← 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 12 of 39

Record Rank for an Elliptic Curve over $\mathbb{Q}$

On hold after review

The specialist primary curve records credit Alpöge and Howell; the model’s precise retained construction or search idea is supplied only broadly by secondary reporting.

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

Upper bound $\Lambda \le 0.1787854$ on the de Bruijn-Newman constant

On hold after review

The repository calls this a human-AI collaboration with replayable interval certificates, but its public summary does not isolate an AI-origin mathematical construction or parameter choice.

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

The $C^\infty$ Carathéodory Conjecture on Umbilic Points

On hold after review

The accessible original formalization PR says Codex helped develop a Lean proof, while the original announcement of the smooth Carathéodory construction was inaccessible; the origin of the mathematical construction is unverified.

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

The DeLaViña–Waller conjecture on the Wiener index

On hold after review

The claimed full Wiener-index result is distinct from earlier partial-class work, but the linked Zenodo manuscript was not retrievable for its theorem and AI disclosure.

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

Separation Between the Ordinary and Strong Kreiss Constants

On hold after review

No documented central model-origin contribution to the Kreiss theorem is isolated from the shared, human-adapted basis and constant optimization.

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

Fourth-moment conjectures for Rademacher sums

On hold after review

The paper reports substantial model assistance but does not identify a retained central model-origin step in either final theorem.

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

Kusner's Conjecture on Equilateral Sets in $\ell_p^n$

Excluded

The 58-point certificate paper credits GPT-5.6 Sol with implementing the author’s computational search strategy and drafting, without crediting it with the strategy or the retained mathematical construction. This entry concerns that narrower p=5 certificate, not the later AI-found construction for every p>4.

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

Pavez-Signe's Length-Control Question for Spanning Subdivisions

On hold after review

The paper credits ChatGPT with assistance developing Lemma 3.1, but does not say which part of the probabilistic partition argument the model originated.

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

The Quartic Hessian Conjecture in Dimension Four

On hold after review

The author reports several models used for candidate arguments, algebraic checks and adversarial review, but does not identify a particular central AI-origin step in the quartic dimension-four theorem.

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

Every PPT channel has finite entanglement-breaking index

On hold after review

The author reports model discussions but does not identify a retained central model-origin step in the finite-index proof.

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

The Radchenko–Viazovska question on Fourier interpolation

On hold after review

Bondarenko and Seip credit ChatGPT with essential exploratory input and calculations for their Fourier-invariant zero-set construction, but do not attribute the kernel-space construction or a named theorem step to it.

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

Courtade's conjecture on volumes of Minkowski sums with the ball

Excluded

The disclosure calls GPT-5.6 Sol an auxiliary tool for examples, determinant tests, and preliminary development, and expressly attributes the final arguments, statements, and computations to the human authors.

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

Strong Graph Reconstruction Conjecture

On hold after review

The original paper gives a graph construction and computational checks but contains no account assigning the construction to AI.

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

Phelps–Rodriguez Conjecture

On hold after review

Tao’s digestion obtains the strict interior statement and hence Phelps–Rodriguez, with heavy AI assistance, but the source does not isolate who supplied the strengthening.

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

Treglown's equitable acyclic colouring conjecture

Excluded

The proposed reduction was identified as prior art, and the source does not identify a novel retained model-origin step in the final result.

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

Hadamard Matrix of Order 668

On hold after review

The order-668 announcement credits Claude as a collaborator without assigning it a mathematical or search step; the linked Legendre-pair paper only reports AI for code, literature and editing.

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

The Hyperkahler Period-Index Conjecture

On hold after review

The disclosure describes two independently obtained LLM-assisted counterexample constructions synthesized by the authors, but does not identify which decisive construction step the models supplied.

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

Teschner's Bondage-Number Conjecture

On hold after review

The shared ChatGPT conversation is not readable as a proof transcript in the available source view; central AI origin and the conjecture’s exact resolved scope remain unverified.

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

The Imbalance Conjecture

On hold after review

The proof was developed with model assistance, but the authors do not identify a retained central idea supplied by either model.

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

The Planar Berenstein Conjecture

On hold after review

The authors supplied the central construction and working code before ChatGPT, which suggested ideas for endpoint lemmas and revised code. The retained central AI contribution to the final counterexample needs attribution review.

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

Polynomial-Time MIMO Detection at the ML Threshold

On hold after review

The linked original MIMO manuscript is a PDF whose content was not readable here; the author’s AI-origin and proof account therefore remain unverified.

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

Log-Submodularity of Zonoid Volume

On hold after review

The acknowledgment limits GPT-5.6 Pro to literature search and exploratory volume computations; it is unclear whether a retained counterexample emerged from those computations.

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

A counterexample to the Howland-Kato problem for positive commutators

On hold after review

The paper only acknowledges AI tools and says humans wrote and checked the final proof. A later author statement reportedly credits Grok with a different valid counterexample, but that original X statement was inaccessible.

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

The Chen-Lawrencenko Conjectures on Cyclic Colorations

On hold after review

The paper reports extensive GPT-5.6 Pro interaction and revised suggestions, but the disclosure does not say which essential construction or proof idea the model supplied for either conjecture.

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

The Generalized Busemann-Petty Problem in Dimensions 2 and 3

On hold after review

The disclosure says ChatGPT helped find the existing Andréief identity and that this led the authors to prove Theorem 3.2. Because the identity may be the decisive bridge to the new result, the contribution is not safely excludable without tracing the proof idea.

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

Tuza's Conjecture for Maximum Degree at Most Seven

On hold after review

Gupta discloses extensive AI proof exploration, code and exact checking, but says he selected the arguments and methods. No specific retained central AI idea is identified.

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

The Inverse Generator Problem on Hilbert Spaces

On hold after review

The source documents AI assistance with a prior-work adaptation and constants, but no central AI-origin step in the Hilbert-space counterexample.

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

Central limit theorem for the random assignment problem

On hold after review

The researcher reports model proof assistance but does not identify a retained central model-origin lemma beyond his prior geometric approach.

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

The Huang-Jiang-Oblomkov Conjecture at a = 3

Excluded

The original paper identifies AxiomProver’s role as generating a Lean certificate for already stated identities; it does not credit the system with the mathematical discovery or proof idea.

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

The Gardner Transition in the Ising pure $p$-spin glass

On hold after review

The two arXiv abstracts describe first and second Gardner transitions, but the available original records do not document AI-origin mathematics or the registry’s claimed withdrawal/dispute scope.

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

Gabor Frames of Totally Positive Functions

On hold after review

The disclosure credits GPT with finding a limit-operator literature connection and simplifying a lemma, while the authors adapted and wrote the arguments; whether a retained central idea came from GPT is unresolved.

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

The Approximation Ratio for Boolean Max-k-CSP

Excluded

The author explicitly says all conceptual contributions, including the Gaussian comparison strategy and orthant-amplification statement, were human; GPT 5.6 Sol Max assisted only with lengthy computations in Theorem 4.1.

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

The Generalized Vanishing Conjecture

On hold after review

The first paper credits GPT with testing a human counterexample and verification code; the later dimension-three result describes Codex monitoring experiments under human steering. Neither accessible account isolates an AI-origin central construction.

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

Schiffer's Conjecture and the Pompeiu Problem

On hold after review

The paper credits models with numerical checks, drafts of Bessel-estimate proofs, exposition, and Lean verification; it does not establish who supplied the central counterexample construction.

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

The Period-Index Conjecture

On hold after review

ChatGPT suggested a flawed quotient example after the author supplied the Hodge strategy; the author then found the working K3-based construction. The retained AI contribution to the final counterexample is unclear.

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

The Bandelt-Dress Quartet Distance Conjecture

On hold after review

The quartet-distance paper presents its theorem, but the accessible original text does not identify AI-origin mathematical work.

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

Real-Rootedness of Ehrhart h*-Polynomials at Large Width

On hold after review

The large-width Ehrhart manuscript gives the new theorem, but the accessible source has not identified a central mathematical idea originated by AI.

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

Graffiti's Residue Problem for Common-Divisor Graphs

On hold after review

The paper says TheoX generated candidates and OpenAI services aided research, but the author independently reconstructed the proofs; it does not identify a retained model-originated part of the degree-preserving construction.

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.