← 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 22 of 39

Tamper-proofing with self-modifying code: threat model, security and necessity of the assumptions

Awaiting detailed review

Pinned project and exact formal contract reviewed. AI assistance in proofs, certificates or packaging is documented, but a contribution-specific central mathematical idea and its human-origin baseline are not yet reconciled. Existing human results and source hypotheses remain separate; no automatic registry promotion.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Bergman projection weak type constants

Awaiting detailed review

The pinned disclosure documents agents formalizing specified existing manuscript results. Establish the particular original mathematical argument supplied by AI, separately from implementation, fidelity changes and manuscript authorship, before inclusion.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Normalizers of Γ_Δ(N): the group M_Δ, finiteness, and a coset count

Excluded

Reviewed scope formalizes named existing human theorems or author-supplied normalizer results. Pinned manifest/statement and project account do not establish a specific new central-AI mathematical contribution; formalization effort and new registry version alone do not qualify. Preserve the original results and dates as background.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Normalizers of Γ_Δ(N), Γ(N) and ±Γ₁(N)

Excluded

Reviewed scope formalizes named existing human theorems or author-supplied normalizer results. Pinned manifest/statement and project account do not establish a specific new central-AI mathematical contribution; formalization effort and new registry version alone do not qualify. Preserve the original results and dates as background.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Brooks' theorem, degree-choosability and blocks

Excluded

Reviewed scope formalizes named existing human theorems or author-supplied normalizer results. Pinned manifest/statement and project account do not establish a specific new central-AI mathematical contribution; formalization effort and new registry version alone do not qualify. Preserve the original results and dates as background.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

A certificate for the triangle variational problem

Awaiting detailed review

Aristotle produced an entropy-only formal proof with author feedback; later Codex work ports/checks the package. Determine whether the retained proof supplies an original central AI argument rather than formalizing the human source; keep the entropy-only statement separate from the full variational problem.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Menger's theorem, Hamiltonian cycles, long cycles and pancyclicity

Excluded

Reviewed scope formalizes named existing human theorems or author-supplied normalizer results. Pinned manifest/statement and project account do not establish a specific new central-AI mathematical contribution; formalization effort and new registry version alone do not qualify. Preserve the original results and dates as background.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Sharp continued-fraction bounds from exact digit runs

Awaiting detailed review

AI-origin maximum inverse estimate and optimal digit-window extensions are explicitly disclosed. Exact contract read; a distinct publishable scope still needs comparison with the ordinary-convergent prior bounds and fixed-word versus variable-index sharpness conventions. Agent reviews and finite exact replays are not outside human assessments.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Barker sequences of odd length have length 1, 3, 5, 7, 11 or 13

Excluded

Reviewed scope formalizes named existing human theorems or author-supplied normalizer results. Pinned manifest/statement and project account do not establish a specific new central-AI mathematical contribution; formalization effort and new registry version alone do not qualify. Preserve the original results and dates as background.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Guarded detection and constrained eligible-set extensions

Awaiting detailed review

Pinned project and exact formal contract reviewed. AI assistance in proofs, certificates or packaging is documented, but a contribution-specific central mathematical idea and its human-origin baseline are not yet reconciled. Existing human results and source hypotheses remain separate; no automatic registry promotion.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

The Alon–Tarsi theorem and 3-choosability of planar bipartite graphs

Excluded

Reviewed scope formalizes named existing human theorems or author-supplied normalizer results. Pinned manifest/statement and project account do not establish a specific new central-AI mathematical contribution; formalization effort and new registry version alone do not qualify. Preserve the original results and dates as background.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Kuhn poker: the value −1/18, all optimal strategies, and the solution at every ante and bet

Awaiting detailed review

Pinned project and exact formal contract reviewed. AI assistance in proofs, certificates or packaging is documented, but a contribution-specific central mathematical idea and its human-origin baseline are not yet reconciled. Existing human results and source hypotheses remain separate; no automatic registry promotion.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Falconer's distance problem for stretched logarithmic gauges

Awaiting detailed review

The pinned disclosure documents agents formalizing specified existing manuscript results. Establish the particular original mathematical argument supplied by AI, separately from implementation, fidelity changes and manuscript authorship, before inclusion.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Exact fault images in priority controllers

Awaiting detailed review

Pinned project and exact formal contract reviewed. AI assistance in proofs, certificates or packaging is documented, but a contribution-specific central mathematical idea and its human-origin baseline are not yet reconciled. Existing human results and source hypotheses remain separate; no automatic registry promotion.

Screening recorded: 2026-10-20 · Decision reviewed: 2026-10-20T07:30:08.090Z

Countable cellularity of arbitrary products via finite subproducts

Excluded

Pinned primary statement and AI disclosure describe formalization of existing human mathematics or an existing supplied proof plan. No separately scoped central AI mathematical contribution is established; proof-assistant use and registry admission alone do not qualify. This is a contribution eligibility decision, not a finding that checking failed.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Exact db2 cascade norms and an optimal uniform constant

Awaiting detailed review

Hold: the exact all-scale db2 norm formula and optimal uniform constant go beyond the historical finite-scale manuscript, but priority is explicitly unresolved and the allocation of the retained sign/recurrence argument between human inputs and agents needs reconciliation. Check source-bound verification dates separately from registration.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Omega-bounded Sigma-products and a sharp compactness criterion

Excluded

Pinned primary statement and AI disclosure describe formalization of existing human mathematics or an existing supplied proof plan. No separately scoped central AI mathematical contribution is established; proof-assistant use and registry admission alone do not qualify. This is a contribution eligibility decision, not a finding that checking failed.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Survival and transience above the compartment-division threshold

Awaiting detailed review

Hold: the strict bf>e(e+d) survival/transience theorem and arbitrary finite immigrant contents are explicit, but the disclosure documents AI formalization and manuscript preparation without identifying the retained central AI mathematical idea. Exact CTMC/physical-time construction reviewed; significance or formal checking cannot replace attribution.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

A Unified Kalman-Type Classification of Controllability for Linear Stochastic Systems

Awaiting detailed review

Hold: revised stochastic controllability theorem, ordinary progressive finite-energy controls, Brownian filtration and inherited dependencies require exact manuscript/revision comparison. AI proof-development assistance is disclosed, but central new mathematical work versus formalizing the authors’ revised argument remains unresolved.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Hamiltonian s–t paths in solid grid graphs are decidable in polynomial time

Awaiting detailed review

Hold: Claude is explicitly credited with the new solid-grid path algorithm. The registered theorem checks algorithm correctness; polynomial running time uses a separate hand-reviewed cost model, and equivalence of king-move escape solidity with the conventional face definition is tested but not proved. Resolve that mathematical scope before presenting a standard-model polynomial algorithm.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Pure infinitely self-modifying code

Excluded

Pinned primary statement and AI disclosure describe formalization of existing human mathematics or an existing supplied proof plan. No separately scoped central AI mathematical contribution is established; proof-assistant use and registry admission alone do not qualify. This is a contribution eligibility decision, not a finding that checking failed.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Systolic growth in every genus

Awaiting detailed review

Hold: the 4/3 all-genus limit-inferior systole bound and exact supremum semantics are stated, but the human-directed goal and agent Lean work do not allocate the central arithmetic/gluing advance. Compare the mathematical origin and prior all-genus result before eligibility.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Paracompact expansion and collectionwise separation

Excluded

Pinned primary statement and AI disclosure describe formalization of existing human mathematics or an existing supplied proof plan. No separately scoped central AI mathematical contribution is established; proof-assistant use and registry admission alone do not qualify. This is a contribution eligibility decision, not a finding that checking failed.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

GromovMilman

Excluded

Pinned primary statement and AI disclosure describe formalization of existing human mathematics or an existing supplied proof plan. No separately scoped central AI mathematical contribution is established; proof-assistant use and registry admission alone do not qualify. This is a contribution eligibility decision, not a finding that checking failed.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Lossy Distance-Shell Tomography on Paths: Recovery from Mean and Covariance

Awaiting detailed review

Hold: lossy path-distance tomography reports mean/covariance reconstruction. Resolve exact identifiable model, noise/loss assumptions, prior moment-based recovery and central AI role before a distinct contribution.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Robbins' theorem on strongly connected orientations

Excluded

Pinned primary statement and AI disclosure describe formalization of existing human mathematics or an existing supplied proof plan. No separately scoped central AI mathematical contribution is established; proof-assistant use and registry admission alone do not qualify. This is a contribution eligibility decision, not a finding that checking failed.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Graham's bounds for list scheduling and LPT on identical machines: 2 − 1/m, 4/3 − 1/(3m) and their tight instances

Excluded

Pinned primary statement and AI disclosure describe formalization of existing human mathematics or an existing supplied proof plan. No separately scoped central AI mathematical contribution is established; proof-assistant use and registry admission alone do not qualify. This is a contribution eligibility decision, not a finding that checking failed.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

The radian nine-gon is Euclidean Ramsey iff e^(i theta) is algebraic

Awaiting detailed review

Hold: compare the radian nine-gon algebraicity equivalence with retained OpenAI Euclidean Ramsey results and its exact angle/ambient-space hypotheses; identify a new retained AI argument rather than another registry identity.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

The Arithmetic of Time: the slowest settling clock on at most three letters is the Padovan substitution, unique up to mirror image, and both minimal rules are chiral

Awaiting detailed review

Hold: compare minimal Padovan settling-clock/chirality classification with the earlier Coxeter/Padovan and substitution artifacts. The two minimal rules and alphabet/model restrictions need a contribution-specific priority and AI-origin decision.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Distinct prime divisors of central binomial coefficients

Excluded

Pinned primary statement and AI disclosure describe formalization of existing human mathematics or an existing supplied proof plan. No separately scoped central AI mathematical contribution is established; proof-assistant use and registry admission alone do not qualify. This is a contribution eligibility decision, not a finding that checking failed.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Spectral bounds on the chromatic and independence numbers

Excluded

Pinned primary statement and AI disclosure describe formalization of existing human mathematics or an existing supplied proof plan. No separately scoped central AI mathematical contribution is established; proof-assistant use and registry admission alone do not qualify. This is a contribution eligibility decision, not a finding that checking failed.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

The local dynamical structure of Δ* sets via a new Furstenberg family algebra

Awaiting detailed review

Human LEAPS mathematics and hand-scaffolded proofs are distinguished from AI helper modules. The disclosed classical Pontryagin step and supplied-proof formalization do not establish central AI work on the main delta-star theorem. Hold any separately claimed new uniform-topology method for exact attribution.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Fréchet–Urysohn Σ-products of first-countable spaces

Excluded

Pinned primary statement and AI disclosure describe formalization of existing human mathematics or an existing supplied proof plan. No separately scoped central AI mathematical contribution is established; proof-assistant use and registry admission alone do not qualify. This is a contribution eligibility decision, not a finding that checking failed.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Dirac's theorem: k vertices of a k-connected graph lie on a common cycle

Excluded

Pinned primary statement and AI disclosure describe formalization of existing human mathematics or an existing supplied proof plan. No separately scoped central AI mathematical contribution is established; proof-assistant use and registry admission alone do not qualify. This is a contribution eligibility decision, not a finding that checking failed.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Planar Pólya–Szegő Buckling Inequality

Awaiting detailed review

Hold: the source explicitly attributes the informal planar Pólya–Szegő proof to Tang and Zhang with ChatGPT assistance, followed by AI formalization. No specific retained central AI idea is allocated. The finite-area domain/equality scope is recorded without inferring that a formalization qualifies.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Elementary bounds for Erdos problem 684

Awaiting detailed review

Hold/link review: implements known Erdős 684 bounds from APSSV26 with weaker elementary constants 514 and 1/8. Preserve the original OpenAI contribution and stronger human follow-up; determine whether removing PNT adds a distinct central AI mathematical advance rather than duplicating the result.

Screening recorded: 2026-10-19 · Decision reviewed: 2026-10-19T07:23:14.226Z

Chordal, split, threshold and cograph structure

Excluded

Classical chordal, split, threshold and cograph results. Pinned entry, disclosure and repository describe formalization of known human mathematics. No separate central AI mathematical contribution established; AI use and checking do not by themselves qualify.

Screening recorded: 2026-10-18 · Decision reviewed: 2026-10-18T07:37:42.537Z

Tutte's f-factor theorem

Excluded

Known Tutte f-factor theorem formalized. Exact source and AI disclosure reviewed; no qualifying central AI discovery or new mathematical method established beyond formalizing the existing human proof.

Screening recorded: 2026-10-18 · Decision reviewed: 2026-10-18T07:37:42.537Z

Additive strengthening of Erdos problem 679: a known refutation

Excluded

The additive refutation and primorial strategy are expressly attributed to an earlier public proof. Codex generated an independent Lean implementation and audit, while the disclosure disclaims mathematical novelty.

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

The graph removal lemma for every fixed graph

Excluded

Classical graph removal lemma and associated known proof plan. Pinned source reviewed; no new central AI mathematical contribution identified beyond formalization of known human work.

Screening recorded: 2026-10-18 · Decision reviewed: 2026-10-18T07:37:42.537Z

Chvátal's and Pósa's degree conditions for Hamiltonian cycles

Excluded

Known Chvátal/Pósa Hamiltonicity criteria. Source documents AI formalization, but no specific qualifying central AI contribution beyond existing human mathematics.

Screening recorded: 2026-10-18 · Decision reviewed: 2026-10-18T07:37:42.537Z

Countable-density Hewitt–Marczewski–Pondiczery theorem

Excluded

Known Hewitt–Marczewski–Pondiczery countable-density theorem formalized. No new central AI mathematical argument established beyond the existing human proof.

Screening recorded: 2026-10-18 · Decision reviewed: 2026-10-18T07:37:42.537Z

Moore graphs of diameter two: the Hoffman–Singleton theorem

Excluded

Classical Moore-graph and Hoffman–Singleton results. Registry checking and agent formalization do not establish a separate qualifying central AI discovery.

Screening recorded: 2026-10-18 · Decision reviewed: 2026-10-18T07:37:42.537Z

Countable-coordinate factorization for compact products

Excluded

Known countable-coordinate factorization for compact products. No new central AI contribution established beyond formalizing a supplied human result and proof approach.

Screening recorded: 2026-10-18 · Decision reviewed: 2026-10-18T07:37:42.537Z

Formalization of Carleson's theorem via the Lacey-Thiele approach

Excluded

Changed Lacey–Thiele Carleson artifact formalizes known human mathematics. Source/version comparison does not identify a separate qualifying central AI result; no automatic restoration of an excluded formalization.

Screening recorded: 2026-10-18 · Decision reviewed: 2026-10-18T07:37:42.537Z

Growth series of the triangle Coxeter groups (p, q, infinity), with the PGL(2,Z) instance: Padovan sphere sizes and growth rate the plastic number

On hold after review

The Coxeter growth formula and plastic-number identities are developed with AI proof drafting, but the author fixed the statement and normal-form design. The source does not identify a distinct retained AI mathematical idea beyond formalization of related classical identities.

Screening recorded: 2026-10-18 · 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.