AI-assisted results, 4 Nov: arXiv of 4 Nov and Hexagon of 2–3 Nov

Your AI and this story

Key facts

• Own entries: Huffman coding with unequal letter costs is NP-complete (Codex) (2611.04444), Colourings Glauber dynamics above (1+1/e)Δ (GPT-6 Astra Pro) (2611.04699), Amplituhedron magic number conjecture: counterexample found by ChatGPT (2611.05216)
• Kissing numbers: Qihong Lin (2611.03682) raises lower bounds in dimensions 32–35 and 37–39 (e.g. dim 32: 347,584 → 352,320; dim 38: 591,900 → 605,322); ‘This work relied heavily on an AI coding assistant, Claude (model Claude Opus 5.5, Anthropic), used through the Claude Code tool … The assistant also found and proved Lemma 5’
• Geometric group theory: Bruno Dular (Luxembourg, 2611.03855) gives discrete faithful purely loxodromic representations of a genus-431 surface group into Isom(H^n) with no Cannon–Thurston map; ‘The construction was found by GPT-6 Astra’, in answer to a prompt to ‘prove or disprove continuity of the boundary map’
• Finsler geometry: Ming Li and Kefeng Liu (2611.05067) prove that Landsberg metrics in dimension ≥ 4 whose Minkowski norms are real-analytic are Berwald, a case of Bao’s ‘unicorn problem’ (Shen’s 2009 Problem 1); ‘The authors used ChatGPT 6 Astra to draft and revise text, to develop and check proofs’
• Percolation: Gefei Cai (2611.05101) determines the monochromatic three-arm exponent ξ₃ = 0.76928375… (open since Beffara–Nolin 2011 showed existence); ‘AI tools were used in carrying out calculations, technical estimates, and proofs in functional analysis, especially for n ≥ 4’
• Algorithms: Feng–Nir (2611.04730) find all integer roots of an integer polynomial in Õ(nb) bit operations, answering Harvey–Hittmeir (2022); ‘The main construction in this paper was generated with the assistance of AI models and verified by the authors’. Also: Logarithmic regret for alternating mirror descent, ‘The mathematical proof in this paper was developed using GPT-5.6 Sol’ (2611.05243); A King for Almost Everyone, lemmas identified by ChatGPT Astra (2611.03838); low-diameter Nash-Williams–Tutte with GPT-6 Astra (2611.05043)
• Other AI-originated items: Zhao–Hu, GK dimension n for mod p representations of GL₂(K), ‘The methods used in this paper were discovered by GPT-6 Astra’ (2611.04350); Hessenberg varieties, ‘The proof … was suggested to the authors through discussions with ChatGPT’ (2611.04130); tensor-triangular geometry of valuation domains, ‘The first proof of Theorem 8.18 was obtained via LLMs’ (2611.05298); nonrational algebraically elliptic double covers found by directing GPT-6 Astra (2611.04983); nine-point crescent configurations, GPT-6 Astra in the search (2611.03688); edge-isoperimetric alternative proof by GPT-6 Astra (2611.04644); automatic partition identities (2611.04020); Strassen rank gap (2611.04502); Haagerup VOAs simplifying AI-assisted proofs (2611.04778); superintegrable QFT spectrum with Claude (2611.05015); smallest-parts congruences ‘arose out of a conversation between the author and AI’ (2611.04178)
• Hexagon 2–3 Nov, now linked: 13 works by Suvrit Sra (2610.00719–00731), mixed authorship; e.g. a sharp Brégman–Minc bound conjectured by Samorodnitsky and Gurvits, ‘developed with GPT-6 (Pro) after extensive back and forth; none were obtained zero-shot’, all parts human-understood (2610.00731); q-Foulkes I–III, surjectivity for b ≥ (a−1)² improving a(a−1), ‘The main text has not yet been vetted line by line’ (2610.00724). Others: see the 3 Nov listing (Tang, Niedbala Giraudin, Vega, Almeida, Arhancet, twinheterodox, Nikzad) and human-written deposits (Zeng, Mahesh Krishna, Kaminsky)