Programme Atlas¶
A map of mathematical work as a sequence of accountable transformations, with governance preserving the meaning of every transition.
Each transformation changes the status of the material. The programme exists to make those changes explicit and to preserve them across revisions.
Three execution rooms and one continuity layer¶
I · Discovery
MATHFORGE
The foundry collects problems, examples, failures, small computations, source trails, and first formulations.
Generative, never authoritative.
II · Campaign
MATHSOLVE
The campaign room builds definitions, reductions, diagrams, Work Packages, exact screens, and next-target statements.
Incomplete, never vague.
III · Certification
MATHCERT
The assay office checks claims through formal proof, exact replay, interval certificates, SAT/SMT, and other auditable routes.
Unimpressed, never ambiguous.
MATH-PROGRAMME governs integration, decision records, publication, and archival maintenance. It appears as a schema pillar for those artifacts, but it is not a fourth mathematical support route.
Artifact ladder¶
| Stage | Artifact | Owner | Promotion condition |
|---|---|---|---|
| Curiosity | Lead note | MATHFORGE | Source can be reconstructed |
| Candidate | Problem card | MATHFORGE | Status and risks recorded |
| Campaign | Work Package | MATHSOLVE | Claim ledger and next target present |
| Local result | Lemma, proposition, obstruction, or exact screen | MATHSOLVE | Support route identified |
| Handoff | Certification packet | MATHSOLVE + MATHCERT | Statement and dependencies clear |
| Certification | Checked artifact | MATHCERT | Proof or replay passes the declared gate |
| Integration | Authoritative artifact | MATH-PROGRAMME | Reviews, terminology, decisions, and continuity agree |
| Publication or archive | Public claim or qualified dossier | MATH-PROGRAMME | Claim boundary remains visible to the reader |
Domain portfolio¶
| Domain | Status | Programme role |
|---|---|---|
| 01 · Union-Closed Sets | Open conjecture | Foundational demonstration domain |
| 02 · Navier–Stokes Critical Integrability | Open problem | Equation-specific analytic campaign |
| 03 · Hodge Conjecture | Open conjecture | Source and equivalence normalization |
| 04 · Birch–Swinnerton-Dyer | Open conjecture | Theorem-ledger and restricted-target campaign |
| 05 · Poincaré Reconstruction | Solved theorem | Qualified reconstruction and bounded-certification archive |
| 06 · Yang–Mills Existence and Mass Gap | Open problem | Axiomatic source and equivalence control |
| 07 · P versus NP | Open problem | Machine, encoding, reduction, and barrier control |
| 08 · Riemann Hypothesis | Open conjecture | Function, zero, equivalence, and barrier control |
Union-Closed remains the programme's first demonstration of the complete route. It no longer exhausts the public domain catalogue. A merged WP00 dossier is documentary progress, not evidence that its terminal problem has moved toward resolution.
Cross-pillar obligations¶
MATHFORGE must give MATHSOLVE enough context to avoid attacking a mirage.
MATHSOLVE must give MATHCERT claims precise enough to check or reject.
MATHCERT must return missing definitions, unsupported assumptions, and proof gaps to the other pillars.
MATH-PROGRAMME must preserve the authoritative artifact, review provenance, terminology, and claim boundary without converting editorial integration into mathematical promotion.
The system improves when each layer makes the others harder to fool.
Status discipline¶
Claim support, artifact lifecycle, and campaign disposition are separate vocabularies. Use the Programme Status Taxonomy before interpreting words such as completed, certified, selected, or referee promoted.