feat(calories): price sub-gate walking minutes from measured cadence (CADENCE-Adults)

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The gap

MOT-02 raised the HR-flex gate to the ACSM moderate floor and its own changelog measured the cost: billed wake minutes fell to 4.9%, median daily active energy to 48 kcal. That was the right call for HR — Keytel has no fitted data below the exercise domain — but it left walking priced at zero: a one-hour walk at 95 bpm adds nothing to Active energy for its entire duration. This is now a user-facing bug report on edge ("Walking calories are not counted": the workout and steps record fine, Active Calories never move). MT-05 already established the 1 Hz accel channel cannot fill this gap (Brage's branches can't read a 1 Hz gravity vector).

The fix

Measured cadence is the one signal on this platform that actually resolves gait — the 100 Hz pedometer — and CADENCE-Adults (Tudor-Locke et al. 2019, IJBNPA 16:8) publishes the cadence↔MET line for exactly this region: heuristic thresholds 100/110/120/130 steps/min ↔ 3/4/5/6 METs.

Calories.dailyEnergy gains an optional cadenceSpmPerMin series, index-aligned with hrPerMin (null = nobody measured that minute):

• A minute the HR gate accepts bills by HR alone, exactly as before — a minute is never billed twice.
• A minute the HR gate refuses (below flex, or no HR at all — measured gait stands on its own), whose measured cadence is at/above the study's own moderate floor, bills (MET − 1) basal-minutes of surplus via the new metFromCadenceSpm — linear between the published anchors, clamped at both ends of the fitted range: under 100 spm the study does not price it (the same "only exercise-domain minutes bill" philosophy the HR gate already holds); over 130 spm is running, which drives HR over the gate and bills there.
• The result record gains a walking component (already folded into active) so callers can disclose how much of the day came from measured walking.
• No cadence series → byte-identical behaviour to today. Misaligned series throws; unusable anchors still abstain, cadence or not.

ALGORITHMS.md gets the row + citation.

Numbers

80 kg / 180 cm / 30 y male (Mifflin 1780 kcal/day): a one-hour walk at 110 spm bills 60 × 3 × 1.24 ≈ 222 kcal of walking surplus — previously 0.

Tests

New walking cadence term (CADENCE-Adults) group: the published MET anchors and clamps, the reported below-gate walk billing, the no-double-billing invariant, unmeasured/ambling/non-finite minutes staying basal, gait-on-off-skin-HR minutes billing, misalignment throwing, and anchor abstention unchanged. dart analyze clean; full suite green (591 tests).

Edge side (per-minute cadence from live_coverage, threading through wakeDayEnergy and the pipeline mirror, kAlgoVersion bump + pin) follows as a draft PR on OpenStrap/edge once this lands.

🤖 Generated with Claude Code

https://claude.ai/code/session_015TxisrChNFxtVMXFFNRGtV

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