← 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 23 of 39

Compact Hausdorff countable-network metrization

Excluded

Known compact-Hausdorff countable-network metrization theorem. Formal proof and agent work alone do not establish a new central AI contribution under current policy.

Screening recorded: 2026-10-18 · Decision reviewed: 2026-10-18T07:37:42.537Z

The compositum of the two Mahler minimizers: exact measure, conjugate census, house, and minimal product recurrence, with the Bedford-Kim plastic family, Lehmer's polynomial, and the E_m Coxeter bridge

On hold after review

The compositum package includes a claimed canonical-pair witness and new exact identities alongside classical Coxeter material. Claude drafted and repaired proofs, but the original mathematical origin of the claimed new parts is not documented.

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

Low-dimensional exact counterexamples to the Recht–Ré inequality

On hold after review

The exact Recht–Ré counterexamples are new candidates, but the disclosure describes AI assistance across research and formalization without naming a retained central AI construction.

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

A sharp asymptotic spectral bound for forbidden subgraphs

On hold after review

The claimed sharp bound comes from a private informal manuscript that cannot be checked here. Codex is described as formalizing and packaging it, so the origin and scope of any AI mathematical contribution remain unresolved.

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

Pseudorandom hypergraph matchings (Ehard–Glock–Joos)

On hold after review

The Ehard–Glock–Joos theorems are prior work, but this proof replaces their Molloy–Reed step with a trimmed-nibble construction. Aristotle proved from supplied plans and Claude designed/reviewed the route; the origin of that replacement is unresolved.

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

Sneider's Gδ-diagonal metrization theorem

Excluded

The source formalizes the classical Sneider Gδ-diagonal criterion, not the cited paper’s new small-diagonal results. Codex authored Lean proofs and tests, with no new mathematical result claimed.

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

Erdos 662: corrected global threshold conjecture

On hold after review

The current package ports an already public counterexample proof and adds a bridge to a corrected global statement. The original archive’s AI/proof origin is not established by this disclosure.

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

Formalization of a discrete Carleson theorem of Stein-Wainger type

Excluded

The discrete Carleson theorem and proof are taken from the two cited Krause–Roos papers. AI made a blueprint and Lean proofs for those source arguments, not a new central mathematical result.

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

A converse to the discrete four-vertex theorem

On hold after review

The source does not identify a central new geometric idea or result supplied by AI beyond human direction and Lean proof engineering.

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

Füredi's stability theorem and the Erdős–Simonovits stability theorem

Excluded

Füredi’s and Erdős–Simonovits’s stability theorems are cited as prior results. Aristotle and Claude generated Lean proofs and plans for those established claims, without a new central mathematical contribution documented.

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

Selection of the electromagnetic source tensor by covariance, conservation and the exchange law

On hold after review

The source presents finite certificates and conservation-only and differentiable-only routes developed in AI-assisted PDT research. Alexander selected the results, but the disclosure does not say whether Codex supplied the central new arguments or only their Lean proofs.

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

Waist

Excluded

The waist theorems are sourced to Gromov, Memarian and Klartag. Aristotle is credited with assisting their Lean formalization, with no central new mathematical idea identified.

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

Erdős Problem 656: translated restricted pair sums

Excluded

The repository says it reproduces a prior AI-assisted Lean proof of Kra–Moreira–Richter–Robertson’s 2024 theorem; this adaptation claims no new mathematical result.

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

Alexandroff–Urysohn cover metrization

Excluded

The source expressly calls the Alexandroff–Urysohn criterion classical and claims no novelty. Codex authored the Lean proofs and packaging; that is not a new mathematical contribution.

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

Graphic sequences: the Erdős–Gallai and Havel–Hakimi theorems

Excluded

Erdős–Gallai and Havel–Hakimi are established characterizations, with Choudum’s sufficiency proof followed. Agent work implements the Lean formalization.

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

Euler's theorem on Eulerian circuits and trails, and Petersen's 2-factor theorem

Excluded

The source formalizes classical Euler–Hierholzer and Petersen theorems and explicitly says no mathematical novelty is claimed. Claude wrote Lean code and proposed proof plans approved by the human author; no new central result is attributed to AI.

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

The Gallai–Hasse–Roy–Vitaver theorem

Excluded

The Gallai–Hasse–Roy–Vitaver theorem is established. The human author chose the result, while Aristotle and Claude generated Lean proofs from supplied formal statements and a proof plan.

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

Connected counterexamples to the exact color-critical two-eigenvalue bound

On hold after review

The connected counterexample family is supplied by a private manuscript that cannot be checked against the repository. GPT-6 is credited with Lean proofs and certificates, not clearly with discovering the family.

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

Erdos 99 Partial Solution

Excluded

The author says he proved the finite-multiplicity Erdős 99 result himself and gave Aristotle a finished manuscript for Lean formalization. The documented AI work is transcription and proof engineering.

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

Solvability of divergence-form elliptic equations (Evans §6.2)

Excluded

The six selected statements are Evans §6.2 solvability results. Claude wrote and refactored Lean proofs under hand-fixed literature statements; the disclosure does not assign AI a new central result.

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

Continuum hypothesis independence: a Flypitch reproduction

Excluded

The project explicitly calls itself an attributed Flypitch reproduction of the established CH independence formalization. AI agents adapted and audited existing Lean proofs.

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

Petersen's theorem

Excluded

The repository derives Petersen’s established matching theorem from Tutte’s theorem. The human author chose the statement and proof plan; Aristotle supplied the Lean proof.

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

Elliptic curves of exact ranks five, six, and seven: conditional formalization

Excluded

The formalization adapts a preexisting elliptic-curve manuscript and leaves its prime asymptotic as a hypothesis. GPT-6 agents checked and formalized that target; the disclosure identifies no AI-origin result.

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

Mader's theorem and Hadwiger's conjecture for t ≤ 4

Excluded

The entry explicitly formalizes classical Mader, Dirac and Hadwiger results and says no mathematical novelty is claimed. Aristotle proved supplied formal statements and proof plans; Claude designed and reviewed them.

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

Classical bounds for graph Ramsey numbers

Excluded

This package selects Greenwood–Gleason, Erdős–Szekeres, and Erdős graph Ramsey bounds; the author chose the classical results and AI generated Lean proofs.

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

Kőnig's theorems and Dilworth's theorem

Excluded

The Kőnig, Kőnig–Egerváry, Dilworth and Mirsky claims are credited to classical sources. The author chose results and routes and supplied statements and plans; Aristotle and Claude generated Lean proofs.

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

Kuratowski's theorem

Excluded

The source formalizes Kuratowski’s 1930 theorem through Wagner’s theorem. It explicitly says the human author chose the result and route, supplied proof plans, and claims no mathematical novelty; agents supplied Lean proofs.

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

Perfect images of metrizable spaces

On hold after review

The cited repository does not expose a root formalization.yaml, so the source theorem and AI/proof disclosure were not readable.

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

Localized two-eigenvalue bound for finite noncomplete graphs

Excluded

The localized spectral bound is tied to the earlier conjecture and Bradač’s scalar argument, with a reused BN spectral lift. Codex is credited for local Lean adaptation and toolchain port, not for a new central mathematical idea.

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

The MDS conjecture over finite fields of even order

Excluded

The disclosure explicitly says Pranava Kumar devised the common-height mathematical argument without automation. Claude translated that proof into Lean and later agents ported it, so the central result is human-origin.

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

CollatzPosDens

On hold after review

AxiomProver generated the Lean proof of Lau’s Collatz density theorem, but the formalization record does not say who supplied the paper’s central mathematical idea.

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

Near-regular hypergraph matchings and the asymptotic triangle-packing gap

Excluded

The three selected results specialize or restate Haxell–Rödl and classical nibble/LP claims; metadata says the human author supplied results and proof plans, AI produced Lean proofs.

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

H2 obstruction to lifting discrete matrix representations

Excluded

The H² lifting criterion is classical, and the human supplied six starting Lean lemmas. Agents completed and compiled this proof and its matrix application without a novelty claim or documented new central mathematical idea.

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

The Beck–Fiala integer-making theorem

Excluded

The strict rational rounding statement and floating-coordinate proof are Beck–Fiala's theorem. Traverso chose the result and route; Claude generated the Lean proofs.

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

Dross's theorem on fractional triangle decompositions

Excluded

Dross’s published 9n/10 theorem and its max-flow route supplied both the statement and proof plan. Aristotle generated Lean proofs from the author’s plans; no new mathematics is claimed.

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

Distinguishing sets and measures from their planar Brownian images

Excluded

The project formalizes all numbered statements of Troscheit’s prior Brownian-image paper. Claude and GPT-6 performed Lean proof development and review, with no disclosed AI-origin mathematical result.

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

A finite counterexample for strict consecutive totient patterns

Excluded

The cutoff-826 totient counterexample and strict-pattern consequence are explicitly attributed to Chojecki’s Proposition 1.2. Codex supplied a finite certificate and a bound derived from the absent pattern; the source claims no new result.

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

Vizing's theorem and equitable edge colourings

Excluded

Vizing’s bound and McDiarmid’s equitable refinement are earlier results. The source says the human author chose the results and route while AI generated Lean proofs.

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

Smirnov's local-to-global metrization theorem

Excluded

The project explicitly formalizes classical Smirnov metrization and claims no new mathematics; Codex wrote the formal proof.

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

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