{"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/","md":"https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing/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","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":[{"n":1,"title":"arXiv 2610.37476: No Connectedness Lemma for Alexandrov spaces (Nienhaus, Wulle)","url":"https://arxiv.org/abs/2610.37476","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"arXiv 2610.37560: Boundary Plateau Laws II (De Lellis, Glaudo)","url":"https://arxiv.org/abs/2610.37560","type":"paper","group":"primary","domain":"arxiv.org"},{"n":3,"title":"arXiv 2610.36215: Explicit Reed–Solomon subspace designs (Alrabiah, Goyal, Guruswami)","url":"https://arxiv.org/abs/2610.36215","type":"paper","group":"primary","domain":"arxiv.org"},{"n":4,"title":"arXiv 2610.36179: Mutation-acyclicity in rank four is decidable but not semialgebraic","url":"https://arxiv.org/abs/2610.36179","type":"paper","group":"primary","domain":"arxiv.org"},{"n":5,"title":"arXiv 2610.36620: Diameter bounds and finiteness of graphs from local intersection data (Kaizhe Chen)","url":"https://arxiv.org/abs/2610.36620","type":"paper","group":"primary","domain":"arxiv.org"},{"n":6,"title":"arXiv 2610.37616: Generic tensor products are not maximal (Tyomkyn)","url":"https://arxiv.org/abs/2610.37616","type":"paper","group":"primary","domain":"arxiv.org"},{"n":7,"title":"arXiv 2610.37246: Non-convergence in heterogeneous Hegselmann–Krause dynamics (Hegarty, Ognissanti, Wedin)","url":"https://arxiv.org/abs/2610.37246","type":"paper","group":"primary","domain":"arxiv.org"},{"n":8,"title":"arXiv 2610.36771: A bounded closed convex set in c₀(ℂ) without modulus support functionals (Luo)","url":"https://arxiv.org/abs/2610.36771","type":"paper","group":"primary","domain":"arxiv.org"},{"n":9,"title":"arXiv 2610.36741: The Costa surface with a free-boundary hole (Kozyrev)","url":"https://arxiv.org/abs/2610.36741","type":"paper","group":"primary","domain":"arxiv.org"},{"n":10,"title":"arXiv 2610.37399: Representation and abelianization growth (Jezernik)","url":"https://arxiv.org/abs/2610.37399","type":"paper","group":"primary","domain":"arxiv.org"},{"n":11,"title":"arXiv 2610.37075: All strict Calabi–Yau threefolds of height one lift to characteristic 0 (Ward)","url":"https://arxiv.org/abs/2610.37075","type":"paper","group":"primary","domain":"arxiv.org"},{"n":12,"title":"arXiv 2610.37659: Sharp stability of Brenier potentials (Letrouit, Manole)","url":"https://arxiv.org/abs/2610.37659","type":"paper","group":"primary","domain":"arxiv.org"},{"n":13,"title":"arXiv 2610.36240: The Keller problem for Dirac operators (Gontier, Van Den Bosch)","url":"https://arxiv.org/abs/2610.36240","type":"paper","group":"primary","domain":"arxiv.org"},{"n":14,"title":"arXiv 2610.36483: Log-concavity of longest increasing subsequence (Yupeng Li)","url":"https://arxiv.org/abs/2610.36483","type":"paper","group":"primary","domain":"arxiv.org"},{"n":15,"title":"arXiv 2610.37512: Coprime matchings of divisor sets (Alekseyev)","url":"https://arxiv.org/abs/2610.37512","type":"paper","group":"primary","domain":"arxiv.org"},{"n":16,"title":"arXiv 2610.35882: A counterexample to a Bourgain–Brezis sum-space estimate (Chenye Zhang)","url":"https://arxiv.org/abs/2610.35882","type":"paper","group":"primary","domain":"arxiv.org"},{"n":17,"title":"arXiv 2610.36577: Unconditional space-approximation lower bound for semi-streaming matching","url":"https://arxiv.org/abs/2610.36577","type":"paper","group":"primary","domain":"arxiv.org"},{"n":18,"title":"arXiv 2610.37635: Classical verification of quantum computation beyond the polynomial hierarchy (Mantri)","url":"https://arxiv.org/abs/2610.37635","type":"paper","group":"primary","domain":"arxiv.org"},{"n":19,"title":"arXiv 2610.36494: Counting by the Book: verifying Alaska's ranked-choice elections (Horowitz)","url":"https://arxiv.org/abs/2610.36494","type":"paper","group":"primary","domain":"arxiv.org"},{"n":20,"title":"Zenodo 23731787: A finitely presented nonindicable subgroup of a free profinite group (Lupini)","url":"https://zenodo.org/records/23731787","type":"paper","group":"primary","domain":"zenodo.org"},{"n":21,"title":"Zenodo 23750303: A torus with eleven convex quadrilateral faces (Seamons)","url":"https://zenodo.org/records/23750303","type":"paper","group":"primary","domain":"zenodo.org"},{"n":22,"title":"Science, 22 Oct: AI biosecurity must include agriculture (Feldman, Feldman, Sabeti)","url":"https://www.science.org/doi/10.1126/science.ael7324","type":"paper","group":"primary","domain":"science.org"},{"n":23,"title":"Science Advances: Machine psychology for language models (Hagendorff et al.)","url":"https://www.science.org/doi/10.1126/sciadv.aec1912","type":"paper","group":"primary","domain":"science.org"}],"official":23,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Anthropic","various researchers"],"title":"AI-assisted results in the 29 Oct 2026 sweep: 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","summary":"Catalogue of AI-disclosing papers from the 28 Oct 2026 arXiv announcement (submissions of 26–27 Oct) and of Zenodo, repository and journal items, beyond those with their own entries. Highlights: Nienhaus and Wulle answer Wilking's 2007 question with counterexamples \"first found by OpenAI's ChatGPT-6-Astra with minimal human input\"; De Lellis and Glaudo's \"Boundary Plateau Laws II\", whose \"main idea … is due to an LLM\"; explicit Reed–Solomon codes list-decodable to capacity with optimal list size, where GPT-5.6 Sol \"found one of the central ideas\" (Alrabiah, Goyal, Guruswami); mutation-acyclicity of rank-four quivers decided, results \"discovered by GPTAstra\" and formalized in Lean; Kaizhe Chen's diameter bounds settling or refuting five named conjectures with ChatGPT 6 Astra; Tyomkyn's counterexamples to Mason's tensor-product conjecture found by ChatGPT 6.","key_facts":["Own entries: 2026-10-06-openai-log-abundance-nonvanishing-claim (Liu, 2610.35913), 2026-10-06-openai-l-equals-rl-equals-bpl-lean-claim (oai-math-revised re-check), 2026-10-27-ramsey-r3333-upper-bound-61-ai-lean-sat (Tatarevic, 2610.36648), 2026-10-27-banach-mazur-distance-cube-sharp-exponent-gpt-6 (Friedland, 2610.36917). Enriched: Reed–Solomon list decoding (Alrabiah–Goyal–Guruswami), BootLoops and Virtual Biotech (Science, 22 Oct issue), the arXiv hallucinated-references ban and Claude's text watermarks (Nature correspondence, 27 Oct), Navier–Stokes (BBC, 28 Oct)","Wilking's Connectedness Lemma fails for Alexandrov spaces, answering 'a 2007 question of Wilking', in both the ordinary and the dual form (Jan Nienhaus, Dennis Wulle; 2610.37476): 'The explicit counterexamples were first found by OpenAI's ChatGPT-6-Astra with minimal human input. The structuring of the exposition, including all statements and proofs as appearing in this article, was done by the authors.'","Boundary Plateau Laws II (Camillo De Lellis, Federico Glaudo; 2610.37560): classifies 2-dimensional cones in ℝ³ that contain a line ℓ and are Almgren minimizing with respect to ℓ, and shows that the cones over the cube's 1-skeleton and the 'thin fish' are not minimizing. Abstract: 'The main idea of this paper is due to an LLM, and the paper was written by an LLM, under the guidance of the authors.' De Lellis sits on the IAS Advisory Group on Mathematics and AI","Explicit Reed–Solomon subspace designs (Omar Alrabiah, Rohan Goyal, Venkatesan Guruswami; 2610.36215): explicit RS codes over extension fields, list-decodable from a 1−R−ε fraction of errors with the optimal list size O((1−R)/ε), plus line decoding and proximity gaps. 'Our key results, and the paper writing were substantially aided by the use of ChatGPT 5.6 Sol and ChatGPT 6 Astra'; GPT-5.6 Sol 'found one of the central ideas in the paper', replacing Guruswami–Xing's subfield evaluation and Frobenius method with a small family of automorphisms generating the Galois group","Rank-four quiver mutation (Kymani Armstrong-Williams, Edward Hirst, Blake Jackson, Kyu-Hwan Lee; 2610.36179): mutation-acyclicity of four-vertex quivers is decidable, and no semialgebraic criterion exists for n ≥ 4. 'After being prompted at length by the authors, the main results were discovered by GPTAstra (OpenAI) and the original statements were formalized in Lean (https://github.com/KTKAW/rank4-paper)'; the paper also corrects the authors' earlier rank-four criterion","Five graph conjectures in one paper (Kaizhe Chen; 2610.36620): diam ≤ 4 + 8 log(k/(λ+2)) for amply regular graphs; the Brouwer–Cohen–Neumaier bound confirmed for μ > λ+1 with counterexamples at μ = λ; the Qiao–Park–Koolen conjecture proved; Terwilliger's 1983 finiteness conjecture for s > 2, c > 2, (s,c) ≠ (4,3); Weetman's conjecture (μ > 1), his stronger one disproved; Soicher's 1992 conjecture. 'The proofs in this paper were developed with substantial contributions from ChatGPT 6 Astra', with the author supplying 'the underlying proof framework and key ideas'","Counterexamples found by models: Tyomkyn (2610.37616) disproves the uniform tensor-product form of Mason's conjecture and the Jackson–Tanigawa hyperconnectivity conjecture ('The counterexamples were found by ChatGPT 6'; it 'found the 9 × 9-counterexample. The rest was routine'); Hegarty, Ognissanti and Wedin (2610.37246) give a non-convergent opinion vector for synchronized bounded-influence Hegselmann–Krause dynamics, finishing the 2012 Mirtabatabaei–Bullo conjectures ('The examples in Section 2 were found by Claude Opus 5.5. Many prompts were tried and failed…'); Wang and Lim (2610.37568) prove Stiefel geodesics have no closed form, after 'ChatGPT-6 Astra … was used to search for a (k, n) = (2, 4) counterexample'; Xin Luo (2610.36771) answers two Deville–Godefroy–Zizler questions negatively: 'The key construction and an initial proof of the main theorem were generated by OpenAI's ChatGPT'","Constructions and arguments by Claude: Kozyrev (2610.36741), an embedded exterior free-boundary minimal surface with three ends from the Costa surface: 'Anthropic's Claude models proposed the construction, carried out the numerical experiments, made the pictures and drafted the text', with the proofs audited by five independent Claude agents; Jezernik (2610.37399), rep_k(G) ≤ exp((d−1)k log k + O(dk))·ab_k(G) and at most exp(O(log⁴ m)) finite primitive subgroups of GL_m(ℂ): 'the outcome of a long conversation with Anthropic's language models Claude Opus 5 and Claude Opus 5.5'; Ward (2610.37075), every strict Calabi–Yau threefold of height one lifts to W(k), disproving an Achinger–Zdanowicz conjecture: 'I'm sure that the models I used (a cheap, lowest-tier Claude subscription) could not have produced this paper on their own. I'm also sure I could not have produced this paper without the months of discussions I had with the models.'","Racing the OpenAI release: Letrouit and Manole (2610.37659) had worked on Letrouit's conjecture without AI since March, but after OpenAI's 6 Oct release claimed it (Proposition 5.1 of an OpenAI document) 'we decided to use AI to find the arguments that we were missing'. Gontier and Van Den Bosch (2610.36240) leave a 3-d zero-mode potential as a conjecture: 'ChatGPT Astra seems to have found a way to construct such a 3-d potential … But since we do not yet fully understand its proof, and since we wanted to keep the present article free of AI generated proofs, we prefer to name this result a conjecture'","Named conjectures proved with AI help: Chen's log-concavity of the longest-increasing-subsequence distribution (Yupeng Li, 2610.36483; GPT-6 Astra 'for assistance with mathematical discussions'); McNew–Pomerance on coprime matchings of divisor sets (Max Alekseyev, 2610.37512; GPT-6 Astra Pro for 'mathematical exploration … proof development and assessment'); Davies–Krawczyk–McCarty–Walczak χ ≤ min{3^{ω−1}, 18ω³} for capped graphs (Hongyang Wang, 2610.37578; ChatGPT for 'the direct elimination argument in the proof of Lemma 2.1'); Clark's finiteness conjecture in ranks ≥ 3 (Zilong He, 2610.37377; GPT-5.6 Sol 'to assist with exploring the proof strategy'); Hoge's B₂ duality (Shota Maehara, 2610.36547; ChatGPT gave 'a first idea to approach Theorem 1.2'); conjectured optimal SSP coefficients for implicit Runge–Kutta orders 2 and 3 (2610.37425); the Akbari–Ghandehari–Hadian–Mohammadian conjecture for even matrix size (2610.37150); Brezis's Open Problem 7.1, refuted in every N ≥ 2 (Chenye Zhang, 2610.35882; GPT-5.6 Sol for 'exploratory calculations, proof organization')","Theoretical CS: the first unconditional pass/approximation lower bound for semi-streaming matching, Ω(log(1/ε)) passes for a (1−ε)-approximation (Yang P. Liu, Kheeran Naidu, Hoai-An Nguyen, Janani Sundaresan; 2610.36577), whose second proof ChatGPT 5.5 Pro drafted 'from an author-provided outline'; classical verification of quantum computation beyond PH relative to an oracle (Atul Mantri; 2610.37635), with GPT-6.1 Sol and GPT-6 Astra contributing 'substantially to developing the proof of Theorem 1.7'; input-queued switch queues within any exponent of the conjectured O(n/(1−ρ)) (Ameen, Wang; 2610.37521): 'GPT 6 Astra was used to write the formal proof in Appendix B'; polynomial-time mixed evacuation (Kamiyama; 2610.37065): 'The main idea of the proof was obtained by using GPT-5.6 Luna and GPT-6 Astra'","Smaller AI roles: Bizoń and Kluszczyński (2610.36784) prove a third self-similar Yang–Mills profile in every odd d ≥ 11 and check uniqueness for 11 ≤ d ≤ 101 with 'AI-assisted exact root-counting computations'; Jeffrey Shallit obtained a lemma in Letouzey's Rocq-certified Hofstadter paper 'with the help of ChatGPT 5.5 Extended' (2610.35994); Aougab–Gaster–Miller (2610.37551): 'The idea for the proof of Lemma 10 was obtained by an LLM which will remain unnamed'; Kania–Kąkol (2610.36194) answer Aliaga's question after asking ChatGPT whether their results could reach it; Gan–Oh–Shin's sharp helical maximal estimates for p > n (2610.37250) used ChatGPT-6 'for discussions'; Bang-Jensen et al. (2610.36895) built an infinite counterexample family with 'AI-assisted tools'","Formal methods: Lucy Horowitz (2610.36494) formalizes Alaska's ranked-choice tabulation in Lean and finds 75 ballot records in 10 of 115 contests counted differently from her reading of the rules, with no winner changed (LLMs helped with proof construction); Sewon Park (2610.37498) builds a model in which global choice holds without excluded middle, developed and formalized in Rocq with Claude Opus 5.5; LeanTrail (2610.35926) audits whether a Lean repository proves what a paper states, with a model matching statements and a deterministic dependency audit","Zenodo (unrefereed): Martino Lupini (Bologna, 23731787) disproves Jaikin-Zapirain's conjecture that free profinite groups are locally indicable, with ChatGPT, Codex and Claude used for 'mathematical exploration, proof development'; John Seamons (23750303) gives a torus with eleven convex quadrilateral faces, refuting a 2009 Grünbaum–Szilassi conjecture ('OpenAI GPT6 was used to assist with computational search strategy, code development, verification workflows'); Henry Shin (23749631) claims Miller's Noetherianity conjecture (ChatGPT for 'proof development'). A four-page Zenodo note (Stefan Best, 23717719) says the OAI Lean libraries behind OpenAI's proofs 'are omitted from the public repository'; the repository's lean/OAI folder with InformationTheory, MeasureTheory, Topology and ModelTheory was present when we checked on 29 Oct. Most other Zenodo hits were off topic or unassessable","Repositories: no new results in google-deepmind/formal-conjectures beyond #777 and #1202 (earlier listings); oai-math-revised added the L = RL = BPL re-check (own entry), Pasechnik's crossing-number forest (in the crossing-number entry), agent notes for the 26 Oct ETH and local-smoothing papers, and a note that 9 comparator configurations (Brenier, DefocusingNLS, EuclideanFiveColor, KServer, LogspaceEquality, Naimark, OccupiedOverlap, Rokhlin, SpinAngle) compared some definitions only by type until OpenAI's 26 Oct fix. New repos from watched accounts (DeepMind's detectorscope, Anthropic's single-agent-loop-kit, Qwen's BlenderWorld, Epoch's chess-puzzles mirror) are tooling, not results","Journals: Science (22 Oct) carried a policy piece by Jonathan Feldman, Tal Feldman and Pardis Sabeti, 'AI biosecurity must include agriculture', and Pietro Michelucci's 'The AI debate is missing half the system'. Science Advances published a review, 'Machine psychology for language models' (Hagendorff, Dasgupta, Binz, Chan, Lampinen, Wang, Akata, Schulz), and a robotics-plus-machine-learning workflow that screened about a billion biobased packaging formulations","Scanned, no AI statement (out of scope, kept in data/_offscope.md): optimality of the Brjuno condition for all neutral polynomials, resolving Douady's 1980s conjecture (Dudko, Luo, Zhang; 2610.37468); the optimal threefold additive energy on lattice circles and Bourgain's toral eigenfunction conjecture for p < 6 (Xie, Zhang; 2610.37423); the Dong–Ren conjecture, the converse of Zhu's modular invariance theorem (Wang, Yang; 2610.36565)"],"key_numbers":[],"tags":["math","computer-science","physics","arxiv","zenodo","catalogue","chatgpt","gpt-6-astra","gpt-6-pro","gpt-6-1-sol","gpt-5-6-sol","claude","claude-opus-5-5","fable-5","codex","lean","rocq"],"science":{"field":"mathematics","subfield":"multiple (Riemannian and Alexandrov geometry, geometric measure theory, coding theory, cluster algebras, algebraic graph theory, matroids, functional analysis, TCS)","problem":"See list","result":"Catalogue of AI-assisted results in the 28 Oct 2026 arXiv announcement, Zenodo and result repositories, beyond those with their own entries","open_since":"","ai_system":["GPT-6 Astra","GPT-6 Astra Pro","GPT-6","GPT-6 Pro","GPT-6.1 Sol","GPT-5.6 Sol","GPT-5.6 Luna","ChatGPT 5.5 Pro","Claude Opus 5","Claude Opus 5.5","Codex"],"human_role":"From model-found counterexamples and model-written papers to AI checking and editing","verification":{"key":"lean","label":"Lean-verified","text":"Unrefereed arXiv and Zenodo preprints; Lean or Rocq formalizations where stated"},"status":"pending","shock":"","verified_by":["preprint","lean"],"kind":"batch"},"body_md":"## What happened\n\nThe arXiv API failed again, so the sweep read the 28 Oct listing pages instead. It found 43 uncited papers with an AI statement and\n42 conjecture papers without one. We then scanned the PDFs of every remaining new or cross-listed submission in math, cs.CC, cs.DS\nand cs.DM (405 papers), since earlier runs showed that strong results often carry no AI word in the abstract. That scan found the\nBanach–Mazur paper, the Reed–Solomon codes, De Lellis–Glaudo and about a dozen other items above. All quotes come from the PDFs. The\nday's biggest finds came through human papers and community checks rather than lab posts: Jihao Liu's priority remark on OpenAI's\nabundance claim, and a volunteer's re-check of OpenAI's Lean proof of L = RL = BPL.\n\n## Why it matters\n\nThe authors' accounts are getting more specific about who did what. Some papers keep model output out on purpose: Gontier and Van\nDen Bosch call a result a conjecture because they do not understand ChatGPT Astra's proof. Others hand the whole idea and the\nwriting to a model, as in the De Lellis–Glaudo paper. OpenAI's release is also changing how human teams work: Letrouit and Manole\nturned to AI only after OpenAI claimed their conjecture.","disputed":[{"label":"Verification","text":"Unrefereed arXiv and Zenodo preprints; Lean or Rocq formalizations where stated","sources":[]}],"related":[{"id":"2026-10-29-ai-assisted-results-october-29-listing-2","url":"https://postcutoff.com/e/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":30,"official":29,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Anthropic","Google DeepMind","various researchers"]},{"id":"2026-10-28-ai-assisted-results-october-28-listing","url":"https://postcutoff.com/e/2026-10-28-ai-assisted-results-october-28-listing/","date":"2026-10-28","date_precision":"day","short_title":"AI-assisted results in the 28 Oct 2026 sweep","deck":"Bialostocki–Lotspeich (1992), part of Gross–Prasad in geometric Langlands, Fuglede in 𝔽₂⁸, a TEMPO structure found by Claude, agent swarms on fractional Chern insulators, and a human digest of GPT-6 Astra's Smale counterexample","takeaway":"The 28 Oct sweep covered the arXiv announcement of 26–27 Oct submissions and late papers from 23–26 Oct. Five results have their own entries: Axiom's Lean proof of the Classification of Finite Simple Groups, OpenAI's spin-one Haldane gap proof (found through Hal Tasaki's follow-up), OpenAI's De Giorgi dimension-eight claim, Morgan–Mullen with Claude and Lean, and formula minimization with GPT-Sol-6.1. This page lists the rest. Claude, GPT-6 Astra and GPT-6 Pro supplied ideas, counterexamples or whole arguments in papers on zero-sum sequences, geometric Langlands, quantum dynamics, fire-blocking and spectral bounds.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":21,"official":19,"filed":"2026-10-28","updated":"2026-10-28","orgs":["OpenAI","Anthropic","Google DeepMind","various researchers"]},{"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-ramsey-r3333-upper-bound-61-ai-lean-sat","url":"https://postcutoff.com/e/2026-10-27-ramsey-r3333-upper-bound-61-ai-lean-sat/","date":"2026-10-27","date_precision":"day","short_title":"R(3,3,3,3) ≤ 61 with AI, Lean and SAT","deck":null,"takeaway":"Milos Tatarevic proves that every 4-colouring of the edges of K₆₁ has a monochromatic triangle, so R(3,3,3,3) ≤ 61. The bound had been 62 since Fettes, Kramer and Radziszowski in 2004, and the best lower bound is 51. The proof combines a double-counting argument, classifications of small neighbourhoods and 56,723 SAT formulas, each refuted by both Kissat and CaDiCaL. A Lean 4 formalization checks the reductions but not the SAT part. The paper says AI tools 'assisted extensively': GPT-6 Astra in Codex contributed one of the reductions, and GPT-5.6 in Codex and Fable 5 in Claude Code the others. It is an unrefereed preprint, and no expert comment was found as of 29 Oct.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-29","updated":"2026-10-29","orgs":["Impossible Research","OpenAI","Anthropic"]},{"id":"2026-10-27-banach-mazur-distance-cube-sharp-exponent-gpt-6","url":"https://postcutoff.com/e/2026-10-27-banach-mazur-distance-cube-sharp-exponent-gpt-6/","date":"2026-10-27","date_precision":"day","short_title":"Sharp exponent 2/3 for the Banach–Mazur distance to the cube","deck":null,"takeaway":"Omer Friedland (Sorbonne Université) proves that some n-dimensional normed spaces are at Banach–Mazur distance at least c·n^{2/3}/(log 2n)^10 from the cube ℓ∞ⁿ. With the n^{2/3} upper bound of Friedland, Naor and Youssef from August 2026, the maximal distance is n^{2/3+o(1)}. That settles the exponent in a problem going back to Grünbaum (1960), after a run of improvements from both sides: 5/9, 4/7 and 5/8 below, and 7/8, 5/6 and 2/3 above. The examples are polars of random Gaussian polytopes. Friedland says the strategy is his, and that 'at the author's request, OpenAI's ChatGPT (GPT-6) generated a proof' of a key proposition. Unrefereed preprint.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-29","updated":"2026-10-29","orgs":["Sorbonne Université","OpenAI"]},{"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":"2026-10-17-2d-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":"2026-10-06-openai-log-abundance-nonvanishing-claim","url":"https://postcutoff.com/e/2026-10-06-openai-log-abundance-nonvanishing-claim/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI claims the abundance conjecture; Jihao Liu raises priority","deck":null,"takeaway":"A manuscript in OpenAI's 6 Oct 2026 math release, 'Log abundance in characteristic zero' (dated 24 Sept), claims the log abundance conjecture in every dimension in characteristic zero, and with it canonical nonvanishing for smooth projective varieties. Both are central open problems of the minimal model program, proved only up to dimension three. Companion papers claim Iitaka's subadditivity conjecture and related results. On 7 Oct Jihao Liu (Peking University) submitted a human-led proof that nonvanishing implies abundance. arXiv announced it only on 28 Oct. His comment line says he was 'forced to submit here due to an announcement of the proof of the abundance conjecture by OpenAI'. In a remark he suggests that an earlier draft, sent to 'codex chat' before July 2026, may have fed OpenAI's work. No birational geometer has assessed the claims publicly, there is no Lean proof, and OpenAI has not responded.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":8,"official":5,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Peking University"]},{"id":"2026-10-06-openai-l-equals-rl-equals-bpl-lean-claim","url":"https://postcutoff.com/e/2026-10-06-openai-l-equals-rl-equals-bpl-lean-claim/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI claims L = RL = BPL with a Lean proof","deck":null,"takeaway":"OpenAI's 6 Oct 2026 math release (family 103, manuscript dated 23 Sept) claims L = RL = BPL. That would mean randomness does not help logarithmic-space computation, a central open problem of complexity theory. The best unconditional bound was Saks and Zhou's O(log^{3/2} n) space, slightly improved by Hoza. A Lean formalization added on 7 Oct proves the equality in an explicit Turing-machine model. The community comparator run of 26 Oct accepted it. A re-check found the proof's definitions identical to the statement file's and the proof built on standard axioms only. It notes that it does not show 'that the machine model is the standard one'. No complexity theorist has assessed it publicly as of 29 Oct.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":7,"official":5,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI"]},{"id":"2026-09-04-reed-solomon-list-decoding-capacity-ai","url":"https://postcutoff.com/e/2026-09-04-reed-solomon-list-decoding-capacity-ai/","date":"2026-09-04","date_precision":"day","short_title":"Reed–Solomon codes list-decoded up to capacity and proximity gaps settled, with GPT-5.6 Sol and ChatGPT 5.6 Pro (Brakensiek–Chen–Putterman–Zhang–Zheng; Jeronimo)","deck":null,"takeaway":"In early September 2026 two preprints settled long-standing problems about Reed–Solomon codes, the most widely used error-correcting codes.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":8,"official":8,"filed":"2026-10-07","updated":"2026-10-29","orgs":["Simons Institute","OpenAI","Ethereum Foundation"]}],"people":[{"id":"jensen-huang","name":"Jensen Huang","url":"https://postcutoff.com/person/jensen-huang/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-29","type":"edit","text":"Science agent run 2: a second pass over the same announcement found more papers with large AI roles, now in part 2 ([AI-assisted results, 29 Oct 2026 (part 2)](https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing-2/)); Choi's 2D Euler paper (2610.37653), Frankl–Wang–Yang–Zhang (2610.37315) and Bun–Juvekar (2610.37634) have own entries"},{"date":"2026-10-29","type":"filed","text":"Created (science agent; arXiv listing pages and PDFs, a beyond-keyword PDF scan of 405 submissions, Zenodo API and PDFs, GitHub API, Crossref, nature.com)"}],"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}