AI-assisted results, 11 Nov: arXiv and Hexagon

Your AI and this story

Key facts

• Own entries: Smale’s mean value constant = 4 (claimed, Lean-checked) (2611.00282, 00283; 00306 is the same author’s 1.1559 update), Talagrand’s Ultimate Matching Conjecture: GPT-6 proof (Hexagon) (2611.00294), Benson–Etingof–Ostrik conjecture: full proof generated by GPT-6 Astra (2611.00301), Large triangles in planar sets of positive density: GPT-6 Astra Pro proof (2611.00302), Explicit RIP matrices reach k = m^(2/3): main theorem by GPT-6 Astra (arXiv 2611.14475); Falconer rewrite (arXiv 2611.13789) added to OpenAI proves the Falconer distance conjecture (Lean)
• Hexagon 11 Nov, primarily AI-generated with named experts: Qiyue Tang’s GPT-6-Pro runs claim Broué’s abelian defect group conjecture for 2-blocks (2611.00288; ‘13 rounds … approximately 90.8 hours’; v2 says a Rethlas-OSV review ‘reported no mathematical issues’; human understanding ‘none’), Watkins’s conjecture for curves with rational 2-torsion (00285, ‘none’), plus Laurent-phenomenon positivity (00279, 00284, 00289) and a counterexample to Boocher–Froehle’s subtraction-free conjecture (00266)
• More Hexagon 11 Nov: Morgan Jones, a Michael space in the Laver model, ‘Claude Fable 5.2 was given the statement of the conjecture … I have not attached my name onto the paper because I didn’t do anything’ (00286); Tzu Chen Huang, torus partition functions just above c = 1 have no fixed spectral gap, proof ‘developed by GPT-6 Astra’, checked by five Claude Fable 5.2 referee passes (00300); Yan Ru Pei, Claude agents found a gap in an OpenAI six-vertex manuscript’s identification step and a Fable agent proved the missing uniqueness theorem (00291); Annanay Kapila, a 51-state beeping Turing machine whose quasihalting is independent of Peano Arithmetic, with a Rocq-checked simulation theorem (00281)
• More Hexagon 11 Nov: Jason Davies, R∞ for crystallographic quotients of spherical Artin groups, Claude Opus 5.5 and GPT-6 Astra with a Lean proof of part of it (‘no sorry and no native_decide’; 00278); Jamie Martin, Meyer’s question on crystalline measures (countably infinite Hamel dimension; 00280; understanding ‘none’); David Niedbala Giraudin, Schur–Siegel–Smyth trace bound 1.8022246 with a ball-arithmetic certificate (00275); Shawn Krisman, irrationality of χ₂ at units of real quadratic fields, e.g. π² − 18 log²φ (00265, Claude Opus 5.5, ‘none’); Vlado Vojdanovski, the Ideal Generation Conjecture for general reduced points, ‘guided exploration by Open AI Astra agents’ (00274); Jacob Crim, the exact second-order term in Ramanujan’s σ(n)/n bound under RH, answering a question of Nicolas, drafted by Claude (00182)
• Hexagon 11 Nov, human-led or mixed: Yair Lavi with GPT-5.6 Sol, GPT-6 Astra and Claude Fable on permanents and cp-rank (00296, 00297, 00298); Samir Hamad, a separable Banach space whose bidual has the Daugavet property (00299, GPT-6 Astra); Kohlmeyer, Howe, Huffman and Kruer, five Codex deposits with partial Lean (00267–00270; 00269 answers Okhotin’s Problem 4: Boolean grammars in DSPACE(n^(3/4))); Boorstein, two Claude-drafted billiards papers in rational triangles (00303, 00304); Banica, ‘Written by Claude Fable’ (00305); Keränen, JT-gravity Wasserstein note with Claude (00295); Man Huang, Zenodo repost with GPT-6.1 Sol and Grok 4.7 (00273); human-written: 00276, 00277, 00287, 00290, 00292
• arXiv (10–11 Nov), AI found the main result: ‘Theorem 1 was proved in one shot using GPT-6 Astra’ (explicit RIP, 2611.14475); ‘obtained a proof purely generated by ChatGPT Astra’ (stationary integral cycles, Xuanyu Li and Zhihan Wang, 2611.14410); ‘the bulk of the technical ideas of the paper originated on the machine side’ (Nick Salter, hyperelliptic linear systems in Hirzebruch surfaces, 2611.14386); ‘The proofs were generated and the draft of this paper was written with GPT-6’ (unilluminable rooms, 2611.13226); ‘The paper originates from the following insight obtained using Anthropic Opus 5.5’ (mixed-integer dual network problems in strongly polynomial time, Zambelli, 2611.14045); GPT-6 Astra found ‘the key arguments’ for the optimal one-shot channel simulation constant (2611.13397)
• arXiv, AI supplied key steps: Ge, Jitomirskaya and You’s supercritical Ten Martini problem (the ten martini problem for the positive-Lyapunov part of the spectrum of any nonconstant real analytic one-frequency Schrödinger operator), strategy human (‘without AI involvement’) but an LLM ‘helped us derive the renormalization estimate in Lemma 5.1 and discover the monotonicity property in the Lemma 3.2’ (2611.13068); Q-valued harmonic functions, Theorem 3.13 ‘strongly supported by AI’ (2611.14409); canonical volumes of threefolds, ChatGPT ‘suggested several key ideas’ (2611.14402); E-symmetric algebras: ‘Amazingly, the AI came up with a suitable definition’ (ChatGPT-6 Astra), and Enomoto’s AI-found counterexample to the Periodicity Conjecture is reused (2611.13889); Appendix B classification ‘obtained by AI tools’ (Anosov representations, 2611.14302); the Baer trick for progression-free sets came from an LLM (2611.14464); GPT-6 Astra built the solvers and Lean checks for online matching bounds (2611.13571)
• arXiv, Lean or formal: Michael Stoll, iterates of x² + a with maximal Galois group, ‘obtained in collaboration with Claude … also formalized in Lean’ (2611.14014); Erdős–Straus-type exceptional sets for K/n = 1/x + 1/y + 1/z with exponent 3/4, every step ‘checked by Lean’s kernel’, Claude used throughout (2611.14167); rank-23 3×3 matrix multiplication with 51 additions, Lean by Claude (2611.12907); Gödel’s theorems in grounded arithmetic, machine-checked with Claude (2611.13697)