Programme Charter¶
The programme is ambitious about mathematics and conservative about claims. This charter states the obligations that keep those two postures compatible.
Preamble
Mathematical understanding is not produced by inspiration alone, nor by formalism alone. It emerges when objects are made visible, obstructions are isolated, partial results remain honestly bounded, and proofs can be checked without losing the idea that made them possible.
Articles¶
- I
The object shall be visible.
No method may arrive before the reader knows what is being studied. Definitions, examples, non-examples, and preserved equivalences belong near the entrance.
- II
The obstruction shall be named.
A programme that cannot explain why its problem is difficult does not yet understand its problem. The obstruction may be combinatorial, geometric, analytic, logical, computational, or conceptual; it must not remain atmospheric.
- III
Every claim shall carry its status.
Literature-derived, heuristic, computed, interval-certified, locally proved, formally checked, superseded, and refuted statements are different mathematical objects. Their labels are part of their meaning.
- IV
Partial progress shall be preserved without promotion.
A reduction, failed route, finite screen, boundary analysis, or useful normal form may materially advance a campaign. It earns a precise record, not a stronger theorem statement.
- V
Failure shall narrow the future.
A failed attempt is valuable when it records the hypothesis tested, the point of failure, the domain eliminated, and the condition under which the route might become viable.
- VI
Certification shall be local and replayable.
No artifact is certified in the abstract. A particular statement, dependency set, support route, and checking environment are certified. The boundary must be explicit enough for independent replay.
- VII
Exposition shall not impersonate proof.
Clarity is a mathematical virtue, but persuasive prose cannot discharge a missing obligation. Conversely, formal syntax that certifies the wrong human statement has not completed the intended work.
- VIII
Proof shall return to understanding.
The final artifact should leave the reader with more than a verdict. It should reveal the object, the obstruction, the decisive move, the dependency boundary, and the reason the result is true.
Operational compact¶
Mark uncertainty, expose dependencies, record failures, and state the next finite obligation.
Distinguish claim classes and respect honestly bounded partial progress.
Test the support route, not the confidence of the voice presenting it.
Promote only what has crossed its declared boundary.
Final article¶
The programme exists to make serious mathematical work more cumulative, more inspectable, and more difficult to fool. Its authority comes not from tone, but from the quality of its boundaries.