-      area: "linear algebra"
-      mathml:
-       - "<math><msub intent='zero-matrix($a1,$a2)'><mn>0</mn><mrow><mi arg='a1'>i</mi><mi arg='a2'>j</mi></mrow></msub></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Zero_matrix"
-    
-    - concept: zero-morphism
-      arity: 2
-      en: zero morphism $1 $2
-      property: "indexed symbol"
-      area: "category theory"
-      mathml:
-       - "<math><msub intent='zero-morphism($a1)'><mn>0</mn><mrow><mi arg='a1'>A</mi><mi arg='a2'>B</mi></mrow></msub></math>"
-      notation: "msub mn 0 mrow X,Y"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Zero_morphism"
-       - "https://ncatlab.org/nlab/show/zero+morphism"
-    
-    - concept: zero-object
-      arity: 0
+    property: symbol
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='zero-ideal'><mo>{</mo><mn>0</mn><mo>}</mo></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ZeroIdeal.html"
+     - "https://ncatlab.org/nlab/show/zero+ideal"
+  
+  - concept: zero-matrix
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 $a2 zero matrix
+    property: "indexed symbol"
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><msub intent='zero-matrix($a1,$a2)'><mn>0</mn><mrow><mi arg='a1'>i</mi><mi arg='a2'>j</mi></mrow></msub></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Zero_matrix"
+  
+  - concept: zero-morphism
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: zero morphism $a1 $a2
+    property: "indexed symbol"
+    subject-area: "category theory"
+    mathml:
+     - "<math><msub intent='zero-morphism($a1)'><mn>0</mn><mrow><mi arg='a1'>A</mi><mi arg='a2'>B</mi></mrow></msub></math>"
+    notation: "msub mn 0 mrow X,Y"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Zero_morphism"
+     - "https://ncatlab.org/nlab/show/zero+morphism"
+  
+  - concept: zero-object
+    arity: 0
+    arguments: []
+    speech:
       en: zero object
-      property: symbol
-      area: "algebra"
-      mathml:
-       - "<math><mrow intent='zero-object'><mo>{</mo><mn>0</mn><mo>}</mo></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Zero_object_(algebra)"
-       - "https://ncatlab.org/nlab/show/zero+object"
-    
-    - concept: zero-ring
-      arity: 0
+    property: symbol
+    subject-area: "algebra"
+    mathml:
+     - "<math><mrow intent='zero-object'><mo>{</mo><mn>0</mn><mo>}</mo></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Zero_object_(algebra)"
+     - "https://ncatlab.org/nlab/show/zero+object"
+  
+  - concept: zero-ring
+    arity: 0
+    arguments: []
+    speech:
       en: zero ring
-      property: symbol
-      area: "ring theory"
-      mathml:
-       - "<math><mrow intent='zero-ring'><mo>{</mo><mn>0</mn><mo>}</mo></mrow></math>"
-       - "<math><mn intent='zero-ring'>0</mn></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ZeroRing.html"
-       - "https://en.wikipedia.org/wiki/Zero_ring"
-    
-    - concept: zero-vector
-      arity: 0
+    property: symbol
+    subject-area: "ring theory"
+    mathml:
+     - "<math><mrow intent='zero-ring'><mo>{</mo><mn>0</mn><mo>}</mo></mrow></math>"
+     - "<math><mn intent='zero-ring'>0</mn></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ZeroRing.html"
+     - "https://en.wikipedia.org/wiki/Zero_ring"
+  
+  - concept: zero-vector
+    arity: 0
+    arguments: []
+    speech:
       en: zero vector
-      property: constant
-      area: "linear algebra"
-      mathml:
-       - "<math><mn intent='zero-vector'>0</mn></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ZeroVector.html"
-    
-    - concept: zeta-function
-      arity: 1
-      en: zeta function of $1
-      property: function
-      area: "number theory"
-      mathml:
-       - "<math><mrow intent='zeta-function($a1)'><mi>ζ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
-      urls: 
-       - "https://mathworld.wolfram.com/ZetaFunction.html"
-       - "https://en.wikipedia.org/wiki/List_of_zeta_functions"
-       - "https://en.wikipedia.org/wiki/Zeta_function_(operator)"
-       - "https://ncatlab.org/nlab/show/zeta+function"
-    
-    - concept: zig-zag-product
-      arity: 2
-      en: $1 zig zag product $2
-      property: infix
-      area: "graph theory"
-      mathml:
-       - "<math><mrow intent='zig-zag-product($a1,$a2)'><mi arg='a1'>X</mi><mo>∘</mo><mi arg='a2'>Y</mi></mrow></math>"
-      urls: 
-       - "https://en.wikipedia.org/wiki/Zig-zag_product"
+    property: constant
+    subject-area: "linear algebra"
+    mathml:
+     - "<math><mn intent='zero-vector'>0</mn></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ZeroVector.html"
+  
+  - concept: zeta-function
+    arity: 1
+    arguments: [$a1]
+    speech:
+      en: zeta function of $a1
+    property: function
+    subject-area: "number theory"
+    mathml:
+     - "<math><mrow intent='zeta-function($a1)'><mi>ζ</mi><mrow><mo>(</mo><mi arg='a1'>x</mi><mo>)</mo></mrow></mrow></math>"
+    urls: 
+     - "https://mathworld.wolfram.com/ZetaFunction.html"
+     - "https://en.wikipedia.org/wiki/List_of_zeta_functions"
+     - "https://en.wikipedia.org/wiki/Zeta_function_(operator)"
+     - "https://ncatlab.org/nlab/show/zeta+function"
+  
+  - concept: zig-zag-product
+    arity: 2
+    arguments: [$a1, $a2]
+    speech:
+      en: $a1 zig zag product $a2
+    property: infix
+    subject-area: "graph theory"
+    mathml:
+     - "<math><mrow intent='zig-zag-product($a1,$a2)'><mi arg='a1'>X</mi><mo>∘</mo><mi arg='a2'>Y</mi></mrow></math>"
+    urls: 
+     - "https://en.wikipedia.org/wiki/Zig-zag_product"
 
diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md
index f2e2adc5..f915c239 100644
--- a/intent-core-concepts/index.md
+++ b/intent-core-concepts/index.md
@@ -32,8 +32,10 @@ title: Core Concept List
 p.langs {margin:1em; padding:1em;background-color: #EEE}
 tr:target >td:first-child {border-left:solid thick black}
 span.cb {margin-right: 2em; white-space:nowrap}
+span.nw {white-space:nowrap}
 .markdown-body table tr.row0, .markdown-body table th.row0 {background-color:#F6F8FA}
 .markdown-body table tr.row1 {background-color:#FEFFFE}
+.markdown-body table tr.subj {background-color:beige;font-size:110%;text-align:left;}
 a.link {font-weight:500}
 a.self {color: black; font-weight:500}
 </style>
@@ -165,9 +167,13 @@ if c.link
 </p>
 </details>
 
-{%- for section in site.data.core.concepts -%}
+{% comment %}
+{% assign cpts = site.data.core.concepts | sort: "subject-area" %}
+{% endcomment %}
+{% assign cpts = site.data.core.concepts %}
 
-### {{section.title}}
+
+{% assign subjt = "" %}
 
 <table style="width:100%">
 <thead>
@@ -182,7 +188,11 @@ if c.link
 </tr>
 </thead>
 <tbody>
-{%- for c in section.intents -%}
+{%- for c in cpts -%}
+{%- if c.subject-area != subjt -%}
+{%- assign subjt = c.subject-area -%}
+<tr class="subj"><th colspan="3">{{subjt}}</th></tr>
+{%- endif -%}
 {%- assign clss = forloop.index| modulo:2 -%}
 {%- assign arityr = c.arity | replace: ">=", "⩾" -%}
 {%- assign arityu = c.arity | replace: ">=", "GEQ" -%}
@@ -191,13 +201,19 @@ if c.link
 {%- for cond in c.conditions -%}
 <tr {% if forloop.first %}id="{{c.concept}}{{arityu}}{{propertyu}}"{% endif %} class="row{{ clss }}">
 {%- if forloop.first -%}<td rowspan="{{c.conditions.size}}"><a class="self" href="#{{c.concept}}{{arityu}}{{propertyu}}">{{c.concept}}</a></td>{%- endif -%}
-{%- if forloop.first -%}<td rowspan="{{c.conditions.size}}">{{arityr}}</td>{%- endif -%}
+{%- if forloop.first -%}<td rowspan="{{c.conditions.size}}">{{arityr}}<br/>
+<span class="nw">[
+{%- for arg in c.arguments -%}
+{{arg}}
+{%- unless forloop.last -%},{% endunless -%}
+{%- endfor -%}
+]</span></td>{%- endif -%}
 {%- if forloop.first -%}<td rowspan="{{c.conditions.size}}">{{c.property}}{%- unless c.default == false or c.arity == 0 -%}*{%- endunless -%}</td>{%- endif -%}
 {%- for language in site.data.languages -%}
 <td class="{{language.language-code}}">
 [{{cond.condition}}]:
-{% if cond[language.language-code] -%}
-{%- for l in cond[language.language-code] -%}
+{% if cond.speech[language.language-code] -%}
+{%- for l in cond.speech[language.language-code] -%}
 {{l}} {%- unless forloop.last -%}<br>{% endunless -%}
 {% endfor %}
 {%- else -%}
@@ -224,12 +240,20 @@ if c.link
 {%- else -%}
 <tr id="{{c.concept}}{{arityu}}{{propertyu}}" class="row{{ clss }}">
 <td><a class="self" href="#{{c.concept}}{{arityu}}{{propertyu}}">{{c.concept}}</a></td>
-<td>{{arityr}}</td>
+<td>
+{{arityr}}<br/>
+<span class="nw">[
+{%- for arg in c.arguments -%}
+{{arg}}
+{%- unless forloop.last -%},{% endunless -%}
+{%- endfor -%}
+]</span>
+</td>
 <td>{{c.property}}{%- unless c.default == false or c.arity == 0-%}*{%- endunless -%}</td>
 {%- for language in site.data.languages -%}
 <td class="{{language.language-code}}">
-{%- if c[language.language-code] -%}
-{%- for l in c[language.language-code] -%}
+{%- if c.speech[language.language-code] -%}
+{%- for l in c.speech[language.language-code] -%}
 {{l}} {%- unless forloop.last -%}<br>{% endunless -%}
 {% endfor %}
 {%- else -%}
@@ -256,7 +280,7 @@ if c.link
 </tbody>
 </table>
 <hr>
-{%- endfor -%}
+
 
 ### Key
 
diff --git a/intent-open-concepts/index.md b/intent-open-concepts/index.md
index 2ecfd3d1..98da64a5 100644
--- a/intent-open-concepts/index.md
+++ b/intent-open-concepts/index.md
@@ -32,23 +32,25 @@ title: Open Concept List
 p.langs {margin:1em; padding:1em;background-color: #EEE}
 tr:target >td:first-child {border-left:solid thick black}
 span.cb {margin-right: 2em; white-space:nowrap}
+span.nw {white-space:nowrap}
 .markdown-body table {font-size:85%}
 .markdown-body table tr.row0, .markdown-body table th.row0 {background-color:#F6F8FA}
 .markdown-body table tr.row1 {background-color:#FEFFFE}
+.markdown-body table tr.subj {background-color:beige;font-size:110%;text-align:left;}
 a.link {font-weight:500}
 a.self {color: black; font-weight:500}
      [arg] { background-color: #ddfafa;}
      [arg]:hover {display:inline;background-color: #add8e6;}
      [arg]:hover::after {display:inline;vertical-align: sub; font-size: 0.7em; }
-     [arg="a1"]:hover::after { content: " $1" ; }
-     [arg="a2"]:hover::after { content: " $2" ; }
-     [arg="a3"]:hover::after { content: " $3" ; }
-     [arg="a4"]:hover::after { content: " $4" ; }
-     [arg="a5"]:hover::after { content: " $5" ; }
-     [arg="a6"]:hover::after { content: " $6" ; }
-     [arg="a7"]:hover::after { content: " $7" ; }
-     [arg="a8"]:hover::after { content: " $8" ; }
-     [arg="a9"]:hover::after { content: " $9" ; }
+     [arg="a1"]:hover::after { content: " $a1" ; }
+     [arg="a2"]:hover::after { content: " $a2" ; }
+     [arg="a3"]:hover::after { content: " $a3" ; }
+     [arg="a4"]:hover::after { content: " $a4" ; }
+     [arg="a5"]:hover::after { content: " $a5" ; }
+     [arg="a6"]:hover::after { content: " $a6" ; }
+     [arg="a7"]:hover::after { content: " $a7" ; }
+     [arg="a8"]:hover::after { content: " $a8" ; }
+     [arg="a9"]:hover::after { content: " $a9" ; }
 math:not(:has(*[intent])) {
     color: red;
     }
@@ -123,9 +125,8 @@ Additional contributions are welcome:
 </p>
 </details>
 
-{%- for section in site.data.open.concepts -%}
-
-### {{section.title}}
+{% assign cpts = site.data.open.concepts | sort: "subject-area" %}
+{% assign subjt = "" %}
 
 <table style="width:100%">
 <thead>
@@ -137,12 +138,21 @@ Additional contributions are welcome:
 <th class="{{language.language-code}}">Speech Template ({{language.language-code}})</th> 
 {%- endfor -%}
 <th style="width:auto">Comments</th>
-<th>Subject</th>
 <th>Sources</th>
 </tr>
 </thead>
 <tbody>
-{%- for c in section.intents -%}
+{%- for c in cpts -%}
+{%- if c.subject-area != subjt -%}
+{%- assign subjt = c.subject-area -%}
+<tr class="subj"><th colspan="3">
+{%- if c.subject-area == null -%}
+00 Unclassified
+{%- else -%}
+{{subjt}}
+{%- endif -%}
+</th></tr>
+{%- endif -%}
 {%- assign clss = forloop.index| modulo:2 -%}
 {%- assign arityr = c.arity | replace: ">=", "⩾" -%}
 {%- assign arityu = c.arity | replace: ">=", "GEQ" -%}
@@ -151,13 +161,19 @@ Additional contributions are welcome:
 {%- for cond in c.conditions -%}
 <tr {% if forloop.first %}id="{{c.concept}}{{arityu}}{{propertyu}}"{% endif %} class="row{{ clss }}">
 {%- if forloop.first -%}<td rowspan="{{c.conditions.size}}"><a class="self" href="#{{c.concept}}{{arityu}}{{propertyu}}">{{c.concept}}</a></td>{%- endif -%}
-{%- if forloop.first -%}<td rowspan="{{c.conditions.size}}">{{arityr}}</td>{%- endif -%}
+{%- if forloop.first -%}<td rowspan="{{c.conditions.size}}">{{arityr}}<br/>
+<span class="nw">[
+{%- for arg in c.arguments -%}
+{{arg}}
+{%- unless forloop.last -%},{% endunless -%}
+{%- endfor -%}
+]</span></td>{%- endif -%}
 {%- if forloop.first -%}<td rowspan="{{c.conditions.size}}">{{c.property}}{%- unless c.default == false or c.arity == 0 -%}*{%- endunless -%}</td>{%- endif -%}
 {%- for language in site.data.languages -%}
 <td class="{{language.language-code}}">
 [{{cond.condition}}]:
-{% if cond[language.language-code] -%}
-{%- for l in cond[language.language-code] -%}
+{% if cond.speech[language.language-code] -%}
+{%- for l in cond.speech[language.language-code] -%}
 {{l}} {%- unless forloop.last -%}<br>{% endunless -%}
 {% endfor %}
 {%- else -%}
@@ -183,7 +199,6 @@ Additional contributions are welcome:
 Aliases: {% for al in c.alias -%}{{al}}{%- unless forloop.last -%}<br>{% endunless -%}{%- endfor -%}
 {%-endif -%}
 </td>{%- endif -%}
-{%- if forloop.first-%}<td rowspan="{{c.conditions.size}}">{{c.area}}</td>{%-endif -%}
 {%- if forloop.first-%}<td rowspan="{{c.conditions.size}}">
 {%- if c.urls -%}
 {% for u in c.urls %}
@@ -214,16 +229,22 @@ arXiv
 {%- else -%}
 <tr id="{{c.concept}}{{arityu}}{{propertyu}}" class="row{{ clss }}">
 <td><a class="self" href="#{{c.concept}}{{arityu}}{{propertyu}}">{{c.concept}}</a></td>
-<td>{{arityr}}</td>
+<td>{{arityr}}<br/>
+<span class="nw">[
+{%- for arg in c.arguments -%}
+{{arg}}
+{%- unless forloop.last -%},{% endunless -%}
+{%- endfor -%}
+]</span></td>
 <td>{{c.property}}{%- unless c.default == false or c.arity == 0-%}*{%- endunless -%}</td>
 {%- for language in site.data.languages -%}
 <td class="{{language.language-code}}">
-{%- if c[language.language-code] -%}
-{%- for l in c[language.language-code] -%}
+{%- if c.speech[language.language-code] -%}
+{%- for l in c.speech[language.language-code] -%}
 {{l}} {%- unless forloop.last -%}<br>{% endunless -%}
 {% endfor %}
 {%- else -%}
-{%- for l in c.en -%}
+{%- for l in c.speech.en -%}
 {{l}} ({{language.language-code}}){%- unless forloop.last -%}<br>{% endunless -%}
 {% endfor %} 
 {% endif %}
@@ -244,7 +265,6 @@ arXiv
 Aliases: {% for al in c.alias -%}{{al}}{%- unless forloop.last -%}, {% endunless -%}{%- endfor -%}
 {%-endif -%}
 </td>
-<td>{{c.area}}</td>
 <td>
 {%- if c.urls -%}
 {% for u in c.urls %}
@@ -276,7 +296,7 @@ arXiv
 </tbody>
 </table>
 <hr>
-{%- endfor -%}
+
 
 ### Key