AI-assisted results, 29 Oct (part 3): Hexagon’s evening batch

Your AI and this story

Key facts

• Own entries: Sharp Berry–Esseen constant claimed: C = Esseen’s 0.4097 (2610.00590), q-colourability threshold of G(n, d/n) exists, says a machine-written paper (2610.00608; with the spherical SK dynamics papers 2610.00609–00610), Deterministic factoring in N^o(1) steps, Lean-checked, ideas by Claude (2610.00600), Gcd in O(log a / log log a) remainder calls refutes Moschovakis’s uniform-process conjecture (2610.00604)
• Added to existing entries: Xiaoyu Li’s Claude-written learning-theory consequences of the ETH refutation (2610.00613) → ETH entry; Baiying Liu’s zero-free half-plane Re s > 0.874468… for Hecke L-functions over every number field (2610.00655) → quasi-Riemann entry; Loher–Mooney–Mouhot ‘From Döblin to Aleksandrov’ with Lean (2610.00618) → kinetic Krylov–Safonov entry; Babanskyy’s unchecked four-uniform Erdős matching proof (2610.00607) → Erdős matching entry; Dupuy’s AI-only report against Hironaka’s characteristic-p proposal (2610.00621) → Hironaka entry; the Hexagon copy of Sra’s McLeod proof (2610.00622) → 13 Oct listing
• Mathematical physics: Mihály A. Csirik (Chalmers/Gothenburg; 2610.00612) proves the quantum Jellium energy per volume (Lieb–Narnhofer) equals the uniform electron gas energy (Lewin–Lieb–Seiringer), known only classically (Lewin–Lieb–Seiringer; Cotar–Petrache); ‘The author made substantial use of the LLMs ChatGPT (OpenAI) and Claude (Anthropic) ... including the development of the proofs ... The author has checked all the proofs by hand’; the lower and upper comparisons and the neutralization construction are in Lean (github.com/xyzw/jellium_ueg) relative to stated hypotheses; Hexagon text ‘primarily AI-generated’, understanding ‘all’
• Vertex algebras: Andrew Riesen (MIT; 2610.00636) proves that C₂-cofiniteness of V implies C₂-cofiniteness of V^G for every finite group G, the nonsolvable case of a longstanding orbifold conjecture (Miyamoto had the solvable case); with McRae’s theorem this gives strong rationality of every finite-group fixed-point algebra of a strongly rational VOA. ‘Generative AI, including ChatGPT, was used extensively ... This assistance contributed substantial portions of the initial arguments and text’; understanding ‘some parts’, ‘a small number of technical points remain under detailed review’
• Ulam’s floating-body problem: Liam Price and Tom de Groot (2610.00629) construct, in every dimension d ≥ 3, nonspherical origin-symmetric strictly convex bodies of revolution with real-analytic boundary that float in equilibrium in every orientation (Ryabogin’s 2022 bodies are at density 1/2, where origin symmetry forces a ball). ‘The original argument for the four-dimensional case was developed by GPT-6 Pro in ChatGPT. GPT-6.1 Sol and GPT-6 Astra, working in Codex, subsequently extended the argument to all dimensions d ≥ 3’
• Group theory and dynamics: Cédric Arhancet (2610.00628) proves Cowling’s conjecture (Haagerup property ⇔ weak amenability with constant 1) for connected Lie groups and almost connected locally compact groups, AI for ‘exploratory mathematical discussions and feedback’; two more Arhancet papers on local fields and quantum groups are ‘work in progress’. Konstantin Slutsky (Iowa State; 2610.00635) answers a question of Glasner, Tsirelson and Weiss with a Boolean Lévy group with a free ergodic nonsingular action: ‘The example presented in this paper was constructed by AI using OpenAI GPT-6-Astra and OpenAI GPT-6.1-sol’
• Suvrit Sra posted four papers: McLeod 1959 (see 13 Oct listing), Lin’s 2017 conjecture λ_j((1−t)A+tB) ≥ σ_j^{1/2}(A^{2(1−t)}B^{2t}) for all t (Drury had t = 1/2; 2610.00623), a spectral Blakley–Roy inequality ρ(AB)^k ≤ ρ(A^kB^k) (2610.00624) and Tsallis metrics via the S-divergence (2610.00602), all with GPT Pro (‘None of the claims were obtained zero-shot’); a fifth (2610.00620) is a purely human revision of a 2021 paper
• Number theory: Grechuk and Ratcliffe (2610.00652), an algorithm deciding whether the integer zeros of any degree-≤2 polynomial are a finite union of polynomial families, proving the nondegenerate case of a result Vaserstein announced without proof (‘the final step in the proof was obtained with ChatGPT 6 Astra’); Niklas Fraccaro (2610.00634), lower limit of the normalised sixth moment of ζ above 41.007 (GPT-6 corrected ‘a significant error in Theorem 2.1’); Darij Grinberg (2610.00591, ‘Produced by GPT-6 Astra’); Marco Ripà (2610.00589, tetration congruence speeds, GPT-6); Chao Liu (2610.00643, 2610.00599, ChatGPT); Khai-Hoan Nguyen-Dang (2610.00644, three cubic trinomial series for 1/π)