AI-assisted results in the 20 Oct 2026 arXiv listing
Poset dimension proofs found by GPT-6 Astra, Hitchin domination from ChatGPT 5.6 Sol’s ideas, the section conjecture for generic curves, Yau’s geometric conjecture, Erdős–Gyárfás r = 5, a Claude-built Gray-code reduction, and a Lean harness solving 6/6 IMO 2026
Awaiting review
The takeaway
Tuesday’s arXiv announcement was the strongest maths batch yet. Seven results have their own entries, among them the Erdős–Szemerédi sunflower conjecture, Erdős–Hajnal for all paths and a non-sofic hyperbolic group. This page catalogues the next tier: about forty papers whose AI disclosures run from ‘the proofs were found by ChatGPT-6 Astra’ to proofreading.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Lean-verified
- Importance
- 3 of 5
- Last verified
- 20 October 2026
Your AI and this story
- GPT-6 Astra173 days after its cutoff
- Claude Opus 5.5112 days after its cutoff
- Gemini 4 Argon203 days after its cutoff
- Grok 4.7142 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 112 days before it.
Key facts
- Own entries: sunflower (2610.26686), Erdős–Hajnal paths (2610.24887), non-sofic hyperbolic group (2610.24836), integer programming (2610.25955), Sard (2610.24080), hyperrigidity (2610.26556), lemniscate (2610.26539). Enriched: zeta two-thirds (Arias de Reyna, 2610.24612), Jacobian conjecture (de Bondt, 2610.24889)
- Poset dimension (Jędrzej Hodor, Piotr Micek, William T. Trotter; 2610.24774): for every d ≥ 3 there is α < 1 with posets excluding the standard example S_d having dimension O_d(n^α); for d = 3, O(n^(2/3) log n) and a construction of dimension Ω(n^(1/3)/log n). AI statement: ‘The proofs were found by OpenAI’s ChatGPT-6 Astra. The authors digested the initially generated output and made an effort to present the argument in a readable and optimized form.’
- Hitchin representations (Subhojoy Gupta; 2610.24606): every Hitchin representation dominates one in Hit_n(S)′ in the Hilbert length spectrum, ‘this confirms a conjecture of Lee-Zhang and, independently, Tholozan who had proved this for n = 3’. ‘The key ideas in this note, specifically the convexity of the log-spectral radius function in Corollary 3.2 and the use of the Brouwer fixed-point theorem in the proof of Theorem 1.1, are due to ChatGPT 5.6 Sol.’ Written entirely by the author
- Grothendieck’s section conjecture for the generic n-pointed genus-g curve (g ≥ 3, n ≥ 1) over function fields of M_g,n over k/Q (Ma Luo, Tatsunari Watanabe; 2610.24986). ‘The authors used OpenAI’s ChatGPT to assist with literature searches, aid their mathematical review, refine notation, and improve the exposition of their original mathematical ideas and arguments.’ Supporting AI role only
- Yau Geometric Conjecture for isolated hypersurface singularities (Siyuan Fu, Stephen S.-T. Yau, Huaiqing Zuo; 2610.24636), ‘a proof of the long-standing Yau Geometric Conjecture’. ‘AI tools (ChatGPT and DeepSeek) were used … to help with checking calculations and arguments, developing details of proofs using standard techniques, and improving the exposition’
- Erdős–Gyárfás balanced colourings, r = 5 (Hai Xia, Stefan Szeider, TU Wien; 2610.24484): K_26 has no balanced 5-colouring, ‘the first new case settled in over two decades’; SAT-based (CaDiCaL), ‘We used generative AI tools to implement the Lean formalizations’; ‘Code and proofs are checked by tests and the Lean kernel’
- Single-track Gray codes (Chris Dzoba; 2610.24758): the Degni–Drisko (2007) necklace conjecture implies optimal codes for every prime, formalized in Lean; with computation, optimal codes for every odd prime n ≤ 47 (open since 1996; previously n ≤ 19). ‘Claude (Anthropic) wrote and ran the searches and verifiers, found the closing pivots of Theorem A by computer search, wrote the proofs and the Lean formalization, and drafted the text … Separate instances refereed the proof and the formalization, and Codex (OpenAI) wrote two further checkers’
- Crossing numbers (Balogh, Layman, Lidický, Pfender, Salazar, Spiro, Volec; 2610.25204): flag algebras give cr(K_n,n) ≥ 0.96936·Z(n,n) + o(n⁴) toward Zarankiewicz’s conjecture, rectilinear ≥ 0.987·Z(n,n). ‘Both Conjectures 1 and 7 were claimed to be true by OpenAI [26, 27]. ChatGPT-6 was used to assist with writing Section 3’; ChatGPT-6 also found an integer-overflow bug in their search program
Show 11 more
- Strong Erdős–Frankl–Füredi cover-free conjecture (Yanan Hu, Leilei Zhang; 2610.24442): T(r) ≥ (r+1)² for all r, with equality when r+1 is a prime power. ‘At an early stage of this work, AI tools were used to assist in developing proofs.’
- Siemons–Wagner property and Bradley’s conjecture (Zhilin Zhang; 2610.24502): classification of 2-transitive groups with property ⋆3, settling Bradley’s thesis conjecture. ‘When this work had long been stalled, it was GPT6-Astra that opened a new line of thought and helped break the impasse’; Astra also wrote and debugged the GAP census scripts
- Super-localization conjecture (Moritz Hauck, Chupeng Ma, Daniel Peterseim; 2610.25230): short proof of the exp(−c n^(1/(d−1))) Kolmogorov n-width decay conjectured by Ma (FoCM 2026). ‘ChatGPT was used to develop the central arguments in the proof of Theorem 1. In particular, it identified the energy-determinant argument of Li and Wang [9] and suggested adapting it’
- Michaelis–Menten networks (Eduardo D. Sontag; 2610.24351): global stability, stated as an open problem by Blanchini–Breda–Giordano–Liessi, holds without connectedness or non-degeneracy hypotheses; ‘The author worked closely with several AI assistants to brainstorm ideas, search the literature, develop proofs, check arguments, and write and edit the paper’
- Counterexamples suggested or generated by AI: wave observability under GCC with a smooth time-periodic potential (Liao, Lü, Zhang; 2610.25327: an AI tool was used ‘in particular, to suggest the counterexample presented in this paper’); heavy-ball non-acceleration in 1D (ETH seminar ‘AI for Mathematics and Optimization’; 2610.25104: ‘Example 3.2 was generated by AI … The counterexample in Section 5 was generated by AI and verified by the authors’); Nesterov gradient restart never occurring (Bao, Chen, Li, Sun; 2610.26546: ‘GPT-6 was used as an auxiliary tool to help develop the counterexample construction’); Reich’s fixed-point problem answered negatively (Luong Van Nguyen; 2610.25156: ChatGPT for ‘assistance in conceptualizing the example’); Costantino–Frigerio–Martelli–Petronio geometric triangulation conjecture refuted with a 2,688-tetrahedron triangulation (Ke Feng, Aijin Lin; 2610.25217; ChatGPT helped explore ‘proof strategies and calculations’)
- Analysis and operator theory: Baranov–Bessonov–Kapustin conjecture proved (Bellavita, Virtanen; 2610.26232: ‘suggestions generated by ChatGPT-6 contributed to the formulation and organization of the argument that appears in Section 4’); CAT(0) maximal monotone vs surjectivity, negative and partial answers (Chaipunya; 2610.25080; Claude Opus 5.5 drafted and revised ‘parts of the text and proofs’); Schoen conjecture for Weil–Petersson circle maps (Martin, Yao; 2610.25580: work predates generative AI, but Claude and GPT, asked ‘what have we missed’, pointed to Riestenberg–Smillie and Ripoll–Tomi, which ‘overcame some gaps in our argument’); translation-invariant pure states with exotic half-chain factors (Liu, Yi, Perimeter; 2610.24154; GPT-5.6 Sol and Claude Opus 5.5 ‘used extensively’)
- Number theory and combinatorics: sum–product holds for fixed-field lattice products, the constructions used to disprove it over R (Lemley, Chew; 2610.26737: models ‘used substantively during the development of proofs, in some cases proposing key arguments’); Huppert’s ρ–σ conjecture, ρ(n) ≤ 4n − 1 + π(2n) and a gap in Bellotti–Keller–Trudgian fixed (Jabara, Keller; 2610.25571: Claude ‘noticed a couple of inaccuracies and fixed them’); Terao’s freeness conjecture for 15 and 16 lines (Anghel, Stan; 2610.25868; Claude for literature search, programming and drafting); Fuglede’s conjecture in F₂⁷ (Kadowaki; 2610.24022; ‘AI-assisted tools were used in the research’); size Ramsey numbers of two-component star forests, a case of Erdős Problem #561 (Chunlin You; 2610.25958; ChatGPT ‘to assist in exploring proof strategies’); non-uniform Baranyai factorizations (Gao, Li; 2610.24695); zero forcing of P(n,3), P(n,4), proving Krishnan’s Conjecture 5 (2610.24059; AI for ‘Lean proof development’); Erdős–Ginzburg–Ziv for finite groups (Qu; 2610.26122; AI for ‘proofs in the sections on finite simple groups’)
- Algorithms and control: promise colouring in adversarial streams, 3- vs 6-colourable in O(n^(3/2) log(n/ε) log n) bits (Thoumi; 2610.24644: ‘Theorem 10 and Appendix A were entirely obtained using GPT Astra; the author … takes no credit, but full responsibility’); strategy recovery for mean-payoff games as hard as solving them (Dorfman, Zwick; 2610.25188; ‘Interactions with ChatGPT 5.6 Pro influenced the content of Section 5.2, Section 6 and Section 7’); Witsenhausen’s counterexample, exact boundary of linear optimality and non-definability in o-minimal structures (Lu, Li; 2610.25853; AI expanded the authors’ arguments into derivations); Coppersmith–Winograd as tensor-contraction aggregation (Solomonik, Bläser; 2610.26563; Gemini, ChatGPT and Claude helped develop embeddings and corrections)
- Methods: Maestro (AWS AI Labs, UIUC, Georgia Tech; 2610.25920), an open Lean harness on top of Claude Code or Codex: with Claude Opus 5 it proves 34 of 48 theorems of the June 2026 arXivLean release (19 for the bare agent), 669/672 PutnamBench, 59/60 Lean-IMO-Bench and 6/6 IMO 2026. Safal Aryal’s proof-theoretic study of AI-generated Lean corpora such as OpenAI’s (2610.25357; code written by Claude Code). A Lean-verified curved simplex Hilbert transform with no AI in the mathematics but ‘AI coding agents’ for the formalization (Durcik, Fraccaroli, Roos; 2610.24850)
- Minor roles (editing, proofreading, figures): center conjecture for cyclotomic Hecke algebras (Hu, Mathas, Shi, Webster; 2610.25101); Ramanujan conjecture and RH for unitary groups over function fields (Lomelí; 2610.23985; Claude for editing); Streets–Tian on homogeneous quotients (Cao, Chen; 2610.25229); Landau score iterations (2610.25780); asymptotic dimension and fat minors (2610.22495; figures)
- Scanned in full text, no AI statement (20 Oct): Ward’s divisibility conjecture bound (2610.26200), hyperplane conjecture (2610.26186), rational hit conjecture (2610.26028), factorial separation conjecture (2610.25661), Property C/D inverse zero-sum conjectures (2610.25271), conformal normal metrics counterexample (2610.24541), real Jacobian conjecture vector fields (2610.19360), Abel limit cycles (2610.19340), mutual f-information (2610.21231), NLS tori (2610.22072), four-qubit contextuality degree 315 (2610.26465) and about fifteen others; the sweep’s ML and physics papers with ‘LLM’ in the text are out of scope here
What happened
Tuesday’s arXiv announcement (20 Oct; submissions of 16–19 Oct), together with papers from 13–17 Oct that the sweep had not listed before, had 94 papers that disclose or mention AI use. We read the full text of every uncited mathematics paper among them, plus 28 uncited “conjecture/open problem” papers without a disclosure. Seven results got their own entries. Two more are expert follow-ups to famous AI results. Juan Arias de Reyna re-proves Claude’s two-thirds theorem on zeta zeros for a textbook. Michiel de Bondt stabilizes Alpöge’s Jacobian counterexample down to cubic maps in dimension 12 and to Zhao’s Vanishing Conjecture.
In the papers listed here, AI plays roles of three kinds:
- The AI found the proof: Hodor–Micek–Trotter on poset dimension (“The proofs were found by OpenAI’s ChatGPT-6 Astra”), Thoumi’s streaming theorem, and Dzoba’s Gray codes (Claude did the search, proofs and Lean under the author’s direction).
- AI ideas at a key step: Gupta’s Hitchin note (ChatGPT 5.6 Sol supplied the convexity and fixed-point ideas), Hauck–Ma–Peterseim (ChatGPT found the argument to adapt), Zhang’s Bradley conjecture (Astra “helped break the impasse”), and five papers whose counterexample was suggested or generated by AI.
- Supporting roles: literature, checking, Lean and editing, including in a few famous-name papers: the section conjecture for generic curves, the Yau geometric conjecture with S.-T. Yau, and Balogh et al. on Zarankiewicz’s crossing-number conjecture.
No Hacker News thread or high-reach X post on any of these papers was found on the morning of 20 Oct (web search; the sweep’s HN and X sections list none).
Why it matters
The day’s papers show AI credited with the decisive step on problems that specialists had studied for decades: sunflowers, Erdős–Hajnal and soficity. Authors are also writing more precise disclosures, often citing the Leiden Declaration and naming the lemmas a model proved. Two labs’ models (OpenAI’s Astra and a DeepMind internal model) reached the same Erdős–Hajnal case independently.
What is disputed or not yet verified
| Verification | Unrefereed arXiv preprints; Lean for Erdős–Gyárfás r = 5, Gray-code implication, zero forcing and the simplex Hilbert transform |
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Sources
23 sources from 1 site. Numbers match the chips in the text.
23 sources: 23 primary
Primary
- arXiv 2610.24774: On dimension of posets excluding a standard example (Hodor, Micek, Trotter)arxiv.org, paper
- arXiv 2610.24606: Length-convexity and domination for Hitchin representations (Gupta)arxiv.org, paper
- arXiv 2610.24986: The section conjecture for generic pointed curves (Luo, Watanabe)arxiv.org, paper
- arXiv 2610.24636: The Yau Geometric Conjecture for isolated hypersurface singularities (Fu, Yau, Zuo)arxiv.org, paper
- arXiv 2610.24484: Erdős–Gyárfás balanced five-colorings (Xia, Szeider)arxiv.org, paper
- arXiv 2610.24758: Optimal single-track Gray codes from Gray-ordered necklaces (Dzoba)arxiv.org, paper
- arXiv 2610.25204: Crossing numbers of complete bipartite graphs (Balogh et al.)arxiv.org, paper
- arXiv 2610.24442: A proof of the strong Erdős–Frankl–Füredi cover-free conjecture (Hu, Zhang)arxiv.org, paper
- arXiv 2610.24502: The Siemons–Wagner property and Bradley’s conjecture (Zhang)arxiv.org, paper
- arXiv 2610.25230: Local approximation of A-harmonic functions and the super-localization conjecturearxiv.org, paper
- arXiv 2610.24351: Global stability of Michaelis–Menten networks (Sontag)arxiv.org, paper
- arXiv 2610.25327: Observability of wave equations with time- and space-dependent potentialsarxiv.org, paper
Show all 23 sources
- arXiv 2610.25104: Non-acceleration of the heavy-ball method in 1Darxiv.org, paper
- arXiv 2610.26546: On the nonoccurrence of gradient restart in Nesterov’s methodarxiv.org, paper
- arXiv 2610.25156: A counterexample to Reich’s fixed point problemarxiv.org, paper
- arXiv 2610.25217: A counterexample to the geometric triangulation conjecturearxiv.org, paper
- arXiv 2610.26232: A proof of the Baranov–Bessonov–Kapustin conjecturearxiv.org, paper
- arXiv 2610.26737: The sum–product conjecture holds for fixed-field lattice product constructionsarxiv.org, paper
- arXiv 2610.25571: On Huppert’s ρ–σ conjecture (Jabara, Keller)arxiv.org, paper
- arXiv 2610.25868: Terao’s freeness conjecture for arrangements of 15 and 16 linesarxiv.org, paper
- arXiv 2610.24644: Improved space bounds for promise graph coloring in adversarial streamsarxiv.org, paper
- arXiv 2610.25920: Maestro: agentic formal proof development by coordination (AWS)arxiv.org, paper
- arXiv 2610.25580: Weil–Petersson circle homeomorphisms and the Schoen conjecture (Martin, Yao)arxiv.org, paper
Changes
- Filed (49 disclosure PDFs and 28 no-disclosure PDFs read in full text)