Submit through a short online form

Route 01

Concrete matroid submissions

The form asks for the mathematical information needed by the checker and a short provenance record:

• the ground-set size \(n\);
• the rank \(r\);
• the claimed exact fraction \(\overline{\alpha}(M)\); and
• exactly one complete description: a matrix, all bases, all circuits, or all hyperplanes.
• the discoverer or discoverers and the discovery date;
• whether AI was used and, if so, its model and version, a brief description of its role, and preferably a public chat or run link.

The ground set is labeled \(0,1,\ldots,n-1\). GitHub automatically supplies the submitter identity, issue URL, and submission timestamp. These are distinct from the requested discoverer names and discovery date: a submitter may be entering someone else's earlier result. A title and brief notes are optional.

Discovery history and AI disclosure

Give at least the month and year, preferably as YYYY-MM; use YYYY-MM-DD if the day is known. If AI was used, identify the provider or system, model, and version as precisely as known, then describe its role in one or two sentences. A public link to the relevant chat or run is preferred whenever one exists. If no AI was used, select No and enter None in the required model and role boxes.

How to enter the data

For example, the row matrix [[1,0,1,1],[0,1,1,2]] over \(\operatorname{GF}(3)\) represents \(U_{2,4}\). Its complete basis list is [[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]].

Optional representability certificate

If the primary description is bases, circuits, or hyperplanes, you may additionally supply a matrix over a specified field. The current trusted input language supports rational fields and all finite fields:

• over \(\mathbb Q\), entries are integers or quoted fractions such as "-3/5";
• over a prime field, entries are integers reduced modulo the characteristic;
• over \(\operatorname{GF}(p^d)\) with \(d>1\), an entry may be a length-\(d\) coefficient list in the polynomial basis \(1,a,\ldots,a^{d-1}\).

The verifier issues a field badge only if the matrix represents the same labeled matroid as the primary description.

What happens after submission

1. The issue is parsed as inert form data. The trusted workflow runs from the repository's default branch.
2. The matroid is reconstructed. Incomplete set lists, invalid axioms, incorrect ranks, and mismatched matrix certificates are rejected.
3. Every eligible pair is checked. The four quantities \(|B^{ij}(M)|,|B_{ij}(M)|,|B^i_j(M)|,|B^j_i(M)|\) are counted exactly and all ratios are compared by integer cross multiplication.
4. The workflow comments on the issue. It either records the verified fraction, size, rank, number of bases, maximizing-pair count, and automatic eligibility classification, or gives a validation error. Editing the issue reruns the check.
5. Curatorial acceptance remains separate. Passing the checker proves the finite claim but does not automatically publish duplicate, poorly attributed, or out-of-scope entries.

Automatic eligibility classification

Exact verification and publication are separate decisions. After a concrete claim is verified, a machine-readable policy assigns one of the following statuses:

The supported field records are currently \(8/7\) over \(\operatorname{GF}(2)\), \(100/81\) over \(\operatorname{GF}(3)\), and \(8/7\) over each of \(\operatorname{GF}(5)\) and \(\operatorname{GF}(7)\). Equality qualifies for the global \(4/3\) challenge; a field record must be beaten strictly. Only a verified representation over that exact finite field counts for the field-specific comparison.

Route 02

Infinite-family submissions

The family form asks for:

• a precise parameter domain and construction of \(M_t\);
• formulas for \(|E(M_t)|\) and rank when available;
• the exact ordinate at every plotted parameter—either the full value \(\overline{\alpha}(M_t)\) or a clearly identified certified lower bound;
• the exact supremum or limsup and whether it is attained by a finite member;
• the numerator and denominator of that exact value in separate fields for automatic threshold screening;
• a complete proof in the issue or a stable paper/preprint reference with a precise theorem or section; and
• discoverers, proof authors, citations, and the discovery date;
• an explicit AI-use declaration, including model and version, a brief role description, and preferably a public chat or run link.

Every accepted family receives a curve. A solid curve means the complete maximum has been proved. A dashed curve means a specified pair or weighting has been evaluated exactly, giving a proved lower bound. Automatically checked small members are useful evidence, but they do not prove a general formula.

The family workflow compares the submitted exact fraction with \(4/3\). A value at least \(4/3\) is marked eligible for human review; a smaller value is marked below threshold. This screening does not verify the construction, existence conditions, curve formula, representability statement, or proof.

As with a concrete submission, GitHub records the submission time automatically. The form asks separately when the family was actually discovered, since discovery, proof, submission, and publication may occur on different dates.

Safety and trust

What happens to your submission

Submissions go through GitHub Issue Forms, so a GitHub account is required. GitHub records you as the submitter — separately from the discoverers you name in the form — and provides the authentication and moderation layer. Editing your issue reruns the automated check.

Your submission is treated purely as data. The checker reads the form's JSON arrays and field values; it never executes code of any kind from a submission, so a verification result reflects exactly the matroid you described and nothing else. Input sizes and checking time are capped, and the verdict is posted back on your issue with a deterministic, downloadable certificate.

Nothing is published automatically. A verified concrete claim, or a family proposal that passes the numeric screening, still goes to a human curator before it appears in the catalog — the automated check proves your claim; curation decides how it is displayed and credited.

Optional local reproduction

Run the same verifier yourself

The online form does not require a local checkout. For reproducible development, the repository still includes the normalized JSON schema and command-line verifier:

julia --project=. scripts/verify_matroid_submissions.jl \
  examples/submissions/uniform-u2-4-matrix.json \
  /tmp/uniform-u2-4.certificate.json

The schema is schemas/matroid-submission.schema.json. The issue workflow uses scripts/verify_matroid_issue.jl to create the normalized data automatically before invoking the same trusted checker.