MATH-
PROGRAMME
A public discipline for turning mathematical curiosity into checked understanding.
Discovery remains free to imagine. Campaigns make obligations precise. Certification decides what crossed the proof boundary. Governance preserves what those decisions mean.
MATH-PROGRAMME is the governance, integration, publication, and archival layer. It is not a fourth proof stage.
The binding maxim
No theorem without a spine. No computation without a ledger. No conjecture without a map. No proof without a reader.
Why this exists
Mathematical work can be valuable long before it becomes a theorem.
A serious programme must preserve that value without inflating its status.
Definitions clarified, false corridors closed, boundary cases isolated, exact screens built, and proof obligations sharpened are genuine advances. They become cumulative only when another reader can inspect what changed and why.
- Without a map
- Promising questions are mistaken for well-posed problems.
- Without a spine
- Local insights never assemble into a proof strategy.
- Without a ledger
- Computation, intuition, and theorem drift into one another.
- Without continuity
- Later artifacts silently change what earlier decisions meant.
What counts as progress
Progress is a controlled change in what the programme knows.
Reconstruct the source, status, and exact object.
Confusion decreases.Turn a broad problem into finite mathematical obligations.
The search space contracts.Build examples, exact screens, diagnostics, and ledgers.
Evidence becomes inspectable.Establish a lemma inside a stated dependency boundary.
A claim earns support.Replay the proof or certificate independently.
Reliance becomes warranted.The proof boundary
Status words describe different objects and must not collapse.
These are compact claim summaries. Artifact lifecycle and campaign disposition are separate vocabularies. Read the status taxonomy.
The current portfolio
Eight domains, each with a different claim boundary.
One method, distinct mathematical states.
Union-Closed Sets remains the foundational demonstration domain. Navier–Stokes, Hodge, Birch–Swinnerton-Dyer, Yang–Mills, P versus NP, and the Riemann Hypothesis are open campaigns. Poincaré is a qualified reconstruction archive for a solved classical theorem.
Inspect the domain catalogue →Choose an entrance