← 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 21 of 39

Lower and Upper Bounds for Glauber Dynamics from Typical States of the Low-Temperature Sherrington–Kirkpatrick Model

Awaiting detailed review

Source manuscript is machine-written under human supervision and adapts several OpenAI SK results. Exact five checked targets distinguish typical-start lower/upper bounds, clocks, thresholds and fluctuation exponents. Reconcile their new improvements versus the existing OpenAI fluctuation/support records and contribution-specific AI roles before inclusion; registration is not a new discovery by itself.

Screening recorded: 2026-10-22 · Decision reviewed: 2026-10-22T07:39:59.456Z

Symplectic Stafford: the affine same-divisor theorem

Awaiting detailed review

Exact pinned statement and provenance read. Human manuscript/prior argument and agent proof-slice, formalization, certificate or packaging roles do not yet isolate a central AI mathematical idea for the retained group, graph, embedded-algorithm or algebraic theorem. No automatic inclusion from complete Lean checking.

Screening recorded: 2026-10-22 · Decision reviewed: 2026-10-22T07:39:59.456Z

Selected Sidon subset theorems of Ma–Tang (partial paper formalization)

Excluded

The full versioned record and pinned challenge concern a known human theorem, earlier human argument or selected partial formalization. AI transcription, proof completion under a supplied argument or checking alone does not qualify as a new central AI contribution. This decision is about the reviewed formalization, not a refutation of the mathematics.

Screening recorded: 2026-10-22 · Decision reviewed: 2026-10-22T07:39:59.456Z

Kriz-Nordentoft non-vanishing for twists of elliptic curve L-series

Excluded

The full versioned record and pinned challenge concern a known human theorem, earlier human argument or selected partial formalization. AI transcription, proof completion under a supplied argument or checking alone does not qualify as a new central AI contribution. This decision is about the reviewed formalization, not a refutation of the mathematics.

Screening recorded: 2026-10-22 · Decision reviewed: 2026-10-22T07:39:59.456Z

Canonical streaming enumeration of eligible detections

Awaiting detailed review

Full registry record and pinned challenge checked. Separate companion controller/streaming encodings or Erdős257/269 kernel extensions from prior related statements. Contribution-specific central AI origin, earlier human source and distinct mathematical advance remain unresolved; model proof development alone is insufficient.

Screening recorded: 2026-10-22 · Decision reviewed: 2026-10-22T07:39:59.456Z

All-base bases and integral relations for the totient kernel

Awaiting detailed review

Full registry record and pinned challenge checked. Separate companion controller/streaming encodings or Erdős257/269 kernel extensions from prior related statements. Contribution-specific central AI origin, earlier human source and distinct mathematical advance remain unresolved; model proof development alone is insufficient.

Screening recorded: 2026-10-22 · Decision reviewed: 2026-10-22T07:39:59.456Z

Erdős problem #257: all base irrationality of the reciprocal Mersenne subseries for every infinite reciprocal summable support, with weighted mass and positive cover extensions, achievement set geometry, and exact greedy membership criteria

Awaiting detailed review

Full registry record and pinned challenge checked. Separate companion controller/streaming encodings or Erdős257/269 kernel extensions from prior related statements. Contribution-specific central AI origin, earlier human source and distinct mathematical advance remain unresolved; model proof development alone is insufficient.

Screening recorded: 2026-10-22 · Decision reviewed: 2026-10-22T07:39:59.456Z

Erdős #269: exact three-prime running-LCM identity and infinite kernel rank

Awaiting detailed review

Full registry record and pinned challenge checked. Separate companion controller/streaming encodings or Erdős257/269 kernel extensions from prior related statements. Contribution-specific central AI origin, earlier human source and distinct mathematical advance remain unresolved; model proof development alone is insufficient.

Screening recorded: 2026-10-22 · Decision reviewed: 2026-10-22T07:39:59.456Z

Erdős #257: irrationality for every reciprocal-summable support and every integer base

Awaiting detailed review

Full registry record and pinned challenge checked. Separate companion controller/streaming encodings or Erdős257/269 kernel extensions from prior related statements. Contribution-specific central AI origin, earlier human source and distinct mathematical advance remain unresolved; model proof development alone is insufficient.

Screening recorded: 2026-10-22 · Decision reviewed: 2026-10-22T07:39:59.456Z

Induced Erdős–Sauer: an n log log n bound

Awaiting detailed review

Pinned metadata describes AI-assisted source manuscripts not all publicly available and the checked n log log n induced Erdős–Sauer target. The fetched guessed paper path404 is not a refutation. The separately public sunflower paper identifies its central GPT theorem, but does not establish all contents or attribution of this distinct induced-graph result.

Screening recorded: 2026-10-22 · Decision reviewed: 2026-10-22T07:39:59.456Z

Ordinary resolution for native encodings and observation wrappers

Awaiting detailed review

Pinned challenge and provenance checked. Reconcile the human manuscript, earlier project variants, supplied target and model proof work before attributing a specific retained mathematical advance to AI. Companion encodings or checking targets are not distinct discoveries by themselves.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

RamanujanNestedRadicals: convergence and exact values of Ramanujan-type nested radicals

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Bounded conjunction and proper-basis algorithms

Awaiting detailed review

Pinned challenge and provenance checked. Reconcile the human manuscript, earlier project variants, supplied target and model proof work before attributing a specific retained mathematical advance to AI. Companion encodings or checking targets are not distinct discoveries by themselves.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Wu 2008 Lemma 2.2, Chen's double sieve inequality, with the range of the last sum repaired

Awaiting detailed review

Pinned source repairs the range of the last sum in Wu’s sieve lemma. Claude’s formalization found a gap, but contribution-specific origin of the essential mathematical repair needs resolution. This does not prove binary Goldbach or refute the whole underlying sieve theorem.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Two-scale Kakeya upper Minkowski lower bound

Awaiting detailed review

Pinned mathematical statement and project disclosure read. Human manuscript/simplification and model proof-completion or formalization roles do not yet isolate a new central AI argument. Retain exact Kakeya, curved-Hilbert or weighted-endpoint hypotheses; no automatic inclusion from Lean checking.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Banach–Mazur determinacy for Baire-property targets

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Hermite's signature theorem and the coprime compositum, with the degree-12 compositum of x^3 - x - 1 and x^4 - x - 1

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

The Riemann hypothesis is equivalent to an asymptotic for the average number of Goldbach representations, after Granville 2007

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Chemical heredity without genetic templates

Awaiting detailed review

Chemical-heredity formalization concerns a supplied template-free reproduction model. A qualifying theoretical-physics contribution and central AI origin are not established by agent-written code or registry admission.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

FixedOrderFactor: the order-r correction factor for mean squares of L(1, chi), and the factor 35/34

Awaiting detailed review

Pinned challenge and provenance checked. Reconcile the human manuscript, earlier project variants, supplied target and model proof work before attributing a specific retained mathematical advance to AI. Companion encodings or checking targets are not distinct discoveries by themselves.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

The Nash–Williams triangle-decomposition theorem

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Improved zero-density estimates for the Riemann zeta function

Awaiting detailed review

Pinned zero-density project reports new native power curves on restricted sigma intervals and standard-axiom checking. Disclosure specifies Codex formalization, closure inspection, rational-frontier auditing and documentation, not the origin of the new mathematical curves. Establish central AI work and compare the actual frontier with later zero-free regions before inclusion. Plots above 7/8 do not improve an already zero region.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Lovász's perfect graph theorems

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Jaeger's 4-flow and 8-flow theorems and Seymour's 6-flow theorem

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Vinogradov's three primes theorem and almost all binary Goldbach, after Heath-Brown 1985, with the Siegel-Walfisz theorem

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Formalization of a curved three-dimensional simplex Hilbert transform

Awaiting detailed review

Pinned mathematical statement and project disclosure read. Human manuscript/simplification and model proof-completion or formalization roles do not yet isolate a new central AI argument. Retain exact Kakeya, curved-Hilbert or weighted-endpoint hypotheses; no automatic inclusion from Lean checking.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Lovász's bound on the Shannon capacity

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Discontinuity of the phase transition for the planar random-cluster and Potts models with q > 4 (Theorems 1.1 and 1.2)

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

The regionally proximal relation for commutative semigroup actions

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Endpoint power weight inequalities for spherical maximal functions in Lean

Awaiting detailed review

Pinned mathematical statement and project disclosure read. Human manuscript/simplification and model proof-completion or formalization roles do not yet isolate a new central AI argument. Retain exact Kakeya, curved-Hilbert or weighted-endpoint hypotheses; no automatic inclusion from Lean checking.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Dual-Horn models and vertex covers in priority controllers

Awaiting detailed review

Pinned challenge and provenance checked. Reconcile the human manuscript, earlier project variants, supplied target and model proof work before attributing a specific retained mathematical advance to AI. Companion encodings or checking targets are not distinct discoveries by themselves.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Stephan 2026: superlinear complexity of the (3/2)^n steering word

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Forest detection and attained healthy-zero maximum weight

Awaiting detailed review

Pinned challenge and provenance checked. Reconcile the human manuscript, earlier project variants, supplied target and model proof work before attributing a specific retained mathematical advance to AI. Companion encodings or checking targets are not distinct discoveries by themselves.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Jin's theorem on dense triangle-free graphs

Excluded

Pinned metadata and formal statement identify a classical human theorem, known human argument or formalization target. Agent transcription and proof-assistant checking alone do not establish a new central AI mathematical contribution under the current policy. This is an eligibility decision on the reviewed formalization, not a negative judgment of the original mathematics.

Screening recorded: 2026-10-21 · Decision reviewed: 2026-10-21T07:53:19.130Z

Normalizers of congruence subgroups at mixed level: Γ_{H₁}(N₁) ∩ Γ_{H₂}(N₂)

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

The Baire product theorem for Choquet spaces

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

Oxtoby's Banach–Mazur characterization of Baire spaces

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

The normalizer of Γ_Δ(N) for every N and every Δ

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 the congruence subgroups Γ_H

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

Unrestricted Boolean multiplicative complexity of four-term polynomial multiplication

Awaiting detailed review

README explicitly says the new n=4 release changes toolchain and verification interface, not the paper’s mathematical claim. Compare its exact certificate/statement with any existing paper assessment before making a verification amendment; do not treat the new registry version as a new discovery.

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

Modular automorphisms of Cartan modular curves of prime level

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

Kneser's conjecture and the octahedral Tucker lemma

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

The normalizer of Γ₀(N): Newman's theorem, and the order and presentations of B(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

Write-Execute Computation and Self-Spectre

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 Lovász Local Lemma and two applications

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

The Erdős–Pósa theorem for cycles

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

Kuratowski–Ulam category theorem for countable pi-base spaces

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

Formalization of L^3 boundedness of the trilinear Hilbert transform

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

Berge's theorem, the Tutte–Berge formula and the Gallai–Edmonds theorem

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

Discovery metadata attribution: What AI Found, CC BY 4.0 · VibeMathed contributors, editorial layer CC BY 4.0. AIProofWatch supplies the screening decisions.