← 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 30 of 39

A proof of the Regts–Sevenster conjecture, formalized

On hold after review

Whistler's conjecture proof was developed with Claude and GPT models, and agents later formalized it. The repository does not isolate which central argument in the original paper was supplied by AI.

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

Spherical maximal functions: theorems of Stein and Bourgain

Excluded

The source expressly formalizes Stein’s and Bourgain’s maximal theorems using a classical proof route. Agents generated most Lean proof code under human supervision, while the mathematical theorems and route predate the project.

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

The sharp finite-field Nikodym exponent

On hold after review

The linked Nikodym repository redirects and its cited formalization disclosure was not retrievable. The title alone cannot establish the origin or exact scope of the sharp exponent.

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

Convex geometry and the Erdős–Ginzburg–Ziv problem: Theorem 1.2

Excluded

The entry formalizes Theorem 1.2 of Zakharov’s previously published human paper. ChatGPT assisted formalization and a revised PDF with a typo correction; no new central AI mathematical claim is identified.

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

The global Kronecker–Weber theorem in Lean 4

On hold after review

The cited Kronecker–Weber repository revision returned 404, so its exact statement and AI disclosure could not be inspected. The registry title alone cannot establish eligibility or exclusion.

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

Li's criterion for the Riemann Hypothesis

Excluded

Both Li’s criterion and its zero-sum coefficient form are attributed to Li and Bombieri–Lagarias. Claude wrote the Lean machinery under the maintainer’s direction; the disclosure identifies formalization of known results, not a new AI mathematical claim.

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

Brill--Noether generality and gonality for chains of cycles and theta graphs

Excluded

The selected Brill–Noether and gonality results are explicitly attributed to earlier named papers. Generative AI primarily created the Lean formalizations, not the mathematical results being formalized.

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

Sharp arithmetic separation in chiral Padovan histories

On hold after review

The return-window results are presented as original, and GPT-family agents built proof modules under Alexander’s detailed direction. The disclosure does not identify whether agents supplied a central construction or executed the author’s mathematical plan.

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

A kernel-checked exclusion certificate for Erdős Problem 647, to 10^8

Excluded

The bounded Erdős 647 certificate was generated by a Python program and checked in Lean; the authors say they wrote the witness format and proof. The disclosed automation is a deterministic generator and replayer, not central AI mathematical work.

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

Combinatorial core of the K₃,₃,₁-redundancy theorem for tetrahedral balls

On hold after review

The paper claims a new K₃,₃,₁-minor redundancy result for tetrahedral balls. Sol and Fable developed the Lean finite and clique-sum layers, but the disclosure does not distinguish their mathematical ideas from Rudolph’s source proof.

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

Radial harmonic functions on a real inner product space: the classification, the Laplacian of radial functions, and the stability of circular orbits for power-law central forces; Ehrenfest's dimensionality argument (1917) as the application

Excluded

The radial-harmonic classification and circular-orbit stability analysis are drawn from Ehrenfest and classical potential theory. AI composed Lean proofs under an author-supplied route and statements.

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

lennrt/palomar-formalizations

On hold after review

The cited repository contains nine different preprints. Its disclosure credits Sol and Fable with formalization and adversarial analysis, but the queue does not identify which preprint each of these four entries represents or a central AI-origin idea.

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

lennrt/palomar-formalizations

On hold after review

The cited repository contains nine different preprints. Its disclosure credits Sol and Fable with formalization and adversarial analysis, but the queue does not identify which preprint each of these four entries represents or a central AI-origin idea.

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

lennrt/palomar-formalizations

On hold after review

The cited repository contains nine different preprints. Its disclosure credits Sol and Fable with formalization and adversarial analysis, but the queue does not identify which preprint each of these four entries represents or a central AI-origin idea.

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

lennrt/palomar-formalizations

On hold after review

The cited repository contains nine different preprints. Its disclosure credits Sol and Fable with formalization and adversarial analysis, but the queue does not identify which preprint each of these four entries represents or a central AI-origin idea.

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

lennrt/palomar-formalizations

On hold after review

This entry points to a repository with nine distinct preprints. The root disclosure credits Sol and Fable with formalization and adversarial analysis but does not identify a central AI-origin contribution for this entry.

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

Tverberg's Partition Theorem, 1D Theorem, and Colorful 1D Theorem

Excluded

Tverberg’s and colorful Tverberg’s theorems are sourced to prior authors. Gemini agents formalized their proofs in Lean under maintainer direction, with no AI-origin theorem identified.

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

Ore's and Dirac's Theorems on Hamiltonian Cycles

Excluded

The Hamiltonian-cycle criterion is Ore's theorem; Dirac's condition is its cited corollary. Agents formalized and golfed these classical proofs under maintainer direction.

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

Levi–Civita connections and metric-determined curvature invariants in Lean

On hold after review

The fixed repository README is a Poincaré formalization roadmap and mentions a curvature subproject, but it does not disclose AI’s role in the selected Levi–Civita and curvature claims.

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

The trace form of a tensor product of algebras and the signature product rule, with the trace forms of Q[x]/(x^3 - x - 1), Q[x]/(x^4 - x - 1) and their compositum as instances

Excluded

The trace-tensor and signature-product statements are presented as general classical results with concrete instances. Claude agents drafted Lean proofs, but the disclosure does not attribute a new mathematical result or idea to them.

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

Chip-Firing with Lean 4

Excluded

Baker–Norine supply the graph Riemann–Roch and Clifford results. Development began manually; later agents refactored, debugged and edited the Lean formalization.

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

heilbronn-convex-3-8

On hold after review

The cited Heilbronn repository could not be read: the root formalization file returned 404 and the cited tree was unavailable. No original AI/proof disclosure was available to assess.

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

Mean Value for Random Ideal Lattices: Lean formalization

On hold after review

ChatGPT and Codex formalized Gargava–Viazovska’s earlier theorem; the README also reports trace, boundary, and Gamma corrections whose mathematical scope and AI origin are unclear.

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

An explicit periodic signing of C_n(1,2) below the conjectured minimum

On hold after review

The formalization credits agents with proof development and checking of Rudolph's periodic signing, but does not establish who discovered the period-8 signing or the decisive certificate.

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

Erdős Problem 625: chromatic versus cochromatic number of a random graph

On hold after review

The full-sequence Erdős 625 bound is presented as original and AI assisted its interactive proof, but the human author selected the theorem and the disclosure does not assign the central argument to AI.

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

Nash's isometric embedding theorem for closed manifolds (Günther's proof)

Excluded

The target and proof route are Nash's and Günther's established theorem, following Wassermann's notes. The disclosure credits Claude and Aristotle with designing the Lean architecture and supplying formal proof bodies, not with an independent mathematical result or proof idea.

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

Salem's theorem: every Pisot number is a two-sided limit of Salem numbers

Excluded

The compared two-sided limit theorem and both named constructions are Salem's 1963 theorem and cases. The cited disclosure says the author fixed those targets and chose the argument route, while Claude drafted and repaired the Lean proofs.

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

Actual F₂ flag homology and the dense extremal counterexample family

On hold after review

The formalization records AI-assisted F₂ chain proofs for Rudolph's dense flag-homology counterexample family. It does not say whether AI originated the paper's family or extremal argument.

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

Grushko--Neumann rank additivity for free products

Excluded

The selected Grushko–Neumann rank theorem is classical. AI materially generated Lean declarations and proof scripts; the human authors selected and reviewed the mathematical result and source relation.

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

The golden family's boundary at n = 3: general-n theorems for x^n = x + 1

Excluded

The compared general-n statements draw on classical results, including the published morphic classification and Selmer/Siegel inputs. The disclosure credits Claude with proof drafting and Lean error-loop work under the author’s statement design, not a retained new mathematical idea.

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

Arrow's theorem via Fourier analysis

Excluded

The source says this formalization was entirely human-written and follows the established Fourier proof of Arrow’s theorem. Its disclosure identifies no AI mathematical role.

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

Proof-Carrying Decreasing-Diagram Confluence Certificates

On hold after review

The decreasing-diagrams criterion belongs to van Oostrom, while this project claims a new finite certificate language, checker boundary and completeness bridge. Codex developed the generic soundness proof, but the disclosure does not separate human design from any retained AI mathematical construction.

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

Howson's theorem through finite cores and Kurosh decomposition

Excluded

Howson’s finite-rank free-group theorem is the historical source. Codex developed the Lean proof against that target; no distinct AI-origin mathematical result is documented.

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

Marshall Hall's theorem through finite cores

Excluded

Marshall Hall’s and Grushko–Neumann’s results are credited to their original human authors. GPT-5 Codex is credited with Lean proof development against cited APIs, with no new mathematical result assigned to it.

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

Native Lean equality-saturation certificate checking

On hold after review

The native e-graph checker may be a new algorithmic contribution, but disclosure identifies GPT-5 Codex only with proof engineering; origin of the design is unresolved.

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

lean-spectral-theory

Excluded

The spectral and Stone theorems follow standard published routes. Claude and Codex built the Lean library and an equivalent publication boundary, but the record does not claim an AI-origin new mathematical theorem or proof idea.

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

JaTaSn/lattice-line-covers

On hold after review

The cited repository does not expose a root formalization.yaml, so its original claim and AI/proof disclosure could not be checked.

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

lean-operator-theory

On hold after review

The target operator inequalities are established, but the disclosure says the final proof used a different smooth-support outer-approximation route after a proposed lemma failed. The source does not establish who devised that route or whether it is a central new proof idea.

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

The Friendship Windmill Structure Theorem (Erdős–Rényi–Sós 1966)

Excluded

The friendship windmill theorem is Erdős–Rényi–Sós’s 1966 result. The agentic workflow formalized it under maintainer direction, with no new AI-origin mathematical claim.

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

lean-malliavin

Excluded

The selected Malliavin and Clark–Ocone statements are established source mathematics; the disclosure credits AI agents with building the Lean proof library, not originating those results.

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

sneed-and-feed/lean-theorems-1

Excluded

Dilworth’s and Mirsky’s decomposition theorems are historical source results. The agentic workflow formalized and polished Lean proofs under maintainer direction; no original AI mathematics is disclosed.

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.