{"schema":"postcutoff/event@1","as_of":"2026-10-30T13:42:00+01:00","url":"https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing-2/","md":"https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing-2/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-10-29-ai-assisted-results-october-29-listing-2","date":"2026-10-29","date_precision":"day","short_title":"AI-assisted results, 29 Oct 2026 (part 2)","deck":"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","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.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2610.37595: On Khovanov local equivalence groups (Lipshitz)","url":"https://arxiv.org/abs/2610.37595","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"arXiv 2610.37417: Nonexistence of Hadamard difference sets in groups of order 4p² (Schmidt)","url":"https://arxiv.org/abs/2610.37417","type":"paper","group":"primary","domain":"arxiv.org"},{"n":3,"title":"arXiv 2610.36459: Classification of reduced free products of nuclear C*-algebras (Elliott, Li, Niu)","url":"https://arxiv.org/abs/2610.36459","type":"paper","group":"primary","domain":"arxiv.org"},{"n":4,"title":"Hexagon 2609.00119: Hilbert-type inequality with primes (Soundararajan)","url":"https://hexagonmath.org/abs/2609.00119v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":5,"title":"Hexagon 2610.00284: A fourteen-dimensional biperfect Lie bialgebra (Etingof; ChatGPT 6 Pro)","url":"https://hexagonmath.org/abs/2610.00284v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":6,"title":"Hexagon 2609.00105: Graded absolute integral closures and Picard groups (Mathew; ChatGPT 6 Pro)","url":"https://hexagonmath.org/abs/2609.00105v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":7,"title":"Hexagon 2610.00566: Deformations of Deligne's S_t (Snyder; Claude)","url":"https://hexagonmath.org/abs/2610.00566v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":8,"title":"Hexagon 2610.00176: Superexponentially decaying sequences in the Erdős similarity problem (Kovač)","url":"https://hexagonmath.org/abs/2610.00176v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":9,"title":"Hexagon 2610.00134: Poisson boundaries of type III factors and the relative bicentralizer conjecture (Zhou)","url":"https://hexagonmath.org/abs/2610.00134v2","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":10,"title":"Hexagon 2610.00384: A counterexample to the Eisenbud–Mazur conjecture (Mok, Xu)","url":"https://hexagonmath.org/abs/2610.00384v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":11,"title":"Hexagon 2610.00529: A counterexample to Huppert's conjecture (Wang, Zheng)","url":"https://hexagonmath.org/abs/2610.00529v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":12,"title":"Hexagon 2610.00303: A counterexample to Beauville's stability conjecture (Gu, Guan)","url":"https://hexagonmath.org/abs/2610.00303v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":13,"title":"Hexagon 2610.00567: The regular pentagonal system and the Smith–Ward problem (Qiu, Sinclair)","url":"https://hexagonmath.org/abs/2610.00567v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":14,"title":"Hexagon 2610.00010: A contractible open four-manifold with a complete metric of uniformly positive scalar curvature (You, Zhang)","url":"https://hexagonmath.org/abs/2610.00010v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":15,"title":"Hexagon 2610.00163: An exponential improvement for Borsuk's problem (Arman, Bondarenko, Prymak, Radchenko; ChatGPT-6 Astra)","url":"https://hexagonmath.org/abs/2610.00163v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":16,"title":"Hexagon 2610.00248: Improved kissing numbers in nineteen and twenty-one dimensions (Kevin Li)","url":"https://hexagonmath.org/abs/2610.00248v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":17,"title":"Hexagon 2610.00516: One of ζ(7), ζ(9), …, ζ(21) is irrational (Krisman)","url":"https://hexagonmath.org/abs/2610.00516v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":18,"title":"Hexagon 2609.00126: Pauli problem in dimension 4 (Grinko)","url":"https://hexagonmath.org/abs/2609.00126v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":19,"title":"Hexagon 2610.00378: Smooth local isometric embeddings of Riemannian manifolds in optimal dimension (Yang, Wang)","url":"https://hexagonmath.org/abs/2610.00378v2","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":20,"title":"Hexagon 2610.00579: Analytic q-inequalities and a proof of Bergeron's conjecture (Phan)","url":"https://hexagonmath.org/abs/2610.00579v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":21,"title":"Hexagon 2610.00571: Thakur's conjectures in function field arithmetic, a report on queries to frontier agents (Dupuy)","url":"https://hexagonmath.org/abs/2610.00571v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":22,"title":"arXiv 2610.36563: O(3)-symmetry of four-dimensional steady Ricci solitons (Fang)","url":"https://arxiv.org/abs/2610.36563","type":"paper","group":"primary","domain":"arxiv.org"},{"n":23,"title":"arXiv 2610.37032: Bridgeland stability and Gieseker stability I (Chunkai Xu)","url":"https://arxiv.org/abs/2610.37032","type":"paper","group":"primary","domain":"arxiv.org"},{"n":24,"title":"arXiv 2610.37630: Approximate counting for mixed p-spin glasses via cluster expansion (Qiang Wu)","url":"https://arxiv.org/abs/2610.37630","type":"paper","group":"primary","domain":"arxiv.org"},{"n":25,"title":"arXiv 2610.37179: Irreducibility testing of sparse polynomials over integers is NP-hard and in PP (Cao, Gao, Huang, Nie)","url":"https://arxiv.org/abs/2610.37179","type":"paper","group":"primary","domain":"arxiv.org"},{"n":26,"title":"arXiv 2610.36207: On the diameter and distribution of Sidon sets (Carter, O'Bryant, Tao)","url":"https://arxiv.org/abs/2610.36207","type":"paper","group":"primary","domain":"arxiv.org"},{"n":27,"title":"arXiv 2610.36522: Constructions for nearly diagonal book Ramsey numbers (Chung, Wesley; the Station)","url":"https://arxiv.org/abs/2610.36522","type":"paper","group":"primary","domain":"arxiv.org"},{"n":28,"title":"arXiv 2610.36495: Quartic Keller maps and tameness in three variables (Wang, Yan)","url":"https://arxiv.org/abs/2610.36495","type":"paper","group":"primary","domain":"arxiv.org"},{"n":29,"title":"arXiv 2610.37122: Matrix samplers and quantum-proof extractors (Cheng et al.)","url":"https://arxiv.org/abs/2610.37122","type":"paper","group":"primary","domain":"arxiv.org"},{"n":30,"title":"Terence Tao's blog, 28 Oct: On the diameter and distribution of Sidon sets","url":"https://terrytao.wordpress.com/2026/10/28/on-the-diameter-and-distribution-of-sidon-sets/","type":"discussion","group":"reactions","domain":"terrytao.wordpress.com"}],"official":29,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Anthropic","Google DeepMind","various researchers"],"title":"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","summary":"Catalogue of AI-assisted results not covered by the first 29 Oct listing: remaining papers of the 28 Oct arXiv announcement with a substantial AI role, and notable items from about 400 uncited works on Hexagon, the repository for AI-generated and AI-assisted mathematics (backlog in data/_hexagon-backlog-2026-10-29.txt). Highlights: Lipshitz's Khovanov local equivalence groups (Claude), Schmidt's nonexistence of Hadamard difference sets of order 4p² (proof found by Claude Fable 5.1), Elliott–Li–Niu's classification of reduced free products (ChatGPT), Soundararajan, Etingof, Mathew, Snyder and Kovač on Hexagon, counterexamples to the Eisenbud–Mazur and Huppert conjectures, the Pauli problem in dimension four, and the first improvement on Schramm's base for Borsuk's partition number.","key_facts":["Own entries from this pass: 2026-10-17-2d-euler-unforced-nonuniqueness-lp-vorticity-ai (Pappalettera–Sorella on Hexagon, Coiculescu, Choi), 2026-10-27-erdos-lovasz-intersecting-covering-number-frankl-ai-construction, 2026-10-27-uppcc-not-closed-under-intersection-gpt-6-astra, 2026-10-28-kisin-serre-artin-character-conjecture-gpt-astra, 2026-10-02-linnik-constant-3-99-naslund-claude-gpt-astra, 2026-10-26-three-dimensional-su2-yang-mills-continuum-limit-aronow-lopatto-ai, 2026-10-05-random-k-sat-satisfiability-conjecture-carenini-openai, 2026-10-07-chenglong-ma-hovey-strickland-openai-chatgpt-upload-provenance","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","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)"],"key_numbers":[],"tags":["math","computer-science","arxiv","hexagon","catalogue","chatgpt","gpt-6-astra","gpt-6-pro","gpt-5-6-sol","claude","claude-opus-5-5","claude-fable-5-1","alphaevolve","danus","lean"],"science":{"field":"mathematics","subfield":"multiple (low-dimensional topology, design theory, operator algebras, number theory, commutative algebra, quantum algebra, combinatorics, geometric analysis, TCS)","problem":"See list","result":"Catalogue of AI-assisted results from the 28 Oct arXiv announcement (second pass) and from the Hexagon repository, beyond those with their own entries","open_since":"","ai_system":["Claude Opus 5.5","Claude Fable 5.1","ChatGPT 6","ChatGPT 6 Pro","GPT-6 Astra","GPT-6 Astra Pro","GPT-5.6 Sol","GPT-5.6 Pro","Gemini 3.1 Pro","AlphaEvolve","Danus","MechMath Agent Team"],"human_role":"From papers written entirely by a model in answer to a prompt (Etingof, Mathew, Snyder) to human proofs that grew out of AI experiments (Tao et al.)","verification":{"key":"lean","label":"Lean-verified","text":"Unrefereed arXiv and Hexagon preprints; partial Lean formalizations where stated; Hexagon's 'human understanding' labels are self-reported"},"status":"pending","shock":"","verified_by":["preprint","lean"],"kind":"batch"},"body_md":"## What happened\n\nThe first 29 Oct listing covered the most visible AI-assisted papers of the 28 Oct arXiv announcement. This second pass read the\nremaining PDFs whose AI statement describes more than editing. It also read Hexagon, the repository Ben Antieau's group opened on 6 Oct for\nAI-generated and AI-assisted mathematics, through its API for the first time. About 400 of its 476 works had never been cited here. They\ninclude papers by Kisin, Soundararajan, Etingof, Mathew, Snyder and Kovač, three claimed proofs of 2D Euler non-uniqueness (one on Hexagon),\nan AI-written improvement of Linnik's constant and a five-part claim on three-dimensional Yang–Mills theory.\n\n## Why it matters\n\nHexagon has become the place where senior mathematicians post work that a model largely did. Its form makes contributors state how much\nthey understand: Kisin and Mathew say all, Naslund some, and the Yang–Mills authors none. Some of these papers answer named questions of\nDrinfeld, Montgomery, Etingof, Eisenbud–Mazur and Huppert and do not appear on arXiv at all. A search that reads arXiv alone now misses\npart of the record.","disputed":[{"label":"Verification","text":"Unrefereed arXiv and Hexagon preprints; partial Lean formalizations where stated; Hexagon's 'human understanding' labels are self-reported","sources":[]}],"related":[{"id":"2026-10-29-ai-assisted-results-october-29-listing","url":"https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing/","date":"2026-10-29","date_precision":"day","short_title":"AI-assisted results in the 29 Oct 2026 sweep","deck":"Counterexamples to Wilking's 2007 question found by GPT-6 Astra, an LLM-written Plateau paper by De Lellis and Glaudo, explicit Reed–Solomon codes with optimal list size (Guruswami et al.), rank-four quiver mutation decided by GPT Astra, and a dozen named conjectures","takeaway":"The 29 Oct sweep covered the arXiv announcement of 28 Oct, which the previous run had read only through keyword queries. This time 43 papers with an AI statement surfaced, and a PDF scan of a further 405 new and cross-listed submissions in math, cs.CC, cs.DS and cs.DM found about 180 more with an AI statement, most of them describing more than editing help. Four results have their own entries: OpenAI's abundance claim and Jihao Liu's priority remark, OpenAI's Lean-checked L = RL = BPL, R(3,3,3,3) ≤ 61 and the sharp Banach–Mazur exponent. This page lists the rest. GPT-6 Astra found the counterexamples to Wilking's 2007 question 'with minimal human input' and discovered the main results of a rank-four quiver paper. Claude found examples in opinion dynamics and proposed a minimal-surface construction. An LLM supplied 'the main idea' of a paper by Camillo De Lellis, a member of the IAS advisory group on AI and mathematics, and wrote it.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":23,"official":23,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Anthropic","various researchers"]},{"id":"2026-10-28-kisin-serre-artin-character-conjecture-gpt-astra","url":"https://postcutoff.com/e/2026-10-28-kisin-serre-artin-character-conjecture-gpt-astra/","date":"2026-10-28","date_precision":"day","short_title":"Kisin proves Serre's 1960 Artin-character conjecture with GPT Astra","deck":null,"takeaway":"In 1960 Serre conjectured that a function built from fixed-point multiplicities of a finite group acting on a regular local ring is the character of an ℓ-adic representation. It is the higher-dimensional analogue of the Artin character of local fields. Tomoyuki Abe proved the positive-characteristic case (Inventiones, 2025). On 28 Oct Harvard's Mark Kisin posted the mixed-characteristic case on Hexagon, which finishes the conjecture. He writes that 'extensive use of GPT Astra was made both to arrive at the proofs … and to write a first draft', and that 'significant human effort' went into checking them. Part of the work was done at 'The Overhang', a San Francisco meeting on 9–10 Sept 2026.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-29","updated":"2026-10-29","orgs":["Harvard University","OpenAI"]},{"id":"2026-10-27-erdos-lovasz-intersecting-covering-number-frankl-ai-construction","url":"https://postcutoff.com/e/2026-10-27-erdos-lovasz-intersecting-covering-number-frankl-ai-construction/","date":"2026-10-27","date_precision":"day","short_title":"Erdős–Lovász covering-number problem: AI-found construction disproves Frankl's 1996 conjecture","deck":null,"takeaway":"Erdős and Lovász showed in 1975 that an intersecting family of k-sets that needs k points to cover it has at most k^k members. The best constructions stayed near (k/2)^(k−1) for 30 years. In 1996 Frankl, Ota and Tokushige conjectured that m(k) < (ck)^k for some c < 1. A 27 Oct preprint by Peter Frankl, Jian Wang and two Sichuan University students builds families of size k^k·exp(−50√(k log k)). With Zakharov's 2024 upper bound this pins m(k) down to k^k·exp(−k^(1/2+o(1))) and refutes the 1996 conjecture. The authors write that 'the construction was found using generative AI tools'. They do not name the models.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":2,"filed":"2026-10-29","updated":"2026-10-29","orgs":["Rényi Institute","Sichuan University"]},{"id":"2026-10-27-uppcc-not-closed-under-intersection-gpt-6-astra","url":"https://postcutoff.com/e/2026-10-27-uppcc-not-closed-under-intersection-gpt-6-astra/","date":"2026-10-27","date_precision":"day","short_title":"Unbounded-error communication is not closed under AND, found with GPT-6 Astra","deck":null,"takeaway":"Unbounded-error communication complexity (UPP^cc) is the communication analogue of PP. Beigel, Reingold and Spielman proved in 1995 that PP is closed under intersection. Whether UPP^cc is closed under intersection had been asked since Halstenberg and Reischuk (1988). In a 27 Oct preprint, Mark Bun and Mandar Juvekar (Boston University) give explicit matrices of sign rank Θ(d) whose AND has sign rank 2^Θ(d). The previous gap, by Bun, Mande and Thaler, was only log versus log². The paper began when they asked GPT-6 Astra how to beat that gap. 'To our (in retrospect, naïve) astonishment,' they write, the model 'discovered what appeared to be complete proofs'.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Boston University"]},{"id":"2026-10-26-three-dimensional-su2-yang-mills-continuum-limit-aronow-lopatto-ai","url":"https://postcutoff.com/e/2026-10-26-three-dimensional-su2-yang-mills-continuum-limit-aronow-lopatto-ai/","date":"2026-10-26","date_precision":"day","short_title":"3D SU(2) Yang–Mills continuum limit claimed in five AI-written papers","deck":null,"takeaway":"Building Yang–Mills theory as a rigorous continuum measure is open even in three dimensions, where the theory is superrenormalizable. On 26 Oct P. M. Aronow (Yale) and Patrick Lopatto (UNC Chapel Hill) posted five Hexagon papers. They claim that flowed Wilson loops of 3D SU(2) lattice Yang–Mills on a torus converge as the lattice spacing goes to zero, to a unique measure on the Cao–Chatterjee state space. The proof is a Bałaban-style multiscale renormalization-group analysis. The provenance statement says proof discovery, verification and writing were done by Opus 5.5, GPT 6 Astra and GPT 6.1 Sol, with only 'limited background formalizations' in Lean. Hexagon records human understanding as 'no parts'. It is not the four-dimensional Clay problem. We found no expert check as of 29 Oct.","category":"science","category_label":"Science & math","importance":4,"confidence":"low","status":{"key":"pending","labels":["Awaiting review"]},"sources":6,"official":6,"filed":"2026-10-29","updated":"2026-10-29","orgs":["Anthropic","OpenAI","Yale University","University of North Carolina at Chapel Hill"]},{"id":"2026-10-17-2d-euler-unforced-nonuniqueness-lp-vorticity-ai","url":"https://postcutoff.com/e/2026-10-17-2d-euler-unforced-nonuniqueness-lp-vorticity-ai/","date":"2026-10-17","date_precision":"day","short_title":"2D Euler non-uniqueness without force claimed three times, all with AI","deck":null,"takeaway":"Uniqueness of 2D Euler solutions is known for bounded vorticity (Yudovich, 1963). With a force, Vishik showed in 2018 that it fails for vorticity in L^p, p > 2. Without a force this stayed open. Within ten days, three groups posted proofs that it fails there as well. On 17 Oct Umberto Pappalettera and Massimo Sorella posted on Hexagon a manuscript 'developed autonomously by ChatGPT 6.1 Sol'. They claim no authorship and run a reading group to check it. On 22 Oct Matei Coiculescu (NYU) posted Part I of a two-part proof whose details, code and text were 'largely produced with Claude Opus 5.5'. His repository has a Lean 4 formalization of the whole proof, with no sorry. On 27 Oct Hyungjun Choi (Princeton) posted an 86-page construction, with ChatGPT completing technical steps. As of 29 Oct we found no expert assessment of any of the three.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":9,"official":6,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Anthropic","Hexagon Mathematics Foundation"]},{"id":"2026-10-07-chenglong-ma-hovey-strickland-openai-chatgpt-upload-provenance","url":"https://postcutoff.com/e/2026-10-07-chenglong-ma-hovey-strickland-openai-chatgpt-upload-provenance/","date":"2026-10-07","date_precision":"day","short_title":"Hovey–Strickland: author says OpenAI's paper matches his ChatGPT-uploaded draft","deck":null,"takeaway":"OpenAI's 6 Oct maths release includes a paper dated 24 Sept that proves Chai's invariant-ideal conjecture and, through Barthel–Heard–Naumann, the Hovey–Strickland classification of thick tensor ideals of dualizable K(n)-local spectra (family 311). The next day Copenhagen mathematician Chenglong Ma posted his own proof on arXiv. In it he writes that OpenAI's 'proof strategy and specific choices of notation are identical to a preliminary version of the present paper that was uploaded to ChatGPT on September 8, 2026.' OpenAI's paper does not mention him. He also reports an independent proof by Ningyi Li. We found no response from OpenAI as of 29 Oct. The allegation has not been examined publicly beyond a GitHub label and a one-comment Hacker News thread.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":6,"official":3,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","University of Copenhagen"]},{"id":"2026-10-06-openai-borsuk-conjecture-dimension-nine-counterexample","url":"https://postcutoff.com/e/2026-10-06-openai-borsuk-conjecture-dimension-nine-counterexample/","date":"2026-10-06","date_precision":"day","short_title":"Borsuk's conjecture fails in dimension 9 (OpenAI claim, Lean-checked)","deck":null,"takeaway":"A manuscript in OpenAI's 6 Oct 2026 maths release (family 156, dated 23 Sept) claims that the compact set of rank-one projectors onto lines in ℝ⁴, a copy of real projective 3-space in a 9-dimensional space, cannot be cut into ten pieces of smaller diameter. That would make 9 the smallest known dimension in which Borsuk's 1933 conjecture fails. The record had been 63, set in May 2026 with a finite 321-point set. The main theorem has a Lean proof, which a community Comparator run accepted. Gil Kalai called it 'a major progress' and said the topological proof 'looks very beautiful', but added that it still needs careful checking. The example is infinite, so for finite sets the record is still 63. Gábor Damásdi showed that every finite subset of it can be split into eight smaller pieces.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":18,"official":10,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI"]},{"id":"2026-10-06-hexagon-repository-llm-assisted-math","url":"https://postcutoff.com/e/2026-10-06-hexagon-repository-llm-assisted-math/","date":"2026-10-06","date_precision":"day","short_title":"Hexagon launches: a new arXiv-style repository for LLM-assisted mathematics papers","deck":null,"takeaway":"It is the first dedicated infrastructure for AI-generated mathematics backed by leading mathematicians, and it accepts work that no human claims to understand.","category":"research","category_label":"Research","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":2,"official":2,"filed":"2026-10-07","updated":"2026-10-29","orgs":["Hexagon Mathematics Foundation"]},{"id":"2026-10-05-random-k-sat-satisfiability-conjecture-carenini-openai","url":"https://postcutoff.com/e/2026-10-05-random-k-sat-satisfiability-conjecture-carenini-openai/","date":"2026-10-05","date_precision":"day","short_title":"Random k-SAT threshold exists for every k ≥ 3: a human proof and an OpenAI Lean-checked proof","deck":null,"takeaway":"The satisfiability conjecture says that random k-SAT switches from satisfiable to unsatisfiable at one limiting clause density α_k. Friedgut proved a sharp but possibly n-dependent threshold in 1999. Ding, Sly and Sun proved the conjecture for large k (Annals, 2022). On 5 Oct 2026 Cambridge PhD student Gaia Carenini posted on ECCC a proof for every fixed k ≥ 3. Her report states that none of its arguments was generated by a language model. The next day OpenAI's maths release included a separate proof, dated 25 Sept, which credits Carenini with priority. Its Lean statement was accepted in the community Comparator run, and it adds Θ(n) hitting-time variance and computability of the 3-SAT threshold. Neither proof has had a published expert assessment as of 29 Oct. Neither determines the value of α_3.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":8,"official":8,"filed":"2026-10-29","updated":"2026-10-29","orgs":["University of Cambridge","OpenAI"]},{"id":"2026-10-02-linnik-constant-3-99-naslund-claude-gpt-astra","url":"https://postcutoff.com/e/2026-10-02-linnik-constant-3-99-naslund-claude-gpt-astra/","date":"2026-10-02","date_precision":"day","short_title":"Linnik's constant ≤ 3.99, written by Claude Opus 5.5 and GPT Astra","deck":null,"takeaway":"Linnik proved in 1944 that the least prime congruent to a mod q is at most q^L for an absolute constant L. Heath-Brown brought L down to 5.5 in 1992 and Xylouris to 5. On 2 Oct Eric Naslund posted on Hexagon a computer-assisted proof that L ≤ 3.99. It rests on a weighted form of a Heath-Brown lemma that Heath-Brown said no neat way of achieving 'seems available'. The paper says it was written, and the research carried out, by Claude Opus 5.5 and GPT Astra 6 under Naslund's prompting and supervision, with some formalization by Grok. Two components are Lean-verified on Palomar; the final bound itself is not. Hexagon lists human understanding as 'some parts', and we found no expert assessment as of 29 Oct.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-29","updated":"2026-10-29","orgs":["Anthropic","OpenAI","xAI"]}],"people":[{"id":"terence-tao","name":"Terence Tao","url":"https://postcutoff.com/person/terence-tao/"},{"id":"benjamin-antieau","name":"Benjamin Antieau","url":"https://postcutoff.com/person/benjamin-antieau/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-29","type":"filed","text":"Created (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](https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing/))"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-10-29","run":null,"sources_read":null,"updated":"2026-10-29","human_review":null,"version":{"date":"2026-10-29"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":182,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":121,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":212,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":151,"in_training_data":false}],"short_url":null}