Grand Challenge Mathematics Programme

Grand Challenge mathematics work is organized as a three-pillar system:

MATHFORGE  ->  MATHSOLVE  ->  MATHCERT
discover       organize       certify

The programme exists to turn mathematical curiosity into checked understanding without confusing evidence, computation, exposition, or certification.

Core repositories and pillars

• MATHFORGE discovers candidate ore: source signals, problem cards, reconnaissance artifacts, finite screens, and route suggestions.
• MATHSOLVE organizes the campaign: theorem spines, work packages, proof-debt registers, exact obligations, and certification handoffs.
• MATHCERT checks the 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 for accessible research handoff.
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 — external 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.

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

Additional supporting files include schemas, templates, exact finite enumerators, small audit outputs, resource notes, and Lean scaffolding for the Union-Closed domain.

How to use this pack

1. Read docs/GRAND_CHALLENGE_READER_GUIDE.md for orientation.
2. Read ARCHITECTURE_OVERVIEW.md to understand the three-pillar split.
3. Read the current operating standards above before starting new work.
4. Use GRAND_CHALLENGE_WORK_PACKAGE_STANDARD.md and templates/work_package_template.md for every MATHSOLVE Work Package.
5. Use docs/ACCESSIBLE_RESEARCH_GUIDE_STANDARD.md and templates/accessible_research_guide_template.md whenever a project needs a human or agentic on-ramp.
6. Treat CLAIM_LEDGER_STANDARD.md as binding. No claim should appear without a type, support route, and promotion condition.
7. Treat CERTIFICATION_LADDER.md as the promotion gate from mathematical development to certified result.
8. Read docs/CROSS_PILLAR_LANES.md when a recurring tactic, witness, or certificate path spans all three pillars.
9. Treat CLASSIFICATION_DISCOVERY_STANDARD.md as binding for subject mappings, knowledge graph assertions, and discovery evidence.
10. Treat schemas/foundational_profile.schema.json as the machine-readable form of the foundation-aware profile.
11. Begin the first domain with DOMAIN_01_UNION_CLOSED_MASTER_PLAN.md, WP01_UNION_CLOSED_STATUS_SPINE.md, and WP02_UNION_CLOSED_LEAN_HANDOFF.md.

Claim boundary

This package does not claim new mathematical results. The included Union-Closed enumerator is a small exact sanity audit for universes up to size 4. It is useful infrastructure, not progress on Frankl's conjecture.

A source can motivate a claim. A computation can suggest a claim. A Work Package can organize a claim. But MATHCERT determines whether a claim is checkable.

The Grand Challenge posture

The desired voice is ambitious, lucid, and exact. It should not sound like marketing. It should not obscure uncertainty. It should not confuse ornament with insight. Decoration is allowed only when it helps the reader see the structure.

A good artifact should leave the reader with four things:

• the object in view;
• the obstruction in focus;
• the claim boundary visible;
• the next move unmistakable.