Importance: modest
A useful, limited step: a narrow result, small benchmark gain, reproduction, or scoped formalization.
Importance: notable
A clear advance: a better bound, stronger construction, faster algorithm, or substantial theorem or formalization.
Importance: major
A recognized open problem resolved, a broad change to a field, or a landmark formalization.
Keep evidence separate
- A major preprint can have only an author claim as evidence.
- A modest contribution can have a fully checked formal proof.
- More checking does not change the impact of the same statement.
- A changed claim or baseline can change its importance rating.
Examples from the catalog
- Catalan’s constant: the reported irrationality proof is major if correct; it has author-claim and accessible-proof evidence.
- Fermat formalization: major for verification capability, rather than a new proof of the theorem.
- AlphaEvolve’s dimension-11 construction: notable for raising a lower bound; the exact kissing number remains undetermined.
- FunSearch’s packing benchmark: modest because the gain applies to tested instances.
- AlphaProof’s competition proofs: modest as reproductions of known results.
Ratings have written reasons. Publicity and benchmark scores alone do not determine them. A narrow result can still matter through useful methods, reusable formal infrastructure, or deployment. Known mathematics does not disqualify substantive formalization.
We use public discussion to find omissions and challenge baselines, then check the original statements and attribution. Read the public-discussion audit and resulting corrections.