Programme Domains¶
The public catalogue of governed mathematical campaigns. Each entry identifies the current claim boundary, canonical repository artifact, and permitted next movement.
The programme has three mathematical execution pillars—MATHFORGE, MATHSOLVE, and MATHCERT—plus the MATH-PROGRAMME governance and integration layer. Domain state is recorded in DOMAIN_REGISTRY.yaml; detailed claims remain authoritative in the linked master plans, Work Packages, ledgers, reviews, and certificates.
Catalogue¶
| Domain | Campaign | Mathematical status | Programme posture |
|---|---|---|---|
| 01 · Union-Closed Sets | UC |
Open conjecture | Foundational demonstration domain; completed baseline with downstream local proofs and bounded certificates |
| 02 · Navier–Stokes Critical Integrability | NS-CI-001 |
Open problem | Equation-specific critical-integral campaign with restricted targets and explicit termination gates |
| 03 · Hodge Conjecture | HC-001 |
Open conjecture | Source-normalization and equivalence campaign; no theorem-strengthening claim |
| 04 · Birch–Swinnerton-Dyer | BSD-001 |
Open conjecture | WP00–WP04 promoted; selected restricted target remains unproved |
| 05 · Poincaré Reconstruction | PC-001 |
Solved classical theorem | Qualified solved-problem reconstruction and bounded-certification archive |
| 06 · Yang–Mills Existence and Mass Gap | YM-001 |
Open problem | Source-normalized axiomatic and equivalence dossier; no construction or gap theorem |
| 07 · P versus NP | PNP-001 |
Open problem | Machine, encoding, reduction, and barrier dossier; no equality, separation, algorithm, or lower bound |
| 08 · Riemann Hypothesis | RH-001 |
Open conjecture | WP00 promoted; WP01/WP02 implemented, merged, and CI-passed, with formal promotion withheld under retained review blockers |
Reading rule¶
A domain landing page is an orientation artifact, not a theorem ledger. Before relying on a mathematical statement, follow its canonical entry to the relevant claim ledger, review record, proof, source, or certificate route.
The programme never infers theorem status from domain activity, document count, Referee disposition, repository merge, CI success, public visibility, or documentary publication.