← Methodology and sources

Considered but not curated.

Sources we considered, with review status and reasons.

Counts and coverage

3070 recorded entries · 652 awaiting detailed review · 584 excluded · 672 on hold · 3 publisher withdrawals · 1159 related to curated records.

  • Includes recorded What AI Found, VibeMathed, OpenAI, and news-led primary-source entries, plus publisher withdrawals.
  • Screening is metadata review, not a proof check. Registry flags are attributed reasons.
  • Entries overlap; OpenAI entries group related papers. Counts are not distinct discoveries.
  • Dates refer to saved decisions. Publication links use the current catalog.
  • Recorded searches do not cover all research.

Individual OpenAI manuscripts · Review criteria

Suggest a missing contribution or correction.

See omissions and decisions reviewed against public discussion.

Subject

Entries without a recorded subject appear only under All subjects. Coverage totals describe all subjects.

Screening decisions

1911 matching entries · Page 2 of 39

The DeLaViña-Waller conjecture on the Wiener index

On hold after review

The registry describes a full DeLaViña–Waller proof, but the linked original Zenodo file could not be checked. Earlier arXiv work proves only selected graph classes.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18T00:00:00.000Z

Criteria and two quadratic instances for Bugeaud's Problem 10.61

On hold after review

A third-party check that the formal statements faithfully encode the intended informal Bugeaud claims is explicitly absent; the notes and Lean statements diverge on higher degree.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18T00:00:00.000Z

Fermat's Last Theorem formalized end to end in Lean 4

Awaiting detailed review

Changed registry/artifact metadata retained for comparison with the existing assessment; no new discovery inferred.

Screening recorded: 2026-10-28 · Decision reviewed: 2026-10-28T08:47:35.674Z

Disputed claim that Catalan's constant is irrational

Excluded

The disputed source is Zhi-Wei Sun’s 2609.04176, criticized by Dane Wachs in 2609.22339. Human supplied the central weighting idea; AI numerical work and proofreading alone do not qualify. This dispute is not a refutation or correction of the separate OpenAI Catalan proof.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Bounded prime gaps improved to 212, with a Lean certificate of the deduction

Excluded

The primary manuscript attributes the analytic method to Stadlmann and its new 212 optimization and parameter verification to the human authors. Appendix A says AxiomProver produced a Lean certificate from the authors' natural-language specifications, conditional on stated analytic estimates and a separately supplied variational certificate. The documented AI work checks the human result rather than supplying its central mathematics.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18

Huang-Jiang-Oblomkov conjecture proved for every torus-knot singularity, with a Lean formalization conditional on two literature inputs

On hold after review

The HJO conjecture and finite identity are proved and formalized, but the collaboration disclosure does not isolate a central AxiomProver-origin mathematical step from author-led strategy and formalization. The current v2 abstract says the Lean result is unconditional.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18T00:00:00.000Z

Finite-time blowup for the IPM equation with uniformly space-time smooth forcing

Excluded

The IPM theorem on the torus with uniformly space-time smooth forcing is distinct from the published Boussinesq theorem. In the IPM manuscript's AI disclosure, the authors attribute the adaptation ideas to themselves and the earlier blowup mechanism to Córdoba and Martínez-Zoroa; Claude and Codex reproduced the earlier argument, handled proof bookkeeping and text, and formalized the authors' argument. The documented AI work does not meet the central mathematical contribution threshold for this claim.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18

Four Color Theorem formalized in Lean 4 by AI agents, in two independent developments

Excluded

Both primary repositories explicitly port Gonthier's earlier Coq proof of the already established Four Color Theorem into Lean 4. The models wrote substantial proof code, but no distinct model-supplied mathematical idea or new theorem is documented beyond formalizing the existing proof.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18

Norm-variation of multiple ergodic averages, including Tao's norm-convergence theorem, autoformalized in Lean in one week

Excluded

The primary repository says humans hand-formalized the main statements and coding agents autoformalized a prepared proof blueprint under human supervision. It includes Tao's earlier norm-convergence theorem and known prerequisite theorems; no model-origin central mathematical idea or result is documented for this scoped entry.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18

Optimal packings of one to seven unit squares in a circle, proved in Lean

Awaiting detailed review

Metadata screened. Requires original-source review of the specific contribution, baseline and central AI work, with separate AI involvement, technical verification, human understanding and importance ratings before publication.

Screening recorded: 2026-10-26

Closed form for the anisotropic Watson integral of the cubic lattice

On hold after review

The toolkit paper says the generic anisotropic Watson integral has no closed form of the sought elliptic-product type, while a special rate has a gamma-value form. The separate Watson paper is listed as in preparation.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18T00:00:00.000Z

719 manuscripts in 372 result families from an unreleased OpenAI model

Awaiting detailed review

Metadata screened. Requires original-source review of the specific contribution, baseline and central AI work, with separate AI involvement, technical verification, human understanding and importance ratings before publication.

Screening recorded: 2026-10-27

Kakeya maximal conjecture in three dimensions and the Kakeya set conjecture in four

On hold after review

This row combines family 074’s three-dimensional maximal-function estimate, already curated, with a separate four-dimensional full-Hausdorff-dimension manuscript not yet curated. Review and link both scoped contributions before resolving the combined row.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18

Proof of the Lyons–White conjecture on rate-monotonic random walks

On hold after review

The primary paper describes human–AI dialogue and formalization, but does not isolate a central AI-origin theorem, proof idea or construction. The model role is too ambiguous under the current inclusion criterion.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18

Negative answer to the hyperinvariant subspace problem on Hilbert space

On hold after review

The WAF row states family 293’s quasinilpotent hyperinvariant-subspace counterexample from its second manuscript. The existing local family 293 record instead selects the first manuscript’s irrational-rotation invariant-projection result, so that record is not an exact match.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18

Massive continuum limit of the two-dimensional O(3) model

On hold after review

This row combines the locally curated family 215 canonical massive O(3) continuum limit with a separate companion claiming all-temperature exponential decay for classical O(n), n≥3. The latter needs its own claim-level review before the combined WAF row can be resolved.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18

Kannan–Lovász–Simonovits conjecture proved in two preprints posted the same day

On hold after review

This entry combines two independent KLS preprints. The published Bizeul–Klartag–Lehec record covers one proof; Song–Zhang proves the same dimension-free bound by a different height-reduction route. Song–Zhang credits collaborative AI work on an intermediate logarithmic bound but attributes the later log-star strategy and final bounded-cost analysis to the authors, leaving the central AI contribution to the final theorem unresolved. Do not link the combined entry to one paper or count a second KLS theorem without a separate scoped review.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18

Lower bound of 21 multiplications for 3×3 matrix multiplication over every field, with a Lean proof

On hold after review

Ivanov's repository states a distinct all-fields rank lower bound of 21 and credits ChatGPT/Codex with substantial mathematical exploration and Lean implementation, but does not identify which retained central lemma or idea came from the models. The record also explicitly makes no novelty or priority claim. Resolve contribution attribution and baseline against field-specific 2026 bounds before inclusion.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18

36 manuscripts across 18 fields from the BootLoops harness run with Claude

On hold after review

The entry aggregates many manuscripts rather than identifying one assessed contribution; the primary toolkit paper treats distinct computations and explicitly says §2 contains no new results.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-18T00:00:00.000Z

Counterexamples to Zak's modified integer round-down conjecture for the skiving stock problem

Awaiting detailed review

Compared source identities and precise claims with every current published record. Existing Barnette, Erdős and NIST results retain their assessments; changed registry presentation is not a new discovery. Other conjecture, nonquadraticity, optimization or circuit-design claims require contribution-specific AI attribution and exact prior-scope comparison; no registry rating or benchmark win substitutes for review.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

NIST elliptic-curve seeds traced to a 1990s C random number generator seeded with the clock

Awaiting detailed review

The NIST seed reconstruction is already a known dated institutional lead. Its empirical generator/clock recovery must be distinguished from a new theoretical cryptographic theorem or attack guarantee; no distinct eligible theoretical advance established in this pass.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Discovery metadata attribution: What AI Found, CC BY 4.0 · VibeMathed contributors, editorial layer CC BY 4.0. AIProofWatch supplies the screening decisions.