Public beta · exact verification
Explore verified constructions, compare infinite families, and collaborate on pushing \(\overline{\alpha}\) higher.
Explore the records
Solid curves are proved exact. Dashed curves are certified lower bounds from a distinguished element pair.
Finite certificates
This is a certificate catalog, not the overall leaderboard; finite members of accepted families remain on their curves above.
| Construction | \(\overline{\alpha}\) | Size | Rank | Discovery | Verified field | Status | Open details |
|---|
Infinite constructions
Each page explains the construction, admissible parameters, plotted formula, proof scope, and whether its benchmark is attained or approached.
Collaborate
Beat the overall threshold on the nose, beat it in the limit, or improve a record with a verified finite-field representation.
Short, GitHub-authenticated forms
Choose a short issue form. GitHub supplies the account identity and public discussion; no fork, branch, JSON file, or pull request is required. Concrete claims are checked exactly, while family proofs receive mathematical review.
Automatically verifiable
Give \(n\), \(r\), a claimed exact \(\overline{\alpha}\), and exactly one of: a matrix with its field, all bases, all circuits, or all hyperplanes. A matrix certificate over a finite field or \(\mathbb Q\) is optional when the primary description is combinatorial.
Mathematical review
Define the parameterized construction, its plotted formula, supremum, attainment behavior, and proof. Small members are encouraged as reproducible evidence and may be submitted separately to the concrete verifier.
Exact verification is installed. The issue workflow reads the form as inert data, reconstructs the matroid, checks its axioms and claimed value, and posts an exact verification result with a challenge classification. Family limits receive numeric screening before human proof review. Nothing submitted by a contributor is executed. Read the submission guide.
Verification language
The site records the unweighted invariant \(\overline{\alpha}(M)=\max_{i\ne j} |B^{ij}(M)|\,|B_{ij}(M)|/ (|B^i_j(M)|\,|B^j_i(M)|)\). See the definitions, family proofs, and representability argument on the mathematics page.
Solid curve
The proof identifies an attaining pair and shows that no other eligible pair has a larger ratio.
Dashed curve
A distinguished pair is evaluated exactly, but it has not yet been proved to maximize the full invariant.
Catalog point
The finite matroid is reconstructed and every eligible pair is enumerated by trusted verifier code.