Grand Challenge Mathematics Programme

Grand Challenge mathematics work uses a three-pillar system:

MATHFORGE  ->  MATHSOLVE  ->  MATHCERT
discover       organize       certify

The programme separates discovery, mathematical development, and certification. This separation keeps claim status visible as work progresses.

What the programme does

The programme turns a mathematical question into a sequence of explicit research states.

• MATHFORGE identifies the object, source, pattern, obstruction, or candidate route.
• MATHSOLVE turns that material into named obligations, work packages, proof routes, and handoffs.
• MATHCERT checks exact statements, evidence, and certificates. It records the claim boundary that survives review.

The three pillars do not assign the same status to every artifact. A source can motivate a claim. A computation can support a claim. A work package can organize a claim. Certification is a separate act.

How a claim moves through the programme

The following state map shows the normal path and the three fail-closed exits. Each exit records the unresolved state instead of converting it into a positive claim.

The visual distinction is operational. MATHFORGE can stop with a recorded obstruction. MATHSOLVE can stop with unresolved proof debt. MATHCERT can refuse promotion. None of these states is silently upgraded by presentation.

Why the pillars are separate

Each pillar controls a different transition.

Pillar	Primary function	Boundary it preserves
MATHFORGE	Reconstruct sources, record signals, run finite screens, and identify candidate routes.	Discovery evidence does not become a mathematical result by presentation alone.
MATHSOLVE	Build theorem spines, proof obligations, work packages, and exact successor moves.	An active solving campaign does not become a completed result.
MATHCERT	Replay exact statements, check certificates, and record claim disposition.	Evidence and exposition do not become certified truth without the required checks.

The distinction is operational:

• MATHFORGE asks: What mathematical object or route is available?
• MATHSOLVE asks: Which obligations must close before the claim can advance?
• MATHCERT asks: Which exact claim survived the applicable checks?

Current programme fronts

This table shows selected material programme work that is active now. It is deliberately not exhaustive. Row order reflects current programme attention within this public view; it does not rank theorem importance or claim strength.

Frontier	Current obligation	Programme significance
BSD-001 — rank-one leading term at literal p=2	MATHSOLVE #243 replays the Burns–Sakamoto–Sano theorem chain at literal p=2. If the replay fails, the campaign must identify the first unrepaired theorem-level dependency.	The work targets one named theorem-level obstruction. It does not generalize the result beyond the retained claim boundary.
VGSE-001 — rigid-panel kinematic semantics	M0 is terminal with a protected partial TE3 realization atlas. M1 #1163 now tests a GCL-defined rigid-panel/body-hinge interpretation across the retained TE3-native family.	The immediate question is whether flat-state infinitesimal mobility is stable across quotient samples and geometric branches. Finite folding and physical response remain outside the current claim boundary.
OZ-001 — order-7 Brown–Zudilin certificate route	MATH-PROGRAMME #964 reduces the 576-dimensional discrete-curl kernel through a degree-minimising Popov or approximant-basis section. The resulting order-7 certificate then requires independent replay.	The work attempts to construct an exact characteristic-zero certificate inside a defined admissible class. Construction and certification remain separate steps.

Other active development includes CMDG CM4 P3-M finite-stage recovery and the NS-CI-001 critical-integrability lane. The public table is a compact orientation surface, not the programme's full active-work registry.

Rows appear here only while the work remains materially active. Issue trackers provide navigation. Protected repository records remain authoritative.

Programme Atlas → · MATHFORGE · MATHSOLVE · MATHCERT

VGSE-001: from TE3 geometry to kinematic semantics

M0 is terminal at TE3_REALIZATION_ATLAS_PARTIAL. The retained atlas contains 40 valid numerical source-contract t-embeddings from 41 independently generated quotient samples, plus multiple valid geometric representatives at one fixed quotient point.

The active frontier is M1. GCL now treats the eight bounded t-embedding cells as rigid panels and the ten internal shared dual segments as ideal revolute hinges, with one panel fixed to remove global rigid motion. K0/K1 computes the flat-state body-hinge Jacobian, infinitesimal mobility, and constraint dependencies across the retained atlas and compares the multiple baseline branches.

This is intentionally kinematic only. It does not infer finite rigid foldability, stiffness, materials, collision freedom, thickness, or product behaviour. M2 inverse design remains blocked and will use GCL-ID-00 when activated.

The phase mandate remains docs/VGSE_MECHANICAL_SEMANTICS_MANDATE.md, with the active M1 contract under research/vgse-ms-m1/.

BSD-001: the current replay problem

WP60R is not a general attempt to “prove BSD at p=2.” It is a replay of two specific BSS theorem steps after a protected replacement stack. The diagram below shows which dependency classes are being replaced and the two admissible outcomes.

The important point is the retained failure of full finite Hypothesis 3.2(iii). The replay must use the admitted restricted replacements where they apply. It must not restore the stronger hypothesis by implication or presentation.

OZ-001: the 576-dimensional kernel

The current order-7 route has two coherent ansatz regimes. Their column counts and ranks differ, but both have nullity 576. The programme reconstruction identifies that common homogeneous kernel with the discrete-curl image.

This diagram also explains why the earlier value 518 is rejected. It came from subtracting the exploratory rank 1106 from the boundary-forced column count 1624. Those quantities belong to different ansatz regimes.

What the programme preserves

The programme is designed so that later work can recover the state of inquiry without relying on informal context.

A continuable campaign should let another researcher or agent answer four questions:

1. What exact object or claim is under study?
2. What evidence supports the current status?
3. Which obligations, limitations, or failure cases remain open?
4. What is the next authorized move?

The programme therefore preserves four properties:

Property	Required result
Traceability	A reader can recover the source, evidence, and decision path for a consequential claim.
Executability	A reader can repeat the relevant computation, reconstruction, proof replay, or validation when reproduction applies.
Bounded claims	A reader can identify the claim type, status, scope, assumptions, and material limitations.
Continuation	A new researcher or agent can resume from the recorded state without reconstructing hidden project context.

This is the practical reason for the programme architecture. The output is not only a mathematical result. The output is a result with enough structure for scrutiny, transfer, and continued work.

Execution model — protected concurrent execution

The programme operates under MP-STREAMLINED-EXECUTION-001 and MP-SUBSTANCE-FIRST-EXECUTION-001.

Routine bounded administration, documentation, engineering, maintenance, routing, synchronization, and campaign execution use standing delegated authority. A moved branch head does not create a new review requirement by itself.

Specialist non-author review remains required for substantive mathematical certification and source-semantic adjudication. It also remains required for constitutional authority expansion, security-sensitive protection weakening, and external claim promotion.

The primary mathematical or technical artifact remains the object of optimization. Governance, CI, provenance, and release controls must remain proportional to the material risk.

Evidence binds to its material evidence closure. It does not bind indiscriminately to every unrelated repository change.

Protected branches can therefore develop concurrently when four conditions hold:

1. the candidate remains mergeable;
2. relevant dependencies are unchanged;
3. affected checks pass;
4. scope and authority have not widened.

Programme policy CI is impact-routed. validate-json is the stable aggregate required context over selected policy shards.

Expensive formal, external, and computational replays use material-identity routing where the policy permits reuse. Scheduled or explicit full sentinels provide broader coverage.

docs/WORKFLOW_COVERAGE.md records the current executable coverage and measured evidence.

The earlier administrative workflow rebuild remains historical evidence at MP-ADMIN-WORKFLOW-REBUILD-001. Its exact-head review sequence records how that transition was admitted at the time.

Core repositories

• MATHFORGE discovers candidate material: source signals, problem cards, reconnaissance artifacts, finite screens, and route suggestions.
• MATHSOLVE organizes solving campaigns: theorem spines, work packages, proof-debt registers, exact obligations, and certification handoffs.
• MATHCERT checks the claim boundary: formal statements, exact replays, certificate validators, and claim ledgers.

Current operating standards

Use these as the current source of truth before opening new doctrine or domain work:

1. docs/GRAND_CHALLENGE_PEDAGOGY_STANDARD.md — rails-before-research exposition standard.
2. docs/PEDAGOGICAL_STYLE_GUIDE.md — sentence- and artifact-level style companion.
3. docs/ACCESSIBLE_RESEARCH_GUIDE_STANDARD.md — prerequisites, examples, fixtures, challenge ladders, certification paths, and continuation graphs.
4. docs/CHAIDEZ_PEDAGOGICAL_PROTOCOL.md — theorem-spine campaign protocol.
5. docs/FOUNDATION_AWARE_MATH_PROGRAMME.md — structured-object and axiom-profile doctrine.
6. docs/CLAIM_BOUNDARY_DOCTRINE.md — claim-status and proof-boundary discipline.
7. CLASSIFICATION_DISCOVERY_STANDARD.md — classification, discovery evidence, and knowledge-graph rules.
8. GRAND_CHALLENGE_WORK_PACKAGE_STANDARD.md — work-package structure and review discipline.
9. CLAIM_LEDGER_STANDARD.md — claim-ledger format, support route, and promotion conditions.
10. CERTIFICATION_LADDER.md — promotion gate from mathematical development to certified result.
11. docs/governance/STREAMLINED_EXECUTION_AMENDMENT.md — delegation, material closure, concurrency, CI proportionality, merge, and readback rules.
12. docs/governance/SUBSTANCE_FIRST_EXECUTION_DISCIPLINE.md — primary-deliverable lock, process proportionality, drift controls, and handoff inheritance.
13. docs/WORKFLOW_COVERAGE.md — executable CI coverage, bounded replay, routing, and operational evidence.
14. docs/governance/AGENT_CADENCE_OPERATING_DESIGN.md — event-driven and campaign-local cadence interpretation.

Presentation and pedagogy companions

• docs/GRAND_CHALLENGE_READER_GUIDE.md
• docs/PROGRAMME_ATLAS.md
• docs/MINDERLINGS.md
• docs/PEDAGOGICAL_STYLE_GUIDE.md
• docs/ACCESSIBLE_RESEARCH_GUIDE_STANDARD.md
• templates/accessible_research_guide_template.md
• docs/CLAIM_BOUNDARY_DOCTRINE.md
• docs/CROSS_PILLAR_LANES.md
• docs/GLOSSARY.md

Supporting files include schemas, templates, finite enumerators, audit outputs, resource notes, and Lean scaffolding retained from earlier domains.

How to use this repository

1. Start with Current programme fronts for work that is materially active now.
2. Read docs/GRAND_CHALLENGE_READER_GUIDE.md for orientation.
3. Read ARCHITECTURE_OVERVIEW.md for the three-pillar architecture.
4. Read the current operating standards before starting governed work.
5. Use GRAND_CHALLENGE_WORK_PACKAGE_STANDARD.md and templates/work_package_template.md for MATHSOLVE work packages.
6. Use docs/ACCESSIBLE_RESEARCH_GUIDE_STANDARD.md when a project needs a human or agentic on-ramp.
7. Treat CLAIM_LEDGER_STANDARD.md as binding for consequential claims.
8. Treat CERTIFICATION_LADDER.md as the promotion gate for certified results.
9. Use docs/CROSS_PILLAR_LANES.md for recurring tactics or certificate paths that span all three pillars.
10. Use CLASSIFICATION_DISCOVERY_STANDARD.md for subject mappings and discovery evidence.
11. Use schemas/foundational_profile.schema.json for the machine-readable foundation-aware profile.
12. For routine execution, identify the primary deliverable and its material acceptance criteria.
13. Classify the material closure, run affected checks, exercise delegated disposition, merge through protection, and read back protected state.
14. Use docs/PROGRAMME_ATLAS.md and governed campaign trackers to locate active, queued, blocked, and historical work.

Historical domain scaffolding remains part of the record. Its presence does not imply current priority.

Claim boundary

This README is a programme map. It is not a mathematical disposition.

Placement in Current programme fronts records current work only. It does not establish proof, refutation, certification, novelty, or priority of discovery.

A source can motivate a claim. A computation can support a claim. A work package can organize a claim. MATHCERT determines the certification status of the exact claim presented to it.

Communication posture

The README follows the same claim-boundary rule as the rest of the programme. Presentation can expose authority. Presentation cannot create authority.

A useful programme artifact keeps four items visible:

• the object under study;
• the current obstruction or obligation;
• the exact claim boundary;
• the next authorized move.