← 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 20 of 39

Erdős Problem 1063: a lower bound for n_k and the structure of the exceptional index

Excluded

Both selected inequalities are already attributed to rickyc’s June/July community proof, including the stronger valuation bound. An independently written AI proof/formalization does not establish a distinct advance over the known human result; finite searches are not a new universal theorem.

Screening recorded: 2026-10-24 · Decision reviewed: 2026-10-24T07:28:43.626Z

Robust absorption for typed triangles

Awaiting detailed review

Primary preprint and companion, six exact selected declarations and successful Lean/NanoDa checking report were read. Central work is certificate/absorber construction for the stated graph-level type families. The disclosure says AI explored and developed proofs beyond transcription, but does not allocate a specific retained new construction sufficiently to distinguish it from human mathematical direction and earlier absorption work. Do not count it as another Nash–Williams discovery. Con-ron declined for capacity; Lean/NanoDa passed.

Screening recorded: 2026-10-24 · Decision reviewed: 2026-10-24T07:28:43.626Z

Almost all graphs are determined by their generalized spectrum

Excluded

The source attributes the paper to Xiang and says the agent followed its proof section by section. Generalized-spectrum formalization, kernel checks and human statement review do not establish central AI origin of the mathematical theorem.

Screening recorded: 2026-10-24 · Decision reviewed: 2026-10-24T07:28:43.626Z

Temporal cliques admit spanners of size O(n log n)

Excluded

Known temporal-clique spanner results supplied by human papers are formalized. The first development part was human-written; the second uses directed AI assistance and source proofs. No distinct AI-origin theorem established.

Screening recorded: 2026-10-24 · Decision reviewed: 2026-10-24T07:28:43.626Z

Control flow obfuscation with irreducible loops and self-modifying code

Awaiting detailed review

The author set the theorem statements and threat model; models mostly wrote formal proofs of the 2022 obfuscation paper with errata. Any new corrected statement must be isolated from the supplied human proof and its structural security assumptions before eligibility can be established.

Screening recorded: 2026-10-24 · Decision reviewed: 2026-10-24T07:28:43.626Z

Fifth dimension subgroups: D₅ = γ₅ when G/γ₂ is finite of exponent 3, candidates for a counterexample, and a reduction of Kourovka 20.84

Excluded

Agents were tasked to formalize specified lemmas of Vorobev’s paper and Tahara’s earlier results. Exact exponent-three/cyclic-cube/finite-2-group assumptions were read; the general Kourovka inclusion remains open. No central new AI argument identified.

Screening recorded: 2026-10-24 · Decision reviewed: 2026-10-24T07:28:43.626Z

The Graham–Pollak theorem

Excluded

Classical Graham–Pollak theorem, with Tverberg’s proof plan supplied to Aristotle. No distinct central-AI mathematical advance.

Screening recorded: 2026-10-24 · Decision reviewed: 2026-10-24T07:28:43.626Z

Stability of planar fronts in reaction-diffusion systems

Excluded

Formalizes de Rijk–van Winden’s supplied planar-front stability proof, with uniqueness omitted. AI coding assistance and author-verified status alone do not establish a central AI mathematical contribution.

Screening recorded: 2026-10-24 · Decision reviewed: 2026-10-24T07:28:43.626Z

Multiplicative bases and standardness of representation-finite algebras

Awaiting detailed review

Human-authored deformation proof of classical multiplicative-basis/standardness theorems is formalized by agents. The mathematics is described as developed with AI assistance, without source-specific allocation of a central retained argument; no inclusion inferred from the large formalization.

Screening recorded: 2026-10-24 · Decision reviewed: 2026-10-24T07:28:43.626Z

Sierpiński's characterization of the rationals

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Brouwer characterization of Cantor space

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

The Bondy–Simonovits even cycle theorem

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Alexandrov–Urysohn characterization of Baire space

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Open Baire-space representation of Polish spaces

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Counting Steiner triple systems: Wilson (1974) and Linial–Luria (2013)

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Carry and divisor-channel criteria for the factorial-minus-one reciprocal series

Awaiting detailed review

Exact carry/moment criteria are distinct from the unauthenticated large computed denominator exclusions. No source-specific central AI mathematical contribution is established by the packaging disclosure.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

An explicit rational-base irrationality region for Zudilin's Lambert series

Awaiting detailed review

Retain coprimality, strict rational-base threshold and the exclusion of 3/2. The selected theorem does not include later all-rank Hankel claims. General AI formalization disclosure does not isolate central AI origin.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Infinite rank of the three-prime running-LCM kernel

Awaiting detailed review

Infinite kernel rank is not irrationality of the running-LCM sum. Earlier companion entries and unit-determinant extensions must remain separate; central AI mathematical origin is unestablished.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Uniform sparse rationalisation of dyadic series

Awaiting detailed review

Exact sparse correction theorem read; the prime-gap countermodel and primality are outside it. General AI formalization disclosure does not establish the origin of the central rationalization construction.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Cubic-rate irrationality for reciprocal sums

Awaiting detailed review

Exact cubic-rate and positivity hypotheses read. AI disclosure identifies formalization, packaging and exposition, without allocating the central new irrationality argument. This does not resolve unrestricted Erdős243.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

The expander mixing lemma and the Alon–Boppana bound

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Continuous open images of Polish spaces

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Helling's theorem: the maximal subgroups of SL₂(ℝ) commensurable with SL₂(ℤ)

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

An exact average Goldbach representation formula, after Goldston and Suriajaya

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Sum of sets in several dimensions

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

The least physical dimension of an inflation-symmetric model set, with the cubic, quartic and degree-12 inflations of x^3 - x - 1 and x^4 - x - 1

Awaiting detailed review

The author fixes the model-set dimension targets; agents draft and repair proofs. The new dimension formula and its known inflation examples need contribution-specific allocation of the central idea and comparison with the cited model-set literature. Do not infer theoretical-physics discovery from cut-and-project terminology.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Szemerédi's theorem with random differences

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Renyi's theorem, Renyi 1948: every large even number is a prime plus a number with at most 8 prime factors

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Noncrossing Two-Nearest-Predecessor Orders on Nearly Circular Ellipses

Excluded

The near-circular ellipse construction is explicitly described as human-directed mathematics with AI-assisted formalization. Its noncrossing ratio bound and exact-real algorithm are not evidence of central AI discovery.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

The Bombieri-Vinogradov theorem, Bombieri 1965 and A. I. Vinogradov 1965, classical form with the maximum over y <= x

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Conditional on RH: the number of Goldbach representations on average, after Languasco and Zaccagnini

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Mann's alpha plus beta theorem for Schnirelmann density, after Mann 1942

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Conditional on RH: the Cesàro average of the number of Goldbach representations, after Goldston and Yang

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Iwaniec's linear sieve at the sifting limit and Jacobsthal's problem

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Shelah's bound for the Hales–Jewett numbers

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Continuity of the phase transition for planar random-cluster and Potts models with 1 <= q <= 4 (Theorems 1, 2 and 3)

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Dimension growth, polynomial in the degree (Castryck–Cluckers–Dittmann–Nguyen)

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Hamiltonian paths in rectangular grid graphs (Itai, Papadimitriou and Szwarcfiter)

Excluded

The reviewed pinned statements formalize the named earlier human theorem or supplied human argument. The exact hypothesis and selected scope were read; no distinct central AI mathematical contribution was established by this formalization. Registry admission and kernel checking do not establish eligibility.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

Fixed-force anomalous dissipation

Awaiting detailed review

The fixed-force torus theorem has exact same-witness all-exponent regularity and source-reported Lean checks. The human authors supplied a private proof with ChatGPT assistance; Aristotle/Codex formalized it. Central AI origin of a distinct retained analytical construction is not established, and the private manuscript was not reviewed.

Screening recorded: 2026-10-23 · Decision reviewed: 2026-10-23T08:28:30.727Z

The fourth consecutive Dirichlet eigenvalue ratio

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

Critical recovery, query lower bounds and binary-native width

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

A universal group with thirteen relators

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

A formal proof that crown graphs maximise the representation number of bipartite graphs

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

Classical Liénard equations of degree n ≥ 6 can have floor((n−1)/2)+4 limit cycles

Awaiting detailed review

The pinned manuscript proves isolated global periodic orbits, an all-degree real-coefficient bound and a rational degree-seven example. Improvements are only for degrees 6–9 against the stated n−2 baseline. Metadata says AI-assisted development but does not isolate who supplied the new sextic construction and degree-raising idea; central AI origin remains unresolved. Distinct from the existing quintic upper bound.

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

Ramanujan congruences for the partition function

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

An XP Algorithm for Maximum-Weight Independent Set in Embedded Graphs, in Lean 4

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

Schnirelmann's theorem: every integer n >= 2 is a sum of at most 30772 primes, after Schnirelmann 1933

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

Brun's theorem: the sum of the reciprocals of the twin primes converges, after Brun 1919, with the twin prime upper bound and every even gap

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

Romanov's theorem: the integers of the form p + 2^k have positive lower density, with Erdős' complement, after Romanov 1934 and Erdős 1950

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

The strong Choquet characterization of Polish spaces

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

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