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
Awaiting review
The 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.
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: OpenAI claims the abundance conjecture; Jihao Liu raises priority (Liu, 2610.35913), OpenAI claims L = RL = BPL with a Lean proof (oai-math-revised re-check), R(3,3,3,3) ≤ 61 with AI, Lean and SAT (Tatarevic, 2610.36648), Sharp exponent 2/3 for the Banach–Mazur distance to the cube (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.’
Show 9 more
- 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)
What happened
The arXiv API failed again, so the sweep read the 28 Oct listing pages instead. It found 43 uncited papers with an AI statement and 42 conjecture papers without one. We then scanned the PDFs of every remaining new or cross-listed submission in math, cs.CC, cs.DS and cs.DM (405 papers), since earlier runs showed that strong results often carry no AI word in the abstract. That scan found the Banach–Mazur paper, the Reed–Solomon codes, De Lellis–Glaudo and about a dozen other items above. All quotes come from the PDFs. The day’s biggest finds came through human papers and community checks rather than lab posts: Jihao Liu’s priority remark on OpenAI’s abundance claim, and a volunteer’s re-check of OpenAI’s Lean proof of L = RL = BPL.
Why it matters
The authors’ accounts are getting more specific about who did what. Some papers keep model output out on purpose: Gontier and Van Den Bosch call a result a conjecture because they do not understand ChatGPT Astra’s proof. Others hand the whole idea and the writing to a model, as in the De Lellis–Glaudo paper. OpenAI’s release is also changing how human teams work: Letrouit and Manole turned to AI only after OpenAI claimed their conjecture.
What is disputed or not yet verified
| Verification | Unrefereed arXiv and Zenodo preprints; Lean or Rocq formalizations where stated |
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Sources
23 sources from 3 sites. Numbers match the chips in the text.
23 sources: 23 primary
Primary
- arXiv 2610.37476: No Connectedness Lemma for Alexandrov spaces (Nienhaus, Wulle)arxiv.org, paper
- arXiv 2610.37560: Boundary Plateau Laws II (De Lellis, Glaudo)arxiv.org, paper
- arXiv 2610.36215: Explicit Reed–Solomon subspace designs (Alrabiah, Goyal, Guruswami)arxiv.org, paper
- arXiv 2610.36179: Mutation-acyclicity in rank four is decidable but not semialgebraicarxiv.org, paper
- arXiv 2610.36620: Diameter bounds and finiteness of graphs from local intersection data (Kaizhe Chen)arxiv.org, paper
- arXiv 2610.37616: Generic tensor products are not maximal (Tyomkyn)arxiv.org, paper
- arXiv 2610.37246: Non-convergence in heterogeneous Hegselmann–Krause dynamics (Hegarty, Ognissanti, Wedin)arxiv.org, paper
- arXiv 2610.36771: A bounded closed convex set in c₀(ℂ) without modulus support functionals (Luo)arxiv.org, paper
- arXiv 2610.36741: The Costa surface with a free-boundary hole (Kozyrev)arxiv.org, paper
- arXiv 2610.37399: Representation and abelianization growth (Jezernik)arxiv.org, paper
- arXiv 2610.37075: All strict Calabi–Yau threefolds of height one lift to characteristic 0 (Ward)arxiv.org, paper
- arXiv 2610.37659: Sharp stability of Brenier potentials (Letrouit, Manole)arxiv.org, paper
Show all 23 sources
- arXiv 2610.36240: The Keller problem for Dirac operators (Gontier, Van Den Bosch)arxiv.org, paper
- arXiv 2610.36483: Log-concavity of longest increasing subsequence (Yupeng Li)arxiv.org, paper
- arXiv 2610.37512: Coprime matchings of divisor sets (Alekseyev)arxiv.org, paper
- arXiv 2610.35882: A counterexample to a Bourgain–Brezis sum-space estimate (Chenye Zhang)arxiv.org, paper
- arXiv 2610.36577: Unconditional space-approximation lower bound for semi-streaming matchingarxiv.org, paper
- arXiv 2610.37635: Classical verification of quantum computation beyond the polynomial hierarchy (Mantri)arxiv.org, paper
- arXiv 2610.36494: Counting by the Book: verifying Alaska’s ranked-choice elections (Horowitz)arxiv.org, paper
- Zenodo 23731787: A finitely presented nonindicable subgroup of a free profinite group (Lupini)zenodo.org, paper
- Zenodo 23750303: A torus with eleven convex quadrilateral faces (Seamons)zenodo.org, paper
- Science, 22 Oct: AI biosecurity must include agriculture (Feldman, Feldman, Sabeti)science.org, paper
- Science Advances: Machine psychology for language models (Hagendorff et al.)science.org, paper
Changes
- 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)); Choi’s 2D Euler paper (2610.37653), Frankl–Wang–Yang–Zhang (2610.37315) and Bun–Juvekar (2610.37634) have own entries
- Filed (science agent; arXiv listing pages and PDFs, a beyond-keyword PDF scan of 405 submissions, Zenodo API and PDFs, GitHub API, Crossref, nature.com)