← 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 25 of 39

Finite Chains of Two-Complexes and Acyclic Covers

On hold after review

The paper reports five months of AI-assisted work on its main proof, with substantial author revision, but does not identify which central ideas came from AI. The repository chiefly documents AI source development and proof repair.

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

Strict Neumann Polya inequality on simply connected planar domains

On hold after review

The Neumann claim is separate and plausible, but the cited repository calls itself a pre-submission snapshot while later listings describe the same commit as registered; AI mathematical origin is broad.

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

Erdős Problem 809: an independent proof of the seven-cycle threshold

Excluded

The seven-cycle threshold and longer odd-cycle argument are credited to prior human papers. AI systems generated certificates and Lean proofs for those published results, not the result itself.

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

A zero-density estimate with exponent 3(1−σ)/(2σ) for the Riemann zeta function

On hold after review

Pinned README/CREDITS credit Mark Lewko with original contribution and Codex with proof development, adaptation, debugging and integration. The AI role in the improved zero-density exponent is not identified as central.

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

The generalized Fermat equation x² + y⁵ = z⁷

On hold after review

The formalization follows Jaswal’s own preprint and discloses AI use for Lean, but the manuscript’s original mathematical authorship and any AI role are not established here.

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

An interval-moment criterion for square-difference-free integer sets

On hold after review

The source does not attribute the central mathematical construction or witness search to AI rather than Naslund; the AI contribution remains unclear.

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

Ginibre Poincaré formalization

On hold after review

The repository formalizes a versioned Ginibre Poincaré paper; agents wrote proofs under human-supplied goals. The paper’s proof-origin account has not established a central AI idea.

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

Area stability of planar plank covers and Bezdek's annulus theorem

Excluded

The annulus and overlap theorems are Bakaev–Yehudayoff's results. Aristotle reconstructed their proof in Lean; Gemini and ChatGPT aided code and submission work. No separate AI plank-covering idea is credited.

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

A strongly tempered Meyer space of countably infinite Hamel dimension

On hold after review

The selected Meyer-space construction comes from a private PR requiring access. The metadata reports AI mathematical agent roles but does not disclose which construction steps originated with them.

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

Sharp Wasserstein propagation of chaos from correlated initial data

Excluded

The sharp propagation theorem is the author’s manuscript theorem. Claude worked on statement design, Lean proof, port and reviews under the author’s mathematical direction; the disclosure identifies no AI-origin mathematical result.

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

Erdős 374: classical square products of factorials

Excluded

The factorial-square constructions, prime obstruction and cutoff are expressly classical; the density question remains unproved. Agents supplied an independent Lean proof of selected known supporting results.

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

The density hypothesis for σ > 3/4

On hold after review

The cited repository does not expose a root formalization.yaml, and the registry page supplies no readable disclosure here. The theorem’s origin and AI role remain unverified.

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

Order Arcs Between Subcontinua

Excluded

The strict order arc is presented as a consequence of Kelley's 1942 lemmas. The human selected the target, Codex built the Lean proof, and the pinned record disclaims mathematical novelty.

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

The CLARK Tile: An Aperiodic Monotile in Five Dimensions

On hold after review

Pinned README says AI made substantive mathematical-analysis contributions but the five-dimensional S54 tile and proof chain came from retained source snapshots with unknown original bibliographic authors. The origin of the central CLARK construction is not resolved.

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

Explicit Szemerédi–Trotter bounds over arbitrary fields

On hold after review

The formalization improves Lewko’s v2 bound by saving a linear m term, and Codex assembled the refined bounds. The disclosure does not establish who derived that improvement mathematically.

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

Alexandroff Property of Metric Indecomposable Continua

Excluded

The Alexandroff property is Todorov–Valov Theorem 3.3, with classical composant foundations. Codex formalized an alternative bridge under human-selected scope; no AI-origin mathematical result is identified.

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

Two partial balayage principles for weak-type estimates

Excluded

The fifteen submitted balayage bounds come from Lin’s human-authored source proofs. GPT-6 formalized selected statements and the author explicitly directed omission of a harder bound.

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

A counterexample to Vaught's conjecture for infinitary logic

On hold after review

Knight supplied the unpublished construction, while later human–AI interaction added unspecified ideas. The record does not identify a retained central idea supplied by AI.

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

Structured orthogonal and unitary matrices: factorization, geometry and singularities

On hold after review

The repository goes beyond the Aliev–Rakhuba paper with unitary results, stronger real singularity ranges and four-layer counterexamples. ChatGPT assisted Lean proof development, but the source does not assign these mathematical extensions to AI.

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

Monotone-Light Factorization of Compact Hausdorff Surjections

Excluded

The compact-Hausdorff factorization and uniqueness are expressly formalized from Daverman’s stronger theorem. Codex is disclosed for Lean development; no new mathematical factorization is attributed to it.

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

A Lean 4 formalization of Catalan's conjecture (Mihăilescu's theorem)

Excluded

The selected Catalan/Mihăilescu theorem is a prior proof following Bilu’s cyclotomic exposition. Agents wrote and ported Lean code under the author’s fixed acceptance criteria; no new mathematical result is claimed.

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

A Hausdorff–packing criterion for self-pinned distance sets

On hold after review

The B_H pinned-distance criterion is Lin’s earlier manuscript Theorem 1.1. Codex is disclosed for submission preparation and audits, while the original proof-development AI history is explicitly undocumented; central AI involvement cannot be determined.

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

FluidSingularSets

On hold after review

The source claims logarithmic gauge nullity and a 25/23 parabolic box bound, but points to local manuscripts. The disclosure names AI proof agents without identifying whether they supplied the central estimates or formalized a human draft.

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

Non-Cut Points of Hausdorff Continua

Excluded

Both non-cut-point assertions are identified as Proposition 29.3 of a topology textbook. Human direction selected the proof route; Codex agents formalized and checked these established statements.

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

Sierpinski Closed Partitions of Continua

Excluded

The countable closed-partition theorem is sourced to the Washington University topology notes. Codex formalized and independently reviewed that established theorem under a human-selected scope.

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

Erdős 1139: large gaps between almost-primes

On hold after review

The source does not identify a retained central AI-origin step in the protected-reserve improvement.

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

Boundary Bumping for Closed Subsets of Continua

Excluded

The component-frontier result is classical boundary bumping, cited to Ball–Hagler–Ormes, with a prior Isabelle formalization. Humans selected the target and Codex constructed the Lean proof.

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

The rank-one Dixmier conjecture for elements of mass at most six

On hold after review

The repository selects the author’s Theorem 1.1 and says Codex assisted proof development, but the source manuscript was pending publication and the retained AI idea is not identified.

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

Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift

Excluded

The main superdiffusive and regularity statements are from the cited Armstrong–Bou-Rabee–Kuusi preprint. Agents formalized them and repaired documented paper errors, but the disclosure says the corrections do not change the statements and identifies no separate AI-origin result.

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

Erdős 1054: sums of smallest divisors

On hold after review

No source assigns a specific central new quantitative or aliquot argument to AI rather than the maintainer or inherited work, so AI involvement is unrated.

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

Erdős 958: planar point sets with distance multiplicities {1, ..., n - 1}

Excluded

The exact negative answer to Erdős 958 and its short-arc construction are credited to Clemen, Dumitrescu and Liu (2025). AI-assisted Lean proof development formalized that prior construction.

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

Erdős 2: minimum modulus of distinct covering systems

Excluded

The negative answer to Erdős 2 was proved by Hough and later Balister et al.; this formalization follows the latter probability-sieve route. AI worked on Lean proof development and audits.

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

Fundamental Groups of Arbitrary Higher-Cell Attachments

On hold after review

The formalization strengthens a textbook fixed-dimension cell-attachment statement to arbitrary mixed dimensions. AI assisted proof construction, but the disclosure does not identify who supplied the generalization or its central argument.

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

Fundamental Groups of Arbitrary Two-Cell Attachments

Excluded

The arbitrary-family two-cell attachment theorem is expressly classical. AI assistance is assigned to construction of the Lean proof and review, not a new mathematical theorem or idea.

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

Erdős 546: sparse graph Ramsey numbers

Excluded

The sparse graph Ramsey bound is Sudakov’s published affirmative solution of Erdős 546. AI developed and checked a Lean reconstruction of that proof, not a new result or documented new proof idea.

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

Erdős 956: unit distances between disjoint convex translates

On hold after review

The selected construction extends Chojecki’s parabolic cap to a four-layer signed grid and a sharper constant. AI-assisted proof development is disclosed, but the origin of that new construction is not assigned.

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

Gallai's conjecture with two exceptional even vertices

On hold after review

Pinned README proves a Gallai path-decomposition subclass and says Codex and Claude assisted mathematical development and Lean work, but does not identify who supplied the central new graph argument.

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

Quantum Pauli basis test

On hold after review

The repository formalizes four MIP*=RE results but also describes an alternate low-degree route and source-proof gap; the AI role in that route is unresolved.

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

Stafford 3.8

On hold after review

Stafford 3.8 and strengthened bounds are research claims, while the disclosure explicitly says the model list does not assign mathematical authorship. Central AI origin remains unresolved.

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

FKS Problem 1 on at most twice the dimension vertices

Excluded

The bounded FKS claim is expressly said to follow from published results and not to be new. AI agents formalized it from supplied statements and proof plans; no central new AI mathematics is documented.

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

Monderer–Shapley Exact-Potential Characterization

Excluded

This is Monderer–Shapley’s classical exact-potential characterization. GPT-6.1 Sol aided primary-source research and Lean proof construction for that source theorem; no new mathematical claim is disclosed.

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

Falmagne–Block–Marschak Random-Utility Characterization

Excluded

Falmagne’s finite random-utility theorem and the flow/Möbius route are credited to earlier papers. The disclosure expressly claims no mathematical novelty; GPT-6.1 constructed and checked their Lean formalization.

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

Milgrom–Shannon's Monotonicity Theorem: the Full Characterization

Excluded

The selected equivalence is Milgrom–Shannon’s 1994 Theorem 4. The disclosure characterizes this as its full Lean formalization and identifies no AI-origin mathematical advance.

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

Continuity of solutions to abstract linear control systems

On hold after review

GPT-6 Pro developed proofs from the author’s notes, but the source does not establish whether a decisive proof idea originated with AI or the notes.

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.