AI-assisted results, 29 Oct 2026 (part 2)
Claude ‘largely carried out’ Lipshitz’s Khovanov research, ChatGPT found Soundararajan’s proof and wrote Etingof’s and Mathew’s papers, George Elliott’s free-product classification ‘carried out using ChatGPT’, and a first read of Hexagon’s backlog
Awaiting review
The takeaway
A second pass over the 28 Oct arXiv announcement and a first full read of Hexagon (hexagonmath.org), which the sweep had never covered, found results with large AI roles signed by senior mathematicians. Robert Lipshitz writes that his Khovanov paper’s research ‘was largely carried out by various Claude models’. Kannan Soundararajan’s proof of a problem from Montgomery’s CBMS book ‘was found by ChatGPT 6’. ChatGPT 6 Pro wrote Pavel Etingof’s answer to a 1999 question and produced Akhil Mathew’s answer to a question of Drinfeld. George Elliott’s classification of reduced free products of nuclear C*-algebras ‘was carried out using ChatGPT’. Eight items have their own entries: the unforced 2D Euler non-uniqueness claims, the Erdős–Lovász covering-number bound, UPP^cc under intersection, Kisin’s Serre conjecture, Linnik’s constant ≤ 3.99, 3D Yang–Mills on a torus, random k-SAT and Chenglong Ma’s Hovey–Strickland provenance claim.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Lean-verified
- Importance
- 2 of 5
- Last verified
- 29 October 2026
Your AI and this story
- GPT-6 Astra182 days after its cutoff
- Claude Opus 5.5121 days after its cutoff
- Gemini 4 Argon212 days after its cutoff
- Grok 4.7151 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 121 days before it.
Key facts
- Own entries from this pass: 2D Euler non-uniqueness without force claimed three times, all with AI (Pappalettera–Sorella on Hexagon, Coiculescu, Choi), Erdős–Lovász covering-number problem: AI-found construction disproves Frankl’s 1996 conjecture, Unbounded-error communication is not closed under AND, found with GPT-6 Astra, Kisin proves Serre’s 1960 Artin-character conjecture with GPT Astra, Linnik’s constant ≤ 3.99, written by Claude Opus 5.5 and GPT Astra, 3D SU(2) Yang–Mills continuum limit claimed in five AI-written papers, Random k-SAT threshold exists for every k ≥ 3: a human proof and an OpenAI Lean-checked proof, Hovey–Strickland: author says OpenAI’s paper matches his ChatGPT-uploaded draft
- Robert Lipshitz (2610.37595, Khovanov local equivalence groups, incl. a nontrivial 2-torsion element): ‘Except for some quotations specifically highlighted below, the tables at the end, and some of the TikZ diagrams, this paper was entirely written by the listed author. The research, however, was largely carried out by various Claude models, with modest prompting by the author.’ Section 5 discusses method and ethics; Claude named the ‘bowtie complexes’
- Bernhard Schmidt (NTU Singapore; 2610.37417): no Hadamard difference sets in groups of order 4p² with p ≡ 3 (mod 4), p ≥ 7. ‘The author posed the problem, chose the method … and directed the investigation. The AI model found the proof of Theorem 1.1 including Lemma 3.1, and produced a first draft of the manuscript’ (Claude, Fable 5.1)
- George A. Elliott, Chun Guang Li, Zhuang Niu (2610.36459), classification of reduced free products of nuclear C*-algebras starting from the countably infinite reduced free product of (C([0,1]), λ): acknowledgement ‘The work was carried out using ChatGPT.’
- Hexagon, senior contributors: Kannan Soundararajan, ‘Hilbert-type inequality with primes’ (2609.00119), answering a problem in Montgomery’s CBMS book: ‘The proof was found by ChatGPT 6, and written up by the author’; Pavel Etingof, a 14-dimensional Lie bialgebra with g and g* perfect (2610.00284), answering Questions 4.1(3)–(4) of Etingof–Gelaki–Guralnick–Saxl: ‘written by ChatGPT 6 Pro in response to the following prompt by Pavel Etingof’; Akhil Mathew (2609.00105), every invertible R[T]-module becomes free after a faithfully flat extension, ‘answering a question of Drinfeld’: ‘Produced by ChatGPT 6 Pro.’
- Hexagon, quantum algebra and analysis: Noah Snyder (2610.00566), every pivotal deformation of Deligne’s S_t comes from varying t, first version ‘written by Claude in response to the following prompt’ (the prompt is quoted in full); Vjekoslav Kovač (2610.00176), a non-universality criterion for the Erdős similarity conjecture beyond geometric decay, ‘generated by OpenAI’s ChatGPT-6 Astra on October 9, 2026’, building on OpenAI’s 5 Oct manuscript on the geometric case; Shuoxing Zhou (2610.00134), the relative bicentralizer conjecture via Poisson boundaries, which ‘overlaps with OpenAI’s concurrent work, but the proofs use fundamentally different methods’ (GPT-6 Astra, Gemini 3.1 Pro)
- Hexagon, conjectures refuted: Chung Pang Mok and Yiqi Xu (2610.00384), a height-five prime in ℚ[[x₀,…,x₅]] with P^(2) ⊄ mP, a prime-ideal counterexample to the Eisenbud–Mazur conjecture (Crelle 1997): ‘The counterexample was discovered by a ChatGPT model’; Shihao Wang and Zhiwei Zheng (2610.00529), PSL₄(5) and an index-2 overgroup in PGL₄(5) with the same character degrees, a counterexample to Huppert’s conjecture; Yi Gu and Lifan Guan (2610.00303), a genus-two cover of an elliptic curve refuting Beauville’s stability conjecture, ‘generated by the Danus system based on gpt-5.6 sol’; Shengwei Qiu and Thomas Sinclair (2610.00567), the regular pentagonal system fails the lifting property, refuting the operator-system form of the Smith–Ward problem, with proofs of Theorems A and C ‘generated by Claude Opus 5.5’; Jiangcheng You and Heng Zhang (2610.00010), a contractible open 4-manifold not homeomorphic to ℝ⁴ with a complete metric of scalar curvature ≥ 1, answering Chang–Weinberger–Yu and Chodosh–Máximo–Mukherjee: ‘GPT-6 constructed a highly intricate counterexample and developed the associated proofs’
- Hexagon, bounds and constructions: Arman, Bondarenko, Prymak, Radchenko (2610.00163), Borsuk’s partition number b(n) ≤ (1.22304666…+o(1))ⁿ, below Schramm’s base √(3/2); ‘The main proof arguments were primarily generated using ChatGPT-6 Astra’; Prymak ‘curates this note but does not claim authorship’. Kevin Li (2610.00248), kissing numbers in dimensions 19 and 21 at least 12460 and 31560 (was 11948 and 29768), found with GPT-6 Astra Pro, Claude Opus 5.5 and Claude Fable 5.1. Shawn Krisman (2610.00516), one of ζ(7), ζ(9), …, ζ(21) is irrational (previously ζ(7), …, ζ(35)), ‘done with a Fable Claude Code session and Opus subsessions’, human understanding ‘no parts’. Dmitry Grinko (2609.00126), three orthonormal bases do not determine pure states in ℂ⁴, so the Pauli problem needs four in every dimension ≥ 3: ‘one-shotted’ by ChatGPT 5.6 Sol Pro
Show 5 more
- Hexagon, large claims with little human checking: Wenchang Yang and Yi Wang (2610.00378), smooth local isometric embedding of every smooth n-manifold, n ≥ 5, into ℝ^{n(n+1)/2}, the smooth form of Janet–Cartan: ‘the detailed technical arguments have not yet been fully verified or understood by humans’; Veronica Phan (2610.00579), Bergeron’s conjecture on differences of Gaussian binomials and Troyka’s strengthening (Claude Opus; understanding ‘no parts’); Taylor Dupuy (2610.00571), a report on Thakur’s function-field conjectures assembled from six AI research runs during a Rochester seminar talk: ‘The proofs, computations, and citations have received AI review only; no human has checked them’
- arXiv, AI found the key step: Hanbing Fang (2610.36563), every complete 4D gradient steady Ricci soliton with positive curvature operator that is κ-noncollapsed at all scales has an isometric O(3) action; ChatGPT-6 Astra and the Danus system expanded the arguments and helped remove the scalar-decay hypothesis. Chunkai Xu (2610.37032), large-volume limits of Bridgeland stability: ‘The key breakthrough came after the release of GPT-6 Astra’. Qiang Wu (2610.37630), algorithms that approximate log Z_N of the SK and mixed p-spin models in weak external fields with a polynomial number of operations: ‘GPT-5.6 Pro proposed a polynomial time algorithm for the higher order case’. Cao, Gao, Huang, Nie (2610.37179), sparse integer polynomial irreducibility is coNP-hard and in PP (the PP bound relies on Cureton–Thorner’s quasi-Riemann hypothesis and Frei–Sofos–Widmer), results ‘obtained through an interactive collaboration’ with the MechMath Agent Team and GPT-Astra, Lean in MechMath/sparse-irr
- arXiv, other notable AI roles: Carter, O’Bryant and Tao (2610.36207), a smaller constant in the second-order term of the upper bound for Sidon sets in [1, N] (Erdős problem #30), via ‘WT-triples’: ‘This work grew out of efforts to use AlphaEvolve’; Tao’s blog notes a slightly sharper constant (0.942809522) obtained since by a different method and adds ‘We also did not try to use 2026-level AI tools to optimize our own bound’. Chung and Wesley (2610.36522), new infinite families with R(B_{n−1}, B_n) = 4n − 1, ‘found with assistance from the Station, a multiagent AI system’. Wang and Yan (2610.36495), every complex Keller map of affine 3-space of degree ≤ 4 is an automorphism, and every automorphism of degree ≤ 4 is tame (GPT-6 Astra for ‘brainstorming, mathematical development, and manuscript drafting’). Cheng et al. (2610.37122), matrix samplers ↔ quantum-proof extractors: ‘we discussed with AI and used it substantially to develop the solutions and proofs’. Pham and Roy (2610.36090), two-step rectified flow: GPT 6-Astra generated the construction of the limiting ODEs
- Smaller AI roles: Jankiewicz–Miri (2610.37641, ‘Some AI tools were used to prove results presented in Section 5’); Jafari–Kaveh (2610.36566, AI ‘used in major ways for both the write-up and proofs’); Hwang (2610.37192, tight bounds for randomized generalized k-server on uniform metrics, AI agents for ‘exploratory discussions’); Cardona–Kepplinger (2610.36212, Claude Opus 5.5 and ChatGPT 5.6 simplified Lemma 6.5 and suggested contact volume growth to lower regularity from C² to C¹); Bockhaus–Glazyrin (2610.36675, exact average-kissing certificates in dimensions 8 and 24 found by ‘a long trial-and-error process’ with AI tools); Schmid–Yang (2610.37620, open ASEP III: ‘AI suggested using log-concavity and total nonnegativity in Section 7.3’)
- How this was found: the sweep’s arXiv list again showed the 28 Oct announcement (arXiv had not issued a new one by 11:05 UTC), so the remaining PDFs were read for AI statements; Hexagon was read through its JSON API (476 works by 29 Oct, of which about 400 maths works had no citation here). Hexagon now has its own sweep section (scripts/sweep.mjs)
What happened
The first 29 Oct listing covered the most visible AI-assisted papers of the 28 Oct arXiv announcement. This second pass read the remaining PDFs whose AI statement describes more than editing. It also read Hexagon, the repository Ben Antieau’s group opened on 6 Oct for AI-generated and AI-assisted mathematics, through its API for the first time. About 400 of its 476 works had never been cited here. They include papers by Kisin, Soundararajan, Etingof, Mathew, Snyder and Kovač, three claimed proofs of 2D Euler non-uniqueness (one on Hexagon), an AI-written improvement of Linnik’s constant and a five-part claim on three-dimensional Yang–Mills theory.
Why it matters
Hexagon has become the place where senior mathematicians post work that a model largely did. Its form makes contributors state how much they understand: Kisin and Mathew say all, Naslund some, and the Yang–Mills authors none. Some of these papers answer named questions of Drinfeld, Montgomery, Etingof, Eisenbud–Mazur and Huppert and do not appear on arXiv at all. A search that reads arXiv alone now misses part of the record.
What is disputed or not yet verified
| Verification | Unrefereed arXiv and Hexagon preprints; partial Lean formalizations where stated; Hexagon’s ‘human understanding’ labels are self-reported |
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Sources
30 sources from 3 sites. Numbers match the chips in the text.
30 sources: 29 primary, 1 reaction
Primary
- arXiv 2610.37595: On Khovanov local equivalence groups (Lipshitz)arxiv.org, paper
- arXiv 2610.37417: Nonexistence of Hadamard difference sets in groups of order 4p² (Schmidt)arxiv.org, paper
- arXiv 2610.36459: Classification of reduced free products of nuclear C*-algebras (Elliott, Li, Niu)arxiv.org, paper
- Hexagon 2609.00119: Hilbert-type inequality with primes (Soundararajan)hexagonmath.org, paper
- Hexagon 2610.00284: A fourteen-dimensional biperfect Lie bialgebra (Etingof; ChatGPT 6 Pro)hexagonmath.org, paper
- Hexagon 2609.00105: Graded absolute integral closures and Picard groups (Mathew; ChatGPT 6 Pro)hexagonmath.org, paper
- Hexagon 2610.00566: Deformations of Deligne’s S_t (Snyder; Claude)hexagonmath.org, paper
- Hexagon 2610.00176: Superexponentially decaying sequences in the Erdős similarity problem (Kovač)hexagonmath.org, paper
- Hexagon 2610.00134: Poisson boundaries of type III factors and the relative bicentralizer conjecture (Zhou)hexagonmath.org, paper
- Hexagon 2610.00384: A counterexample to the Eisenbud–Mazur conjecture (Mok, Xu)hexagonmath.org, paper
- Hexagon 2610.00529: A counterexample to Huppert’s conjecture (Wang, Zheng)hexagonmath.org, paper
- Hexagon 2610.00303: A counterexample to Beauville’s stability conjecture (Gu, Guan)hexagonmath.org, paper
Show all 29 sources
- Hexagon 2610.00567: The regular pentagonal system and the Smith–Ward problem (Qiu, Sinclair)hexagonmath.org, paper
- Hexagon 2610.00010: A contractible open four-manifold with a complete metric of uniformly positive scalar curvature (You, Zhang)hexagonmath.org, paper
- Hexagon 2610.00163: An exponential improvement for Borsuk’s problem (Arman, Bondarenko, Prymak, Radchenko; ChatGPT-6 Astra)hexagonmath.org, paper
- Hexagon 2610.00248: Improved kissing numbers in nineteen and twenty-one dimensions (Kevin Li)hexagonmath.org, paper
- Hexagon 2610.00516: One of ζ(7), ζ(9), …, ζ(21) is irrational (Krisman)hexagonmath.org, paper
- Hexagon 2609.00126: Pauli problem in dimension 4 (Grinko)hexagonmath.org, paper
- Hexagon 2610.00378: Smooth local isometric embeddings of Riemannian manifolds in optimal dimension (Yang, Wang)hexagonmath.org, paper
- Hexagon 2610.00579: Analytic q-inequalities and a proof of Bergeron’s conjecture (Phan)hexagonmath.org, paper
- Hexagon 2610.00571: Thakur’s conjectures in function field arithmetic, a report on queries to frontier agents (Dupuy)hexagonmath.org, paper
- arXiv 2610.36563: O(3)-symmetry of four-dimensional steady Ricci solitons (Fang)arxiv.org, paper
- arXiv 2610.37032: Bridgeland stability and Gieseker stability I (Chunkai Xu)arxiv.org, paper
- arXiv 2610.37630: Approximate counting for mixed p-spin glasses via cluster expansion (Qiang Wu)arxiv.org, paper
- arXiv 2610.37179: Irreducibility testing of sparse polynomials over integers is NP-hard and in PP (Cao, Gao, Huang, Nie)arxiv.org, paper
- arXiv 2610.36207: On the diameter and distribution of Sidon sets (Carter, O’Bryant, Tao)arxiv.org, paper
- arXiv 2610.36522: Constructions for nearly diagonal book Ramsey numbers (Chung, Wesley; the Station)arxiv.org, paper
- arXiv 2610.36495: Quartic Keller maps and tameness in three variables (Wang, Yan)arxiv.org, paper
- arXiv 2610.37122: Matrix samplers and quantum-proof extractors (Cheng et al.)arxiv.org, paper
Reactions
- Terence Tao’s blog, 28 Oct: On the diameter and distribution of Sidon setsterrytao.wordpress.com, discussion
Changes
- Filed (arXiv PDFs of the 28 Oct announcement, Hexagon API and abs pages, Tao’s blog; part 1 is AI-assisted results in the 29 Oct 2026 sweep)