← 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 13 of 39

Written on the Wall II, Graph Conjecture 144

On hold after review

The merged proof PR credits ChatGPT and Codex with exploration, analysis, Lean API work, and proof engineering but does not identify a central model-origin mathematical idea.

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

Autonomous Lipschitz Fast Dynamo on the Three-Torus

On hold after review

The revision credits GPT models with assistance and simplifications, but does not identify a model-originated central construction for this autonomous Lipschitz torus result; a related AI-discovered random dynamo is a separate paper.

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

Hoa's Conjecture on Maximal Non-Hamiltonian Graphs

On hold after review

The author says ChatGPT assisted development and checking of constructions, but does not identify whether it originated the retained counterexamples.

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

Written on the Wall II, Graph Conjecture 322

Excluded

The credited Aristotle argument addresses a misformalized statement; the corrected proof has separate provenance and needs its own assessment.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-19T00:00:00.000Z

Two-Variable Factorial Conjecture

On hold after review

The current manuscript credits ChatGPT with exploration, drafting, symbolic checking and review, and says OpenAI work suggested proof directions; it does not identify a retained central AI-origin idea for the two-variable theorem.

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

Finitude of the Fibers of Complementary Bell Numbers

On hold after review

The author reports extensive GPT-5.6 Pro interaction during exploration and proof development, with suggestions revised and checked, but does not identify which central 2-adic idea came from the model.

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

Minimum reverse-complement-invariant decycling sets

On hold after review

The versioned repository and linked claim-boundary page could not be read, so attribution for the minimum-set construction remains unresolved.

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

Prime values of digital functions along the primes

On hold after review

The available account credits models with manuscript writing and Lean formalization but does not identify a model-originated idea for the generalized prime-value theorem.

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

Sharp Hardness for MAX-3-CUT

On hold after review

The original arXiv paper gives conditional sharp hardness results but its readable text provides no AI-use disclosure or attribution for the mathematical idea; metadata alone does not establish central AI work.

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

Pólya's Conjecture for Neumann Balls in Dimensions Three and Higher

On hold after review

The authors credit AI with developing several Appendix C technical lemmas and the rigorous algorithm, but do not identify whether those lemmas supply a central new idea for the Neumann-ball proof.

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

Han's Conjecture

On hold after review

The original counterexample paper is accessible, but the source record has not established a specific central AI-generated step.

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

Signature of Connected Line Graphs

On hold after review

The paper says the counterexamples arose from AI-assisted searches, while its acknowledgments credit the concrete examples and proofs to the two human authors; retained model-origin work is not isolated.

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

The Tu-Deng Conjecture

On hold after review

The repository advertises GPT-aided Lean formalization of a separate Tu–Deng proof, but the accessible source does not identify a new AI-origin mathematical idea beyond that proof.

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

Written on the Wall II, Graph Conjecture 217

On hold after review

The original PR links a Lean proof and discloses ChatGPT/Codex use during proof development, but does not assign the central mathematical argument to AI. A later PR also describes bounded mechanical subtasks.

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

Graffiti Conjecture 6

On hold after review

The linked original PDF could not be read through the available source; the registry attributes a counterexample family to GPT-5.6 Thinking, which needs primary confirmation.

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

Sombor-Energy Conjecture

On hold after review

The only listed original proof is a GitHub PDF that could not be read, and its repository has no readable AI or proof disclosure.

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

Huneke-Wiegand Conjecture

On hold after review

The registry claims GPT found a counterexample, but the original repository labels it an unreviewed candidate and its accessible README does not attribute the construction to AI.

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

Lami-Regula Conjecture on Entanglement Irreversibility

Excluded

The paper credits ChatGPT only with some technical proof details and says the authors checked them; it does not credit AI with the non-Gaussian counterexample families or the central result.

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

Erdős Problem #106

On hold after review

The Erdős page was inaccessible (403); the linked counterexample repository has not yet established a readable original AI-origin disclosure.

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

Written on the Wall II, Conjecture 284

Excluded

The paper credits ChatGPT with adversarial checking, proof exploration, and Lean formalization, while the human author takes responsibility for the counterexamples. No central AI-origin construction is documented.

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

Improved Bounds for Distinct Multiples in Intervals

On hold after review

The newer paper describes ChatGPT only as an exploratory and proof-auditing tool; an earlier related paper credits GPT with suggesting a change of scale, but the retained contribution here is not isolated.

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

The Modified Lyons–Sidorova Conjecture for Bounded-Variation Paths

On hold after review

The linked bounded-variation signature manuscript gives the mathematical classification but no AI-use or provenance statement was found. A central model contribution cannot be attributed from this original alone.

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

The 4^k Barrier for the k-Distinct Language

On hold after review

The disclosure lists proof verification, simplification and parameter optimization by models, but does not locate a retained model-origin idea behind the 4^k improvement.

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

Existence of Bipartite Bound Information

On hold after review

The authors call ChatGPT’s discovery of an earlier zero-key proposition decisive, but they directed the question and do not clearly credit it with the retained source construction or new proof strategy.

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

Probabilistic Automatic Complexity Is At Most Three

On hold after review

The acknowledgment documents model collaboration but not a retained central model-origin idea; the released Lean statement also has an extra final-digit hypothesis.

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

The Hall-Ho Heat Flow Conjecture for Random Matrices

On hold after review

The author reports AI ideation and technical help at coauthor level, plus proof checking and editing, but does not assign a specific retained central argument to a model.

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

Infinitely Many Components in Auslander–Reiten Quivers over Perfect Fields

On hold after review

The authors credit themselves with the main theorem and proof strategy, but say ChatGPT helped extend the result to perfect fields through specific lemmas and a proposition. The disclosure leaves unclear whether retained AI work is central to this title claim.

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

Chafai-Dadoun-Youssef Questions on Logarithmic Energy Monotonicity

On hold after review

The author describes AI ideation and technical help at a co-author level but does not identify which retained counterexample or central argument was supplied by AI.

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

Kinetic Trace Estimates in the Gaussian Model

On hold after review

The source does not establish whether the final bounded-domain Gaussian counterexample retains a central AI-origin construction.

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

Kuperberg's Six-Cylinder Conjecture

On hold after review

The published certificate was reconstructed and checked by the authors, but the source does not identify a retained central Claude-origin idea.

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

The Covering Number $C(12,6,4)$

On hold after review

The author reports LLM help with exploratory analysis, computational search and code, but the disclosure does not identify who devised the decisive rigidity reduction and SAT encoding.

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

Zero Forcing versus Independence in Subcubic Graphs

On hold after review

The original counterexample manuscript is accessible, but a specific AI-originated construction has not been established from its author account.

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

Brezis's Open Problem 5.6 on Universal Fourier Summation

On hold after review

The paper credits AI with preliminary drafts, while the author checked, revised, and fixed the final Fourier-summation argument. It does not establish that the central construction came from AI.

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

Carrasco's Conjecture on the O'Shea-Zames-Falb Test

On hold after review

The original stability-test manuscript does not yet establish a model-originated counterexample or proof step in the available provenance.

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

Erdős Problem #768

On hold after review

The author credits models with technical lemmas but does not identify a retained central model-origin construction or theorem.

Screening recorded: 2026-10-17 · Decision reviewed: 2026-10-19T00:00:00.000Z

Erdős Problem #684

On hold after review

The registry records retraction after a deterministic counterexample to key Lemma 18; the original AI role and any surviving result need a separate scope review.

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

The Graveyard Problem for Dissipative Barrier Truncations

Excluded

The authors expressly say AI was an initial search aid whose outputs were incorrect, and that AI produced no mathematical arguments or paper content beyond minor language editing.

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

A Five-Variable Counterexample to the Hessian Conjecture

Excluded

The authors explicitly credit the second human author with finding the Schur descent that creates the five-variable counterexample; LLMs served as auxiliary search and exact-arithmetic scripting tools.

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

Strichartz-Tse $L^p$-Integrability on the Sierpinski Gasket

On hold after review

Tsougkas reports GPT-5.6 exploration and support for technical development of the Sierpiński-gasket integrability bounds, without isolating the model’s role in the general or special-direction theorem.

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

Reiner's Conjecture on Higher Bruhat Orders in Corank 3

On hold after review

The note lists ChatGPT as search engine and proof assistant and says humans digested its outputs, but does not credit a central homotopy argument to the model.

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

The Target-Free Clique Conjecture for Threshold-Linear Networks

On hold after review

The acknowledgments say Codex and Claude Code helped with proof exploration and criticism, but do not identify a model-origin six-neuron counterexample or central proof step.

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

Petersen Coloring Conjecture

On hold after review

The fixed graph and certificates are documented, but the source does not identify a central AI-origin graph construction.

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

Araujo-Piga-Schacht Question on Tight Hamilton Cycles

On hold after review

The original tight-Hamilton-cycle paper states a quasirandom 3-graph theorem but the readable manuscript contains no AI disclosure for its proof; the batch metadata supplies no central-origin evidence.

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

Uniqueness of the Faber–Krahn Position of Convex Bodies

On hold after review

The disclosure credits ChatGPT on related arguments but does not identify a retained central AI-origin step in the uniqueness theorem.

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.