← 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 28 of 39

Weighted support criteria for reciprocal Mersenne subseries

On hold after review

The selected weighted-support criterion is original to Cook’s papers, but the entry credits AI with formalization and exposition while the repository describes AI-assisted mathematical research; the origin of the criterion is unclear.

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

Shapley value axiomatic characterization

Excluded

The source explicitly calls its Shapley axiomatization a reusable formalization of the 1953 characterization; AI assistance is identified as proof engineering.

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

Dimension-independent Hlawka constants for Schatten norms

On hold after review

The source does not identify a central existence or diagonal lemma originated by AI rather than supplied in human proof material.

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

Classical Seifert–van Kampen theorem for the fundamental groupoid

Excluded

The selected Seifert–van Kampen pushout is the classical groupoid theorem, adapting an existing directed Lean formalization. The agent supplied Lean proof engineering under human scope direction, not a new mathematical theorem.

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

Erdős 1007, dimension five: fifteen edges, attained by K6 and K1,3,3

Excluded

The exact dimension-five graph results are Chaffee and Noble’s 2016 Theorems 8 and 10. The detailed AI campaign reproduced upstream statements and proved them in Lean; it did not originate the mathematical results.

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

The Favard-length decay exponent of the four-corner Cantor set is at least 1/4

On hold after review

Favard quarter exponent: pinned source says an unpublished manuscript was produced in a human-directed ChatGPT project and Claude formalized it, but does not allocate the new joint negative-moment idea between human and AI; hold for primary AI-role evidence.

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

Verified finite automata for finitely generated subgroups of F₂

Excluded

The finite automata theorem and folding construction are attributed to Stallings. Codex developed the Lean proof with human-directed scope; no distinct AI-origin mathematical contribution is documented.

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

Unit-distance graphs of dimension four with nine edges

On hold after review

The main extremal graph theorem follows Chaffee–Noble, but Claude constructed hypothesis-drop counterexamples and filled two proof steps omitted from the paper. Their independent mathematical value and centrality are unclear.

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

Positive density of Collatz convergence at every rate above 3/log(4/3)

Excluded

The formalized Collatz density statements come from Shaik’s prior manuscript. The disclosure says the author supplied the mathematical research and plan while agents assembled, extracted and checked Lean proofs.

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

Zero density theorems for short intervals

Excluded

The zero-density results come from Fiori’s source preprint. AI wrote and checked the Lean formalization and numerical certificate scripts under his work list; the mathematical direction and preprint are his.

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

CaffarelliKohnNirenberg

On hold after review

The three Caffarelli–Kohn–Nirenberg conclusions are older results, but the manuscript was corrected during agent-assisted proof development. The authors say they decided the mathematics and corrections; the exact AI role in the direct-iteration route remains unclear.

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

SCOPE and REACH with almost-surely finite stopping times

Excluded

SCOPE, REACH and their Rao–Blackwell variance argument come from the cited paper. Astra formalized the paper’s estimator statements under a maintainer-specified objective and did not claim to originate them.

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

A transexponential o-minimal structure

On hold after review

The private manuscript and available disclosure do not identify whether the central construction came from AI or the human author.

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

Lower bounds for sets without perfect-power differences

On hold after review

The source describes a cooperative improvement without identifying which central support, width or allocation idea originated with AI.

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

Regular configurations, Palm deficits and the cumulant obstruction

On hold after review

The manuscript reports substantial AI assistance with lemma exploration as well as Lean development, while Pouly directed the research. The disclosure does not identify whether an AI proposed a central new lemma or merely helped develop human ideas.

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

Microscopic signed fields and empirical Poisson laws

On hold after review

The source does not identify which central mathematical step, if any, came from AI.

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

An atomic decomposition of one-dimensional metric currents without boundary

Excluded

The five main results come from the cited 2025 paper, with a paper author auditing the statements. Claude workers wrote Lean proofs and review artifacts; no new AI mathematical result is disclosed.

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

One-Sided Affine Obstructions in Complete Bipartite Hat Guessing

Excluded

The disclosure expressly calls the no-go theorem human-authored mathematical work. Codex assisted the Lean proof and mechanical audit only.

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

Microscopic boundary, prefixes and longest runs

On hold after review

The source does not identify which central mathematical step, if any, came from AI.

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

The order-six stable-marriage finite-poset bound

On hold after review

The finite-poset bound is a theorem from Jo’s stable-marriage paper. The disclosure reports AI proof exploration and auxiliary lemmas, but says the human author selected the final route; the origin of any central new proof step remains unresolved.

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

Fischer's 24-vertex zero-forcing counterexample

Excluded

Fischer’s 24-vertex graph and its invariants are the source result. AI assistance formalized and audited that known counterexample without claiming a new mathematical construction.

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

Erdős 973: power sums cannot all be exponentially small

Excluded

The exact exterior power-sum lower bound was proved earlier by Luo–Yang–Zhu. This Lean proof follows Tan–Wang–Huang–Chen's residual-polynomial route; generic AI proof-development credit identifies no new AI power-sum idea.

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

A formal proof of the Kung–Traub conjecture

On hold after review

Colbrook’s paper presents a claimed proof of the Kung–Traub conjecture and counterexamples; the disclosure says ChatGPT assisted discussion and checking, without identifying a central AI-originated argument.

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

Improved SparseStack Constants

On hold after review

The cited SparseStack source was not retrievable. The title alone does not establish whether AI found improved constants or only formalized them.

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

Typical dictionaries, exact marks and compound Poisson clusters

On hold after review

The paper reports substantial AI lemma exploration, drafting and Lean work, but the disclosure does not identify which central Poisson-field or exact-mark result AI supplied. The two registry entries need separate claim-level attribution.

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

Critical Poisson fields and information-adapted conditioning

On hold after review

The paper reports substantial AI lemma exploration, drafting and Lean work, but the disclosure does not identify which central Poisson-field or exact-mark result AI supplied. The two registry entries need separate claim-level attribution.

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

Erdős 689: eventual double covering by prime residue classes

On hold after review

The selected double-covering theorem follows Chojecki’s Theorem 1.1, but the Lean project replaces a cited Green–Tao step with a direct Fourier proof and reports AI-assisted local research. The originality and AI origin of that replacement need checking.

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

Finite tight Blackwell approachability-to-improper phi-regret reduction in Lean

Excluded

The selected improper phi-regret families and reduction barriers come from Dann, Mansour, Mohri, Schneider and Sivan (2025). GPT-5 Codex is disclosed for proof engineering rather than originating the paper’s central mathematics.

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

definable-saturated

On hold after review

The source does not separate the AI contribution to the central consistency construction from supporting lemmas and formalization.

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

Irrationality of the 7-adic zeta value ζ₇(3)

On hold after review

The claimed ζ₇(3) irrationality proof is new, and AI was used for mathematical derivations and exploration. Yi Taifeng supplied the proof architecture and repeatedly redirected the work, so the central AI-origin step remains unidentified.

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

BKARForestFormula

Excluded

The selected BKAR forest formula is a formalization of the Brydges–Kennedy source, under stronger smoothness assumptions. AI wrote Lean code, but the source does not claim a new formula or construction.

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

NKBesicovitch

On hold after review

The supplied human manuscript and notes are not public in the cited snapshot, preventing a line-by-line origin comparison for the central continuous projection estimate.

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

Sharp symmetry bounds for real plane algebraic curves (Theorem 1)

Excluded

Perassi wrote the working note and its theorem before formalization. Agents wrote and repaired Lean code under his direction; the source does not assign the sharp bounds or equality classification to AI.

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

Birnbaum’s principles in Venn diagrams: Extended version with Lean verification

Excluded

The authors' article supplies the statistical reformulation and finite-setting results. Its disclosure limits GPT-6 Astra to Lean proofs and manuscript-to-formalization cross-checking, so no central mathematical discovery is attributed to AI.

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

Yu-Wang-Samworth 2015: population-gap eigenspace and singular-subspace perturbation bounds

Excluded

The selected perturbation bounds derive from Yu–Wang–Samworth’s 2015 paper. Agents formalized and audited source defects; the human maintainer adjudicated the corrections. The record does not attribute a new central mathematical result to AI.

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

Komlós conjecture

Excluded

The Komlós and Beck–Fiala bounds follow Karingula–Lovett’s earlier proof. Claude implemented it in Lean and GPT revised the code under human-directed statement and proof style.

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

Endpoint estimates for Stein's purely quadratic Carleson operator

Excluded

The four selected quadratic-Carleson endpoint claims are identified as Theorems 1 and 2 of Fragkos–Krause–Lacey's original paper. The metadata assigns mathematical scope and statement selection to humans and Codex to Lean development and repository preparation.

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

Superdiffusion

Excluded

The superdiffusion theorems are the Armstrong–Bou-Rabee–Kuusi paper’s results. Models wrote the Lean code under author supervision, but the source does not assign them the original mathematical results.

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

Sectorial asymptotics for centered Riemann-xi coefficients

On hold after review

The centered-xi asymptotic is a new analytic input developed with substantial AI help, but the disclosure does not identify the origin of its saddle-point argument or derivative estimates.

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

A formalization of Chang, Liu, and Liu's proof of Chvátal's conjecture

Excluded

GPT-6 prepared a formalization of Chang, Liu and Liu’s human proof of Chvátal’s conjecture. The source identifies no retained new AI mathematical contribution beyond formalizing their result.

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

Chain Bounding

Excluded

The core chain-bounding results were published in the 2024 paper and first formalized without AI. GLM-assisted work was a later toolchain port and one formalization step, not a new mathematical contribution.

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

Termination of the classical inflation hierarchy on pair-source networks

On hold after review

The manuscript preceded the Lean work and AI agents formalized its statements, but the disclosure does not establish who originated the unpublished classification and obstruction theorems.

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.