AI-assisted results, 5 Nov: arXiv of 5 Nov and Hexagon of 4 Nov

Your AI and this story

Key facts

• Own entries: 3-uniform hyperclique hypothesis refuted with ChatGPT Sol 6.1 (2611.06813), Elliptic-curve torsion in degrees 6–9, mostly by GPT-6.1 Sol (Hexagon 2611.00073), Serre modularity over real quadratic fields, primarily AI-generated (Hexagon 2611.00071, 00067, 00096)
• Functional analysis: Sun–Wei–Xu–Zhang (2611.06579) give a separable MAP space whose dual has AP but not BAP, and an ℓ1-isomorphic MAP space whose dual has BAP but not MAP, answering questions stated by Oja (2010); ‘the authors used AI tools to assist in developing the constructions’. Tanaka (2611.06493): nonisomorphic separable Banach spaces at Lipschitz distance one, building on OpenAI’s graph-space construction, ‘developed through an extended mathematical dialogue between the author and an AI assistant provided by OpenAI’
• Algorithms: Parter–Tzalik (2611.06857), first deterministic fault-tolerant connectivity oracles with subquadratic space; ‘The main ideas behind both the upper- and lower-bound space arguments were found by ChatGPT-6 Astra’. Constant-round MPC approximate metric MST, ideas ‘developed … through discussions with ChatGPT-6 Astra’ (2611.06092). Differentially private synthetic graphs with n·polylog n additive error, Eliáš, Kamath, Kulkarni et al.; ‘The first proofs of our main privacy theorems were developed independently by multiple groups using AI systems’ (2611.06670). Subquadratic cut-query protocol for directed reachability, ‘initially discovered through interactive prompting of LLMs’ (2611.06906)
• Graph colouring: Lizhong Chen (2611.05423) proves the Borodin–Kostochka inequality χ ≤ max{ω, Δ−1} for Δ ≥ 750 (cf. the 4583 threshold of 20 Oct); ‘The author used GPT-6 Astra to assist with exploring candidate estimates, numerical parameter trials, coding, checks of local arguments’
• Probability and dynamics: Beiglböck–Hasenbichler–Pammer (2611.06758), Bass martingales need not stretch, ‘substantial assistance of OpenAI’s GPT-6 Astra in obtaining a preliminary version of the construction in Section 3’; Zhangsong Li (2611.05794), near-linear mixing of random-cluster Glauber dynamics, ‘The core ideas of the proof were generated using GPT-6 and the Pharos system’; Bianchi–Ji–Xie (2611.06211), equilibrium webs for families of endomorphisms of P^k, ‘Proposition 3.1, whose main idea was suggested by GPT-6 Astra Ultra’
• Counterexamples: Tokareva’s bent-sum decomposition conjecture fails for symmetric F_n, n = 2^k ≥ 8, found with GPT-6.1 Sol via Codex during NSUCRYPTO 2026 (2611.06744); Wesle (2611.06617), counterexample to the weak Gibbs and regularity conjectures, LLMs used for ‘exploration of models and proof strategies’
• Algebraic geometry: Bishop (2611.06014), integral Chow rings of A_3 and M_3 (λ3 of order 504 and 252), ‘GPT-6 Astra assisted with the “dirty work” in the excision computations’; Categorical Torelli for hypersurfaces, ‘results … obtained through interaction with ChatGPT 6’ (2611.05915); Homology of partially ordered fields ‘written in its entirety by GPT6Astra’ (2611.06261)
• Hexagon 4 Nov: Turán’s pure power sum problem (Erdős #519), lim sup R_n ≤ 0.68637 improving Harcos’ 0.69368, Bakeas–Pinho with Claude Opus/Sonnet 5.5 (2611.00069); Baiying Liu, explicit Landau–Siegel zero-free region over varying number fields (1−β)(log D_K+…) ≥ 1/1370 and a zero-free half-plane Re s > 0.8734 for Hecke L-functions, ‘mix’, Codex GPT-6.1 Sol and Claude Opus 5.5, Lean in progress (2611.00080, 2611.00082); five Bolzano-project works with Václav Rozhoň, ‘The manuscript received only limited human checking’ (2611.00051–00055); Tulsyan’s subexponential Eulerian-circuit counting and sparse-circuit amplitudes ‘assuming the new #SAT algorithms’ (2611.00088, 00090); Jason Davies’ sharp 16n−3 cube-frame bound, Lean, GPT-6 Astra and Claude Opus 5.5 (2611.00070); 12 Claude Opus works by David Niedbala Giraudin, ‘understanding: none’, e.g. site percolation 0.556921 ≤ p_c ≤ 0.6463 (2611.00065)