{"schema":"postcutoff/event@1","as_of":"2026-10-30T13:42:00+01:00","url":"https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing-3/","md":"https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing-3/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-10-29-ai-assisted-results-october-29-listing-3","date":"2026-10-29","date_precision":"day","short_title":"AI-assisted results, 29 Oct (part 3): Hexagon's evening batch","deck":null,"takeaway":"Hexagon published 58 new works on 28–29 Oct that we had not cited. Four have their own entries: the claimed sharp Berry–Esseen constant (Kołodziejek–Rodziewicz), the existence of the q-colourability threshold (Aronow–Lopatto, machine-written), deterministic factoring in N^o(1) (Rudich–Rousseau, Lean, ideas by Claude) and the refutation of Moschovakis's uniform-process lower bounds for gcd (Davies, Lean). Others claim the quantum Jellium = uniform-electron-gas energy (Csirik), C₂-cofiniteness of all finite-group orbifolds (Riesen), analytic floating bodies of equilibrium in every dimension ≥ 3 (Price–de Groot, GPT-6 Pro) and Cowling's conjecture for almost connected groups (Arhancet). From the backlog: S(13) = 45 comparators for sorting 13 inputs and an area law for 3D U(1) Wilson lattice gauge theory (Tomar, Lean), Enomoto's settlement of the third Brauer–Thrall conjecture over algebraically closed fields (GPT-6 Astra) and Soberón's counterexample to Matschke's table conjecture.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"Hexagon 2610.00612: Equality of the Jellium and the Uniform Electron Gas Energies (Csirik)","url":"https://hexagonmath.org/abs/2610.00612v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":2,"title":"Hexagon 2610.00636: C₂-cofiniteness of finite-group orbifolds (Riesen)","url":"https://hexagonmath.org/abs/2610.00636v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":3,"title":"Hexagon 2610.00629: Analytic symmetric floating bodies (Price, de Groot)","url":"https://hexagonmath.org/abs/2610.00629v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":4,"title":"Hexagon 2610.00628: Cowling's conjecture, the almost connected case (Arhancet)","url":"https://hexagonmath.org/abs/2610.00628v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":5,"title":"Hexagon 2610.00635: A Boolean Lévy group with a free nonsingular action (Slutsky)","url":"https://hexagonmath.org/abs/2610.00635v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":6,"title":"Hexagon 2610.00623: On Lin's arithmetic–geometric means conjecture for singular values (Sra)","url":"https://hexagonmath.org/abs/2610.00623v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":7,"title":"Hexagon 2610.00624: A spectral Blakley–Roy inequality (Sra)","url":"https://hexagonmath.org/abs/2610.00624v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":8,"title":"Hexagon 2610.00602: Tsallis metrics on density matrices (Sra)","url":"https://hexagonmath.org/abs/2610.00602v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":9,"title":"Hexagon 2610.00652: Polynomial parametrization of quadratic Diophantine equations (Grechuk, Ratcliffe)","url":"https://hexagonmath.org/abs/2610.00652v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":10,"title":"Hexagon 2610.00634: A lower bound for the sixth moment of the Riemann zeta function (Fraccaro)","url":"https://hexagonmath.org/abs/2610.00634v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":11,"title":"Hexagon 2610.00619: Universal test rings for rational Gersten injectivity (Feld)","url":"https://hexagonmath.org/abs/2610.00619v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":12,"title":"Hexagon 2610.00650: Symmetric volume descent from U4 (Hangang Wang)","url":"https://hexagonmath.org/abs/2610.00650v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":13,"title":"Hexagon 2610.00645: Algebraicity of rank-two scattering wall functions (Qiyue Tang)","url":"https://hexagonmath.org/abs/2610.00645v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":14,"title":"Hexagon 2610.00638: Infinite divisibility of hitting times for symmetric stable processes (Min Wang)","url":"https://hexagonmath.org/abs/2610.00638v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":15,"title":"Hexagon 2610.00549: Sorting networks on 13 inputs need 45 comparators (Tomar)","url":"https://hexagonmath.org/abs/2610.00549v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":16,"title":"Hexagon 2610.00552: Area law for 3D U(1) lattice gauge theory with the Wilson action (Tomar)","url":"https://hexagonmath.org/abs/2610.00552v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":17,"title":"Hexagon 2610.00179: Representation embeddings and the third Brauer–Thrall conjecture (Enomoto)","url":"https://hexagonmath.org/abs/2610.00179v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":18,"title":"Hexagon 2610.00182: A counterexample to Han's conjecture over arbitrary fields (Qiyue Tang)","url":"https://hexagonmath.org/abs/2610.00182v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":19,"title":"Hexagon 2610.00484: A counterexample to the table conjecture on the sphere (Soberón)","url":"https://hexagonmath.org/abs/2610.00484v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":20,"title":"arXiv 2609.26576: Periodic tilings of cardinality twice a prime or nine in arbitrary dimension (Tan, Zhang)","url":"https://arxiv.org/abs/2609.26576","type":"paper","group":"primary","domain":"arxiv.org"},{"n":21,"title":"Hexagon 2610.00591: Integrality of iterated averages and pointwise prime powers (Grinberg)","url":"https://hexagonmath.org/abs/2610.00591v1","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":22,"title":"Hexagon 2610.00617: Natural cohomology of general Steiner bundles (Vojdanovski)","url":"https://hexagonmath.org/abs/2610.00617v1","type":"paper","group":"primary","domain":"hexagonmath.org"}],"official":22,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Anthropic","Google","various researchers"],"title":"AI-assisted results, 29 Oct 2026 (part 3): Hexagon's 29 Oct batch, from the Berry–Esseen constant and the q-colourability threshold to deterministic factoring, plus Lean-checked S(13) = 45 for sorting networks and the third Brauer–Thrall conjecture from the backlog","summary":"Catalogue of the 58 Hexagon works of 28–29 Oct that the evening sweep listed as uncited, read through Hexagon's API (provenance statements) and, for the main claims, the PDFs; plus nine lines of the Hexagon backlog and one arXiv lead. Hexagon does not judge correctness; its labels for authorship mode and human understanding are self-reported. Own entries: Berry–Esseen constant, q-colourability threshold, deterministic factoring in N^o(1), and the Euclidean algorithm among uniform processes. Items that extend existing entries were added there (ETH refutations, quasi-Riemann hypothesis, kinetic Aleksandrov estimates, Erdős matching conjecture, Hironaka, unit distances, Vaught, Milne's rationality conjecture, McLeod).","key_facts":["Own entries: 2026-10-29-berry-esseen-constant-esseen-sharp-certificate-claim (2610.00590), 2026-10-29-q-colorability-threshold-existence-aronow-lopatto-ai (2610.00608; with the spherical SK dynamics papers 2610.00609–00610), 2026-10-29-deterministic-factoring-n-o1-lean-claude-rudich-rousseau (2610.00600), 2026-10-29-euclidean-algorithm-not-optimal-moschovakis-lean (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)","Fast AI sessions: Qiyue Tang (Tsinghua) posted six representation-theory and cluster-algebra papers (2610.00645, 00640, 00639, 00615, 00614, 00603) whose results were obtained 'during a two-hour research conversation with ChatGPT-6-Pro', 'in one round of ChatGPT-6-Pro' or in 88-minute to three-hour Codex sessions with GPT-6 Astra, reviewed by Rethlas-OSV; understanding 'some parts'","Other: Niels Feld (Rennes; 2610.00619), universal test rings for rational Gersten injectivity, 'mostly written by Sol 5.6 and GPT-6 Astra, under strict supervision'; Hangang Wang (2610.00650, supervised by Andriy Prymak), a volume-decreasing deformation of the 4D constant-width body U₄ and a lower bound 0.17872203; Vlado Vojdanovski (2610.00617), natural cohomology of general Steiner bundles (Palomar-registered Lean); Min Wang (2610.00638), the hitting time of a point by a symmetric α-stable process is infinitely divisible iff α ≤ α* ≈ 1.66707 (AI-generated, understanding 'none'); Babanskyy (2610.00616), a candidate proof that the fourth deck determines binary subsets of cyclic groups (Pebody's problem; understanding 'none'); Morgan Jones (Oklahoma; 2610.00611), a Claude-assisted book on quantum channel divergences; Shelley and Bosch (Stanford; 2610.00601), collision systems with Danus, Codex and Claude","Not AI-significant or minor (listed for completeness): human-written papers by Zeng Chunping (incl. 'An Integral-Structure Inflation in the Hull Operation of IUT Corollary 3.12', 2610.00646), K. Mahesh Krishna (2), Zhenyu Sun (2), Changxia Lin, Jon Bohlin and Agrawal et al.'s automated-conjecturing survey (2610.00631); Sida He's two AI-only immersed-boundary papers (understanding 'none'); Deep Bhattacharjee (2); Tejasvi Singh Tomar's Darwin Gödel Machine port (2610.00598)","Backlog, sorting networks: Tejasvi Singh Tomar (2610.00549, 26 Oct) proves S(13) ≥ 45, so the least size of a sorting network on 13 inputs is 45, matching Juillé's network; the lower bound comes from a computer search whose certificate is checked by a separate verifier and by two Lean 4 proofs, one with every computation in Lean's kernel; it also repairs Van Voorhis's P(2,N) bound, whose proof Mericanii showed invalid. Hexagon: mixed text, understanding 'all'","Backlog, lattice gauge theory: Tomar (2610.00552, 26 Oct), 3D U(1) lattice gauge theory with the Wilson action confines at every coupling (area law); for the Villain action this is Göpfert–Mack, for the Wilson action 'cited as known but has remained open'. 'Generative AI tools were used to find and prove the results, to write the programs and the Lean formalization ... and to draft the text'; main theorem kernel-checked in Lean 4","Backlog, representation theory: Haruhisa Enomoto (2610.00179, 10 Oct) shows every representation-infinite finite-dimensional algebra over an algebraically closed field has indecomposable modules of each infinite dimension, settling Simson's (third Brauer–Thrall) conjecture there; 'GPT-6-Astra ... found and developed the proof presented here and wrote the earlier drafts', revised with Claude Opus 5.5. Qiyue Tang (2610.00182, 10 Oct), a counterexample to Han's conjecture over every field, AI-generated, understanding 'none'","Backlog, geometry: Pablo Soberón (Baruch/CUNY; 2610.00484, 23 Oct) disproves Matschke's table conjecture on S² with H(x,y,z) = 14z³ − 6z + y + xz; 'ChatGPT 5.6 was used to generate examples ... The solution was written up completely by the author'. Also from the backlog: Naslund's unit-distance exponent 1.043171 (2610.00016) → unit distance entry; Ackerman–Freer–Knight (2610.00188) → Vaught entry; Madapusi's Milne rationality (2610.00226) → Hodge entry; Davies's Pierce expansions (2610.00588) → Euclid entry","Lead resolved: Hu Tan and Ying Zhang (arXiv 2609.26576, 22 Sept), every finite tile of ℤ^d with 2q (q an odd prime) or 9 cells has a fully periodic tiling complement, in every dimension (arXiv abstract); its AI statement, as quoted in our 29 Oct lead (written while reading the paper for the family-155 entry), says ChatGPT (Codex) was used 'for mathematical exploration, proof drafting and checking'"],"key_numbers":[],"tags":["math","computer-science","mathematical-physics","hexagon","catalogue","chatgpt","gpt-6-astra","gpt-6-pro","gpt-6-1-sol","claude","claude-opus-5-5","claude-fable-5-1","codex","lean","palomar"],"science":{"field":"mathematics","subfield":"multiple (probability, random graphs, complexity, logic, mathematical physics, vertex algebras, convex geometry, operator algebras, number theory, representation theory, sorting networks)","problem":"See list","result":"Catalogue of Hexagon works of 28–29 Oct and nine backlog items, beyond those with their own entries","open_since":"","ai_system":["ChatGPT","GPT-6 Pro","GPT-6 Astra","GPT-6.1 Sol","GPT-5.6 Sol","Codex","Claude Opus 5.5","Claude Fable 5.1","Gemini","Danus","Rethlas-OSV"],"human_role":"From papers whose contributors wrote nothing (Davies, Rudich–Rousseau) to human proofs with AI help on examples (Soberón)","verification":{"key":"lean","label":"Lean-verified","text":"Unrefereed Hexagon preprints; Lean or Palomar for some (Davies, Rudich–Rousseau, Tomar, Vojdanovski, Loher–Mooney–Mouhot, Csirik in part); Hexagon's understanding labels are self-reported"},"status":"pending","shock":"","verified_by":["preprint","lean"],"kind":"batch"},"body_md":"## What happened\n\nHexagon, the repository for AI-generated and AI-assisted mathematics, published 58 works on 28–29 Oct that the evening sweep found\nuncited. We read every provenance statement through Hexagon's API and opened the PDFs of the main claims. Four results got their own\nentries, nine extended existing entries, and the rest are listed above. We also worked through nine lines of the Hexagon backlog,\nfamous problems first.\n\n## Why it matters\n\nThe day's batch shows how quickly AI-produced claims now arrive on famous problems: a 70-year-old probability constant, a 1999 random\ngraph question and deterministic factoring all came the same day. Contributors differ widely in how much they checked. Some ran full Lean\nor Palomar checks, some checked every proof by hand, and some say no human has understood any part. Hexagon records those differences\nbut does not judge correctness.","disputed":[{"label":"Verification","text":"Unrefereed Hexagon preprints; Lean or Palomar for some (Davies, Rudich–Rousseau, Tomar, Vojdanovski, Loher–Mooney–Mouhot, Csirik in part); Hexagon's understanding labels are self-reported","sources":[]}],"related":[{"id":"2026-10-29-berry-esseen-constant-esseen-sharp-certificate-claim","url":"https://postcutoff.com/e/2026-10-29-berry-esseen-constant-esseen-sharp-certificate-claim/","date":"2026-10-29","date_precision":"day","short_title":"Sharp Berry–Esseen constant claimed: C = Esseen's 0.4097","deck":null,"takeaway":"The Berry–Esseen inequality bounds how far a normalised sum of i.i.d. variables is from the normal law. Its best constant has been open since Esseen showed in 1956 that it cannot be below (3+√10)/(6√(2π)) ≈ 0.4097; the best published upper bound is Shevtsova's 0.4690. On 29 Oct Bartosz Kołodziejek and Kacper Rodziewicz (Warsaw) posted on Hexagon a claimed proof that Esseen's value is the exact constant for every sample size n. The proof combines analytic reductions with exact finite certificates in 13 index ranges, checked end to end by their own programs, with a one-command Docker replay. They used ChatGPT, Codex and Gemini/Antigravity 'extensively'. It is not a Lean proof, and no specialist had checked it by 29 Oct.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":7,"official":6,"filed":"2026-10-29","updated":"2026-10-29","orgs":["Warsaw University of Technology","University of Warsaw","OpenAI","Google"]},{"id":"2026-10-29-q-colorability-threshold-existence-aronow-lopatto-ai","url":"https://postcutoff.com/e/2026-10-29-q-colorability-threshold-existence-aronow-lopatto-ai/","date":"2026-10-29","date_precision":"day","short_title":"q-colourability threshold of G(n, d/n) exists, says a machine-written paper","deck":null,"takeaway":"Achlioptas and Friedgut proved in 1999 that q-colourability of the random graph G(n, d/n) has a sharp threshold, but only along a sequence that might depend on n. Whether that sequence converges to a constant d_q was recorded as an open problem and is widely called well known. On 29 Oct P. M. Aronow (Yale) and Patrick Lopatto (UNC Chapel Hill) posted on Hexagon a proof that it converges for every q ≥ 3, with a window of O(n(log n)^(−3/2)) steps for the hitting time. The authors' note says the whole document except that note is machine-written. The provenance names Opus 5.5, GPT 6 Astra, GPT Luna 6 and GPT 6.1 Sol, and says the results were formalised in Lean, but the paper links no Lean repository. Human understanding: 'some parts'. Two companion papers on the dynamics of the spherical Sherrington–Kirkpatrick model came the same day.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-29","updated":"2026-10-29","orgs":["Anthropic","OpenAI","Yale University","University of North Carolina at Chapel Hill"]},{"id":"2026-10-29-deterministic-factoring-n-o1-lean-claude-rudich-rousseau","url":"https://postcutoff.com/e/2026-10-29-deterministic-factoring-n-o1-lean-claude-rudich-rousseau/","date":"2026-10-29","date_precision":"day","short_title":"Deterministic factoring in N^o(1) steps, Lean-checked, ideas by Claude","deck":null,"takeaway":"The best proven deterministic factoring algorithms ran in time N^(1/5+o(1)) (Harvey; Harvey–Hittmeir). On 29 Oct Isaac Rudich and Louis-Martin Rousseau (Polytechnique Montréal) posted on Hexagon a Lean 4 proof that one deterministic Turing machine finds the smallest prime factor of every N within C_k·2^(n/k) steps for every k, i.e. N^o(1). The 13-line statement uses only Mathlib and is registered in Palomar; the proof is about 36,000 lines. The authors say every idea and all Lean code came from Claude agents, which they asked to apply the ETH refutation to factoring; they audited the statement, not the proof. The algorithm is 'galactic' and slower than the randomised and heuristic methods used in practice; what is new is a proven deterministic N^o(1) bound.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":2,"filed":"2026-10-29","updated":"2026-10-29","orgs":["Anthropic","Polytechnique Montréal"]},{"id":"2026-10-29-euclidean-algorithm-not-optimal-moschovakis-lean","url":"https://postcutoff.com/e/2026-10-29-euclidean-algorithm-not-optimal-moschovakis-lean/","date":"2026-10-29","date_precision":"day","short_title":"Gcd in O(log a / log log a) remainder calls refutes Moschovakis's uniform-process conjecture","deck":null,"takeaway":"Van den Dries and Moschovakis asked whether Euclid's algorithm is optimal among algorithms that compute the gcd from the remainder function. On 29 Oct Jason Davies posted on Hexagon a proof that every pair a ≥ b has a derivation of gcd(a, b) using O(log a / log log a) remainder calls, while Euclid needs order log a in the worst case. That refutes Moschovakis's conjectured logarithmic lower bounds for uniform processes and answers a closure-depth question of van den Dries and Moschovakis; Moschovakis's Main Conjecture for actual algorithms stays open. GPT-6 Astra found the principal result in Codex; GPT-6 Astra and Claude Opus 5.5 wrote the Lean proofs and the paper, and Palomar's comparator confirms the 22 compared statements. Davies says he wrote none of the text or code.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Anthropic"]},{"id":"2026-10-29-ai-assisted-results-october-29-listing-2","url":"https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing-2/","date":"2026-10-29","date_precision":"day","short_title":"AI-assisted results, 29 Oct 2026 (part 2)","deck":"Claude 'largely carried out' Lipshitz's Khovanov research, ChatGPT found Soundararajan's proof and wrote Etingof's and Mathew's papers, George Elliott's free-product classification 'carried out using ChatGPT', and a first read of Hexagon's backlog","takeaway":"A second pass over the 28 Oct arXiv announcement and a first full read of Hexagon (hexagonmath.org), which the sweep had never covered, found results with large AI roles signed by senior mathematicians. Robert Lipshitz writes that his Khovanov paper's research 'was largely carried out by various Claude models'. Kannan Soundararajan's proof of a problem from Montgomery's CBMS book 'was found by ChatGPT 6'. ChatGPT 6 Pro wrote Pavel Etingof's answer to a 1999 question and produced Akhil Mathew's answer to a question of Drinfeld. George Elliott's classification of reduced free products of nuclear C*-algebras 'was carried out using ChatGPT'. Eight items have their own entries: the unforced 2D Euler non-uniqueness claims, the Erdős–Lovász covering-number bound, UPP^cc under intersection, Kisin's Serre conjecture, Linnik's constant ≤ 3.99, 3D Yang–Mills on a torus, random k-SAT and Chenglong Ma's Hovey–Strickland provenance claim.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":30,"official":29,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Anthropic","Google DeepMind","various researchers"]},{"id":"2026-10-29-ai-assisted-results-october-29-listing","url":"https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing/","date":"2026-10-29","date_precision":"day","short_title":"AI-assisted results in the 29 Oct 2026 sweep","deck":"Counterexamples to Wilking's 2007 question found by GPT-6 Astra, an LLM-written Plateau paper by De Lellis and Glaudo, explicit Reed–Solomon codes with optimal list size (Guruswami et al.), rank-four quiver mutation decided by GPT Astra, and a dozen named conjectures","takeaway":"The 29 Oct sweep covered the arXiv announcement of 28 Oct, which the previous run had read only through keyword queries. This time 43 papers with an AI statement surfaced, and a PDF scan of a further 405 new and cross-listed submissions in math, cs.CC, cs.DS and cs.DM found about 180 more with an AI statement, most of them describing more than editing help. Four results have their own entries: OpenAI's abundance claim and Jihao Liu's priority remark, OpenAI's Lean-checked L = RL = BPL, R(3,3,3,3) ≤ 61 and the sharp Banach–Mazur exponent. This page lists the rest. GPT-6 Astra found the counterexamples to Wilking's 2007 question 'with minimal human input' and discovered the main results of a rank-four quiver paper. Claude found examples in opinion dynamics and proposed a minimal-surface construction. An LLM supplied 'the main idea' of a paper by Camillo De Lellis, a member of the IAS advisory group on AI and mathematics, and wrote it.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":23,"official":23,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Anthropic","various researchers"]},{"id":"2026-10-26-openai-eth-false-subexponential-sat-claim","url":"https://postcutoff.com/e/2026-10-26-openai-eth-false-subexponential-sat-claim/","date":"2026-10-26","date_precision":"day","short_title":"OpenAI claims ETH is false","deck":null,"takeaway":"Anthropic independently posted a different Lean-checked refutation the next day (separate entry). OpenAI's model output claims a deterministic algorithm that counts the satisfying assignments of any k-CNF in time 2^(n/(log n)^(1/2+o(1))). If correct, it refutes ETH, SETH, Gap-ETH and NSETH, the assumptions behind hundreds of fine-grained hardness results. OpenAI says the main theorem is formalized in Lean. A working group led by ETH's proposers, Russell Impagliazzo and Ramamohan Paturi, with Ryan Williams, will examine the proof. No expert has assessed it in public yet.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":32,"official":10,"filed":"2026-10-26","updated":"2026-10-30","orgs":["OpenAI"]},{"id":"2026-10-13-ai-assisted-results-october-2026","url":"https://postcutoff.com/e/2026-10-13-ai-assisted-results-october-2026/","date":"2026-10-13","date_precision":"day","short_title":"October 2026: the arXiv stream of conjectures settled with disclosed AI help continues","deck":null,"takeaway":"In the first nine days of October 2026 the stream did not slow down: each arXiv listing brought several named conjectures with a disclosed AI role, and two new patterns appeared.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":17,"official":17,"filed":"2026-10-13","updated":"2026-10-29","orgs":["OpenAI","Anthropic","Google DeepMind","various mathematicians"]},{"id":"2026-10-12-erdos-matching-conjecture-large-matchings-ai","url":"https://postcutoff.com/e/2026-10-12-erdos-matching-conjecture-large-matchings-ai/","date":"2026-10-12","date_precision":"day","short_title":"Erdős Matching Conjecture (1965) proved for every fixed k and all large s, via a sharp tail bound whose k ≥ 6 cases generative AI completed","deck":null,"takeaway":"Three Shanghai Jiao Tong mathematicians prove Erdős's 1965 matching conjecture for all n once the matching size is large, by first settling a probability conjecture of Łuczak, Mieczkowska and Šileikis. Their disclosure credits AI with the unified argument for k ≥ 6 and with closing a gap.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":2,"filed":"2026-10-14","updated":"2026-10-29","orgs":["Shanghai Jiao Tong University"]},{"id":"2026-10-10-vaught-conjecture-infinitary-counterexample-lean","url":"https://postcutoff.com/e/2026-10-10-vaught-conjecture-infinitary-counterexample-lean/","date":"2026-10-10","date_precision":"day","short_title":"Vaught's conjecture fails for infinitary logic","deck":"Ackerman, Freer and Knight post a Lean-verified counterexample, built over 8 months with Claude Code and Codex","takeaway":"A sentence of L_ω1,ω with exactly ℵ1 countable models and no perfect set of them refutes the infinitary Vaught conjecture (1961). It follows Robin Knight's 2002 approach, which was never accepted, and the whole argument is now certified in Lean.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":6,"official":5,"filed":"2026-10-14","updated":"2026-10-29","orgs":["Harvard University","MIT","University of Oxford","Anthropic","OpenAI"]},{"id":"2026-10-09-kinetic-krylov-safonov-pucci-conjecture-gpt-6-astra","url":"https://postcutoff.com/e/2026-10-09-kinetic-krylov-safonov-pucci-conjecture-gpt-6-astra/","date":"2026-10-09","date_precision":"day","short_title":"\"We need ABP\": six PDE specialists publish GPT-6 Astra's proofs of the kinetic Krylov–Safonov theorem and of Pucci's 1966 conjecture, with full chats (Loher, Mooney, Mouhot, Niebel, Silvestre, Zhu)","deck":null,"takeaway":"Six analysts, among them Clément Mouhot and Luis Silvestre, say the missing estimate behind a long-open regularity theorem for kinetic equations was found by GPT-6 Astra Ultra on 6 Sept 2026 with no human contribution. They wrote a human exposition and published the prompts, chats and AI manuscripts, and state that they claim no credit.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":8,"official":8,"filed":"2026-10-12","updated":"2026-10-29","orgs":["OpenAI","University of Cambridge","University of Chicago","UC Irvine"]},{"id":"2026-10-08-rank-3x3-matrix-multiplication-f2-is-23-lean-tomar","url":"https://postcutoff.com/e/2026-10-08-rank-3x3-matrix-multiplication-f2-is-23-lean-tomar/","date":"2026-10-08","date_precision":"day","short_title":"Laderman's 23 multiplications are optimal for 3×3 matrices over F_2 and over the integers","deck":"AI-found proof checked in Lean (Tomar)","takeaway":"Whether 3×3 matrices can be multiplied with fewer than Laderman's 23 multiplications has been open since 1976. A preprint claims the answer is no for coefficients in F_2 or the integers, ending a 2026 race in which the lower bound rose from 19 to 20, 21, 22 and now 23. The author says generative AI found and proved the result.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":8,"official":8,"filed":"2026-10-12","updated":"2026-10-13","orgs":["independent"]},{"id":"2026-10-06-quasi-riemann-hypothesis-openai","url":"https://postcutoff.com/e/2026-10-06-quasi-riemann-hypothesis-openai/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI model claims the quasi-Riemann hypothesis","deck":"No zeta or Dirichlet L-function zeros with Re s > 7/8, and no Landau–Siegel zeros (Lean-formalized)","takeaway":"If correct, this is the largest advance on the zeros of ζ since the 19th century, and it would remove the Siegel-zero obstruction that runs through modern analytic number theory.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":19,"official":14,"filed":"2026-10-07","updated":"2026-10-29","orgs":["OpenAI"]},{"id":"2026-10-06-hodge-conjecture-cm-abelian-varieties-openai","url":"https://postcutoff.com/e/2026-10-06-hodge-conjecture-cm-abelian-varieties-openai/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI release proves the rational Hodge conjecture for all CM abelian varieties, giving the Tate conjecture for abelian varieties over finite fields; Lean proof added 26 Oct, human-written proof by van Hoften and Sempliner, and Milne calls it proved","deck":null,"takeaway":"Family 032 of OpenAI's 6 Oct 2026 math release claims the rational Hodge conjecture for every complex abelian variety with complex multiplication, in every dimension and codimension.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":12,"official":8,"filed":"2026-10-07","updated":"2026-10-29","orgs":["OpenAI"]},{"id":"2026-10-06-hironaka-resolution-of-singularities-lean-fable-agents","url":"https://postcutoff.com/e/2026-10-06-hironaka-resolution-of-singularities-lean-fable-agents/","date":"2026-10-06","date_precision":"day","short_title":"Hironaka's resolution of singularities formalized in Lean by agents","deck":null,"takeaway":"Resolution (resolution.org) reports that an orchestrated team of agents, mostly Claude Fable 5.1 with occasional checks by GPT-6 Astra, autoformalized Hironaka's 1964 theorem in characteristic zero between 4 and 10 Sept 2026, together with refinements by Kollár, Włodarczyk and Bierstone–Milman. That took about 100B input tokens, 300M output tokens and roughly $135k. A human mathematician intervened about 30 times. The repository says neither library contains a sorry.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":5,"official":4,"filed":"2026-10-26","updated":"2026-10-29","orgs":["Resolution","Anthropic"]},{"id":"2026-10-06-hexagon-repository-llm-assisted-math","url":"https://postcutoff.com/e/2026-10-06-hexagon-repository-llm-assisted-math/","date":"2026-10-06","date_precision":"day","short_title":"Hexagon launches: a new arXiv-style repository for LLM-assisted mathematics papers","deck":null,"takeaway":"It is the first dedicated infrastructure for AI-generated mathematics backed by leading mathematicians, and it accepts work that no human claims to understand.","category":"research","category_label":"Research","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":2,"official":2,"filed":"2026-10-07","updated":"2026-10-29","orgs":["Hexagon Mathematics Foundation"]},{"id":"2026-05-20-ai-disproves-erdos-unit-distance-conjecture","url":"https://postcutoff.com/e/2026-05-20-ai-disproves-erdos-unit-distance-conjecture/","date":"2026-05-20","date_precision":"day","short_title":"OpenAI model disproves Erdős's 80-year-old unit distance conjecture","deck":null,"takeaway":"This is the moment AI crossed from solving competition problems to settling a famous open research conjecture, reshaping debate about AI's role in mathematics.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":9,"official":3,"filed":"2026-09-29","updated":"2026-10-29","orgs":["OpenAI"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-29","type":"filed","text":"Created (Hexagon API records of all 58 works, PDFs of 2610.00590, 00600, 00604, 00608, 00612, 00629, 00636, 00549, 00552; arXiv API for 2609.26576; HN search found no threads)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-10-29","run":null,"sources_read":null,"updated":"2026-10-29","human_review":null,"version":{"date":"2026-10-29"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":182,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":121,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":212,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":151,"in_training_data":false}],"short_url":null}