{"schema":"postcutoff/event@1","as_of":"2026-10-30T13:42:00+01:00","url":"https://postcutoff.com/e/2026-10-30-ai-assisted-results-october-30-listing/","md":"https://postcutoff.com/e/2026-10-30-ai-assisted-results-october-30-listing/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":"2026-10-30-ai-assisted-results-october-30-listing","date":"2026-10-30","date_precision":"day","short_title":"AI-assisted results, 30 Oct: arXiv announcement of 29–30 Oct","deck":null,"takeaway":"The 30 Oct sweep listed 374 arXiv papers that mention AI. We skimmed all their AI statements and read about 35 PDFs. Six results got their own entries: Das–Fox's Murty–Simon proof (GPT-5.6 Sol found the bound), Colbrook–Stepaniants's spectral isometry proof (found by GPT-6 Astra, Lean), the Θ(log k log log k) ratio of greedy for online Steiner forest (GPT Astra, Lean), Gáspár's Laczkovich solution (key proposition by ChatGPT), Ren's pure-semisimplicity counterexample (GPT-6 Astra, Lean) and Petty's conjecture in dimension 5 (Tencent's hyprover agent). PNNL's OpenConjecture study also has one. This listing has the rest, among them a single-author ChatGPT 6 Pro proof of the Alon–Seymour–Thomas separator conjecture, b₄ ≤ 7 for Borsuk's problem and Fiedorowicz's conjecture from a Claude idea.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2610.40270: On separators in K_t-minor-free graphs (Xinheng Lin)","url":"https://arxiv.org/abs/2610.40270","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"arXiv 2610.39078: Borsuk number in four dimensions is at most seven","url":"https://arxiv.org/abs/2610.39078","type":"paper","group":"primary","domain":"arxiv.org"},{"n":3,"title":"arXiv 2610.38760: On a Conjecture of Fiedorowicz (Ben-Bassat)","url":"https://arxiv.org/abs/2610.38760","type":"paper","group":"primary","domain":"arxiv.org"},{"n":4,"title":"arXiv 2610.38877: A proof of Kroó's conjecture (Colbrook)","url":"https://arxiv.org/abs/2610.38877","type":"paper","group":"primary","domain":"arxiv.org"},{"n":5,"title":"arXiv 2610.39838: The Kawatani–Okawa conjecture in dimensions three and four","url":"https://arxiv.org/abs/2610.39838","type":"paper","group":"primary","domain":"arxiv.org"},{"n":6,"title":"arXiv 2610.38427: Witt liftability of quasi-F-split Calabi–Yau varieties (Takamatsu)","url":"https://arxiv.org/abs/2610.38427","type":"paper","group":"primary","domain":"arxiv.org"},{"n":7,"title":"arXiv 2610.38414: The Borisov–Nuer conjecture (Wang, Yi)","url":"https://arxiv.org/abs/2610.38414","type":"paper","group":"primary","domain":"arxiv.org"},{"n":8,"title":"arXiv 2610.38073: Determining norm-Euclidean complex cubic fields (Bagger, Booker, Trudgian)","url":"https://arxiv.org/abs/2610.38073","type":"paper","group":"primary","domain":"arxiv.org"},{"n":9,"title":"arXiv 2610.37945: Van der Waerden's Problem for Cubic Surfaces (O'Dorney)","url":"https://arxiv.org/abs/2610.37945","type":"paper","group":"primary","domain":"arxiv.org"},{"n":10,"title":"arXiv 2610.38870: An asymptotic Jensen–Pólya criterion for GRH (Ono)","url":"https://arxiv.org/abs/2610.38870","type":"paper","group":"primary","domain":"arxiv.org"},{"n":11,"title":"arXiv 2610.38515: The asymptotics of off-diagonal book Ramsey numbers","url":"https://arxiv.org/abs/2610.38515","type":"paper","group":"primary","domain":"arxiv.org"},{"n":12,"title":"arXiv 2610.39021: Hook monomial immanants are Kazhdan–Lusztig positive (McNulty)","url":"https://arxiv.org/abs/2610.39021","type":"paper","group":"primary","domain":"arxiv.org"},{"n":13,"title":"arXiv 2610.39481: e-Positive caterpillars have maximum degree at most three","url":"https://arxiv.org/abs/2610.39481","type":"paper","group":"primary","domain":"arxiv.org"},{"n":14,"title":"arXiv 2610.39430: Diameter-two graphs with mutual-visibility chromatic number equal to chromatic number (Chaubal)","url":"https://arxiv.org/abs/2610.39430","type":"paper","group":"primary","domain":"arxiv.org"},{"n":15,"title":"arXiv 2610.39228: Every group is the automorphism group of a Yang–Baxter solution (Militaru)","url":"https://arxiv.org/abs/2610.39228","type":"paper","group":"primary","domain":"arxiv.org"},{"n":16,"title":"arXiv 2610.39242: The Liouville property for geometric graphs in the plane","url":"https://arxiv.org/abs/2610.39242","type":"paper","group":"primary","domain":"arxiv.org"},{"n":17,"title":"arXiv 2610.40291: Reverse isoperimetric problem for λ-convex bodies (Drach, Tatarko)","url":"https://arxiv.org/abs/2610.40291","type":"paper","group":"primary","domain":"arxiv.org"},{"n":18,"title":"arXiv 2610.38055: On the Hodge Extension of Local Kähler Forms (Shafikov)","url":"https://arxiv.org/abs/2610.38055","type":"paper","group":"primary","domain":"arxiv.org"},{"n":19,"title":"arXiv 2610.37899: Hierarchical laminates counterexample (Cao)","url":"https://arxiv.org/abs/2610.37899","type":"paper","group":"primary","domain":"arxiv.org"},{"n":20,"title":"arXiv 2610.38481: Carnot geodesics with Hölder controls","url":"https://arxiv.org/abs/2610.38481","type":"paper","group":"primary","domain":"arxiv.org"},{"n":21,"title":"arXiv 2610.37808: Symplectomorphism invariance of the wrapped Fukaya category (Hu, Shende)","url":"https://arxiv.org/abs/2610.37808","type":"paper","group":"primary","domain":"arxiv.org"},{"n":22,"title":"arXiv 2610.37703: Simple torsion-free linear groups from global division algebras","url":"https://arxiv.org/abs/2610.37703","type":"paper","group":"primary","domain":"arxiv.org"},{"n":23,"title":"arXiv 2610.38640: Transfer kernels and the Schur multiplier (Lemmermeyer)","url":"https://arxiv.org/abs/2610.38640","type":"paper","group":"primary","domain":"arxiv.org"},{"n":24,"title":"arXiv 2610.37691: Two-colour zig-zag Numberlink with Lean verification","url":"https://arxiv.org/abs/2610.37691","type":"paper","group":"primary","domain":"arxiv.org"},{"n":25,"title":"arXiv 2610.39355: Proof of the Amari–Kobayashi conjecture","url":"https://arxiv.org/abs/2610.39355","type":"paper","group":"primary","domain":"arxiv.org"},{"n":26,"title":"arXiv 2610.38961: First-order phase transition in spin-imbalanced BCS theory","url":"https://arxiv.org/abs/2610.38961","type":"paper","group":"primary","domain":"arxiv.org"},{"n":27,"title":"arXiv 2610.38143: Comparison categories (Claude Sonnet 5.5-generated article)","url":"https://arxiv.org/abs/2610.38143","type":"paper","group":"primary","domain":"arxiv.org"},{"n":28,"title":"arXiv 2610.40551: Ramanujan Challenge Results","url":"https://arxiv.org/abs/2610.40551","type":"paper","group":"primary","domain":"arxiv.org"},{"n":29,"title":"arXiv 2610.40503: Algebraic World Model: From Exploration to Proofs","url":"https://arxiv.org/abs/2610.40503","type":"paper","group":"primary","domain":"arxiv.org"},{"n":30,"title":"arXiv 2610.39641: Rebuilding a field's open-problem catalog from the literature","url":"https://arxiv.org/abs/2610.39641","type":"paper","group":"primary","domain":"arxiv.org"},{"n":31,"title":"arXiv 2610.39462: Balancing tautological intersection numbers","url":"https://arxiv.org/abs/2610.39462","type":"paper","group":"primary","domain":"arxiv.org"},{"n":32,"title":"arXiv 2610.38474: Motivic approach to the Abhyankar rectifiability problem","url":"https://arxiv.org/abs/2610.38474","type":"paper","group":"primary","domain":"arxiv.org"},{"n":33,"title":"Hexagon 2610.00662: Integral crystalline Tate classes at supersingular points of Mumford's fourfolds (Hippeläinen)","url":"https://hexagonmath.org/abs/2610.00662","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":34,"title":"Hexagon 2610.00625: A true theorem Lean can state but can never verify (Banks)","url":"https://hexagonmath.org/abs/2610.00625","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":35,"title":"Hexagon 2610.00659: The random graph ideal and fractional coloring (López-Callejas)","url":"https://hexagonmath.org/abs/2610.00659","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":36,"title":"Hexagon 2610.00614: The Mirković–Vilonen basis and cluster pointedness (Qiyue Tang)","url":"https://hexagonmath.org/abs/2610.00614","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":37,"title":"Hexagon 2610.00558: Uniform sheafy Tate rings that are not stably uniform (Birkbeck, Torzewski)","url":"https://hexagonmath.org/abs/2610.00558","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":38,"title":"Hexagon 2610.00586: Elliptic curves with torsion Z/2 x Z/4 and rank at least six (Jaswal)","url":"https://hexagonmath.org/abs/2610.00586","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":39,"title":"openai/math history.md: CM Hodge comparator fix (29 Oct)","url":"https://github.com/openai/math/commit/204e5f8f8a301d647f4bea76a5834e04fd2399ff","type":"code","group":"primary","domain":"github.com"},{"n":40,"title":"oai-math-revised: family 378 notes and executable toy model (McElveen)","url":"https://github.com/mathcommunity/oai-math-revised/commit/86f07ab7df75e83d9248b07c904a1a00244cf649","type":"code","group":"primary","domain":"github.com"},{"n":41,"title":"oai-math-revised: Pasechnik's crossing-number forest","url":"https://github.com/mathcommunity/oai-math-revised/commit/dfa574c8f8bb1f2d8b99f6577957a89a3f6e891f","type":"code","group":"primary","domain":"github.com"},{"n":42,"title":"formal-conjectures: Palomar submission linter","url":"https://github.com/google-deepmind/formal-conjectures/commit/d9f6ffa8dd7fc2b8b597dd1f7a824d27b12b88af","type":"code","group":"primary","domain":"github.com"}],"official":42,"filed":"2026-10-30","updated":"2026-10-30","orgs":["OpenAI","Anthropic","Google","Tencent","various researchers"],"title":"AI-assisted results in the 30 Oct 2026 sweep: Murty–Simon, the spectral isometry conjecture, online Steiner forest, Laczkovich's Lipschitz problem, pure semisimplicity and Petty in dimension five, plus Borsuk b₄ ≤ 7, Alon–Seymour–Thomas separators, Fiedorowicz, Kroó, Kawatani–Okawa and Borisov–Nuer","summary":"Catalogue of AI-disclosing papers from the arXiv announcements of 29–30 Oct 2026 (submissions of 26–29 Oct), the Hexagon works of 29 Oct not yet cited, and the week's result-repository commits, beyond the items with their own entries. Statements are quoted from the PDFs; none of these papers is refereed. Highlights: Xinheng Lin's claimed proof of the Alon–Seymour–Thomas conjecture (1990) with ChatGPT 6 Pro; Arman–Bondarenko–Prymak–Radchenko's b₄ ≤ 7 for Borsuk's problem in ℝ⁴ after exploring with ChatGPT Astra; Ben-Bassat's proof of Fiedorowicz's conjecture from an idea that 'arose in a conversation' with Claude Opus 5.5; Colbrook's proof of Kroó's 2004 conjecture with ChatGPT 6; Wu–Zhang's Kawatani–Okawa conjecture in dimensions 3–4 ('ChatGPT 6.0 was used to fill in the gaps'); Booker, Trudgian and Bagger's completeness of the 58 norm-Euclidean complex cubic fields, 'solved' with Claude Opus 5.","key_facts":["Own entries: 2026-10-28-murty-simon-conjecture-proof-gpt-5-6-sol-das-fox (2610.39032), 2026-10-29-spectral-isometry-conjecture-c-star-algebras-gpt-6-astra (2610.40470), 2026-10-29-online-steiner-forest-greedy-log-k-loglog-k-gpt-astra-lean (2610.40569), 2026-10-28-laczkovich-lipschitz-mapping-problem-chatgpt-gaspar (2610.38834), 2026-10-29-pure-semisimplicity-conjecture-counterexample-gpt-6-astra-lean (2610.39883), 2026-10-29-petty-equilateral-set-conjecture-dimension-five-tencent-hyprover (2610.39967), 2026-10-29-openconjecture-random-conjectures-gpt-models-pnnl (2610.40382). Added to an existing entry: Viaclovsky's infinitely many inequivalent complex structures from the Alpöge–Claude construction (2610.39102) → Hopf S⁶ entry","Alon–Seymour–Thomas conjecture (Xinheng Lin, Fuzhou University; 2610.40270): every n-vertex K_h-minor-free graph has a balanced separator of size ≤ min{n, 21h√n}, the O(h√n) bound conjectured in 1990 (earlier bounds cited in the paper include Kawarabayashi–Reed's O(h√n + f(h)) and a 2026 preprint by H. Le, arXiv 2605.05494). 'This manuscript presents a proof of the Alon–Seymour–Thomas conjecture developed under the author's guidance using ChatGPT 6pro. The author has checked every formula and theorem by hand … GPT 6.1 Sol (Max) was also used to check the proof repeatedly.' Single author, 17 pages, famous conjecture: treat as a claim until specialists comment","Borsuk's problem in ℝ⁴ (Andrii Arman, Andriy Bondarenko, Andriy Prymak, Danylo Radchenko; 2610.39078): every set of diameter 1 in ℝ⁴ is covered by seven balls of diameter < 0.9999, so b₄ ≤ 7, via contact points of the circumball and an exact computation over 23,494 parameter boxes (github.com/andriyprm/4d7balls). 'An earlier version of this work established the weaker bound g₄ ≤ 8 … We subsequently explored the problem with ChatGPT Astra, initially seeking purely analytic arguments … This led to the approach based on the circumradius and substantially reduced the computational search space'","Fiedorowicz's conjecture (Oren Ben-Bassat; 2610.38760): every finite simply connected CW complex is homotopy equivalent to the classifying space of a finite monoid; explicit 1795-element monoid for ℂP². 'The key idea of realizing CP² by a finite monoid arose in a conversation between the author and Anthropic's Claude Opus 5.5. Starting from that idea, the author supplied all of the theoretical arguments … All of the content in the GitHub repository was written by Claude' (github.com/OrenXGitHub/monoid-computations)","Kroó's 2004 conjecture (Matthew J. Colbrook; 2610.38877): on every origin-symmetric convex body, continuous functions on the boundary are uniform limits of sums of homogeneous polynomials of degrees n and n+1; also Kroó's 2019 weighted conjecture. 'the author interacted with and guided ChatGPT 6, which suggested proof strategies and intermediate arguments … ChatGPT 6, accessed through Codex, also assisted with the formalisation in Lean'","Algebraic geometry: Kawatani–Okawa conjecture in dimensions 3 and 4 (Dongjian Wu, Nantao Zhang; 2610.39838; 'The authors manually proved the conjecture in dimension three and developed a strategy for the dimension-four case. ChatGPT 6.0 was used to fill in the gaps'); Witt liftability of quasi-F-split Calabi–Yau varieties (Teppei Takamatsu; 2610.38427; 'The proofs of Theorems A and B, as well as nearly all of the other original mathematical arguments in this paper, were developed by the author through extensive discussions with OpenAI's ChatGPT (GPT-6 Astra)'); balancing tautological intersection numbers (2610.39462, GPT-6 Astra organised the proofs of Sections 4–6); Abhyankar rectifiability with ChatGPT Sol 6.1 (2610.38474)","Number theory: Borisov–Nuer conjecture settled, with Ulrich line bundles on unnodal Enriques surfaces (Haowu Wang, Shaoyun Yi; 2610.38414; 'Generative AI was used interactively in the subsequent mathematical exploration, including the development, testing, and refinement of parts of the construction and proof'); Cavallar–Lemmermeyer's list of 58 norm-Euclidean complex cubic fields is complete (Gustav Kjærbye Bagger, Andrew R. Booker, Tim Trudgian; 2610.38073; 'We used Claude Opus 5 to solve this problem through a series of prompts over two days in late July 2026'); Evan O'Dorney, van der Waerden's problem for cubic surfaces, G_S ≠ W(E₆) for O(H^(19+1/21+ε)) forms (2610.37945; the title page says 'Written by ChatGPT 6'); Ken Ono, asymptotic Jensen–Pólya criterion for GRH for every number field, with Theorem 3 'formalized in Lean 4 using AxiomProver' (2610.38870)","Combinatorics: off-diagonal book Ramsey numbers r(B_⌈αn⌉, B_n) determined asymptotically for all α (Dai, Fan, Lin; 2610.38515; 'used ChatGPT to explore this direction'); hook monomial immanants are Kazhdan–Lusztig positive, the hook case of Stembridge's and Haiman's conjectures (Keith McNulty; 2610.39021; Claude Code wrote and ran the software and drafted text); e-positive caterpillars have maximum degree ≤ 3, the caterpillar case of the Dahlberg–She–van Willigenburg conjecture (2610.39481; GPT-5.5, GPT-5.6, GPT-6 Astra and Codex); diameter-two graphs with χ_μ = χ beyond complete bipartite (Siddhesh Chaubal; 2610.39430; Claude Opus 5.5 'designed and ran the computer searches that found G₁₁ … produced the proofs of Theorems 3.4 and 3.8'); every group is the automorphism group of a set-theoretic Yang–Baxter solution (G. Militaru; 2610.39228; Claude Opus 5.5 'to explore and develop constructions and proofs'); Liu–Luo–Luo–Rao Liouville property for Delaunay triangulations (2610.39242; 'The key idea of the proof of Theorem 1.1 is produced with the assistance of ChatGPT')","Geometry and analysis: Borisenko's reverse isoperimetric conjecture for λ-convex bodies in all dimensions (Drach, Tatarko; 2610.40291), after 'Deniz's proposed solution to the problem in Euclidean space, obtained with the assistance of LLM'; Hodge extension of local Kähler forms with a counterexample 'found with the help of AI, specifically Claude Fable 5.1, which proposed the original construction' (Rasul Shafikov; 2610.38055); hierarchical laminates do not reach all effective tensors of planar two-phase composites with 16-component potentials (Lianghao Cao; 2610.37899; GPT-5.6 Sol Ultra, GPT-6 Astra Ultra and GPT-6.1 Sol Ultra used 'extensively'); Carnot geodesics with Hölder controls (2610.38481; example and first proof 'obtained with ChatGPT Astra-Ultra')","Symplectic geometry: Mingyuan Hu and Vivek Shende (2610.37808), any symplectomorphism of Weinstein manifolds induces an equivalence of wrapped Fukaya categories, improving two mirror-symmetry statements; the PDF says 'All results are obtained using ChatGPT Astra'","Other AI-found or AI-proved items: Kourovka Problem 16.78 candidate (an infinite torsion-free nonabelian simple linear group from a degree-15 division algebra; Ivan Samuil Nnuga Mongo; 2610.37703; 'The argument was generated using an AI system and has not yet been independently verified by human mathematicians'); transfer kernels and the Schur multiplier (Franz Lemmermeyer; 2610.38640; 'The proof was found with the help of the free version of Claude'); two-colour zig-zag Numberlink with Lean ('Nearly the entirety of the work … was done by Claude (Opus 5.5)'; 2610.37691); Amari–Kobayashi Fisher-information conjecture for Boolean pairs (Chen, Watanabe, Yu; 2610.39355; ChatGPT for Academic Researchers grant); spin-imbalanced BCS first-order transition with GPT-5.5 Pro (2610.38961); strictly AI-generated category-theory article by Claude Sonnet 5.5 from an author's draft (2610.38143)","Meta-studies: Ramanujan Challenge results, an AI-assisted evaluation pipeline for multi-format proofs of research-level number-theory formulas (Technion's Ramanujan Machine group; 2610.40551); Algebraic World Model, kernel-checked Lean proofs of impossible game levels in all six runs where Claude Opus 5.5 and GPT-6 Astra with tools produced none in twelve (2610.40503); a two-layer knowledge graph rebuilding a field's open-problem catalogue (2610.39641)","Checked, no AI statement in the PDF (sweep list): Segal conjecture for large objects and a short proof for C_p (2610.40209, 2610.39440), Terao's conjecture for at most nine planes (2610.40028), Michael's problem answered affirmatively (2610.39260), Serre's conjectures for ℚ(√13) (2610.38884), a five-species counterexample to the Hofbauer–Kon–Saito conjecture (2610.38374), soliton resolution for Benjamin–Ono (2610.38198), counterexample to the Carlet–Solé conjecture (2610.36687); Erdős–Straus, real Jacobian and 'Gauss–Fourier' titles in the same list look like crank claims and were skipped","Hexagon, 29 Oct works not cited before (sweep list of 34; most were summarised in the 29 Oct part 3 listing without their ids): Antti Hippeläinen, integral crystalline Tate classes in codimension 2 at supersingular points of Mumford's fourfolds, conditional on a Markman preprint (Hexagon 2610.00662, Claude Opus 5.5, understanding 'none'); William Banks, an exposition of why Lean cannot verify its own consistency (Hexagon 2610.00625, Claude Fable 5.0, 'claims no new mathematics'); Jay Thrussell, the realizability operator for Riemannian 3-manifolds in ℝ⁴ (Hexagon 2610.00658, understanding 'none'); Carlos López-Callejas, the random graph ideal is pathological, answering López-Abad et al. and Filipów–Tryba (Hexagon 2610.00659); Qiyue Tang's Kamnitzer ICM-survey Conjecture 6.6 (MV basis contains cluster monomials) and Question 6.5 (theta basis biperfect), Elgin–Reading–Stella factorial denominators, Burcroff et al. Conjecture 9.2 and Li–Liu–Mou–Pan counterexamples (Hexagon 2610.00614, 2610.00603, 2610.00615, 2610.00639, 2610.00640; understanding 'some parts'); Arhancet's local-fields/quantum-groups pair (Hexagon 2610.00648, 2610.00649); Bhattacharjee (Hexagon 2610.00627, 2610.00594); Sida He's Parts II–III (Hexagon 2610.00592, 2610.00593); human-written: Zeng Chunping (Hexagon 2610.00630, 2610.00651, 2610.00646), K. Mahesh Krishna (Hexagon 2610.00653, 2610.00595), Zhenyu Sun (Hexagon 2610.00654, 2610.00642), Changxia Lin (Hexagon 2610.00606), Jon Bohlin (Hexagon 2610.00583), Suvrit Sra's revision (Hexagon 2610.00620), Agrawal et al. (Hexagon 2610.00631); already summarised by id on 29 Oct: Hexagon 2610.00598, 2610.00644, 2610.00643, 2610.00616, 2610.00611, 2610.00601, 2610.00599, 2610.00589","Result repositories (28–29 Oct): openai/math only fixed namespaces in the CM Hodge Comparator challenge (history.md, 29 Oct), no new family or withdrawal; oai-math-revised added Chelsea McElveen's executable toy model of the ETH paper (family 378), Dima Pasechnik's 'crossing-number forest' reading guide (crossing number of K_{m,n}) and ZHAO Han's definition-body re-check for L = RL = BPL; google-deepmind/formal-conjectures added statements of 22 Erdős problems, the Gyárfás–Sumner, Manickam–Miklós–Singhi and Razborov–Pudlák disjoint-NP-pair conjectures, a linked Lean proof of Erdős 670 (choose_two variant), and a linter that enforces Palomar submissions","Hexagon backlog (8 lines processed): Christopher Birkbeck and Alex Torzewski answer Question 7 of Kedlaya's Nonarchimedean Scottish Book with uniform, strongly sheafy Tate rings that are not stably uniform, 'The two main results are due to ChatGPT 5.6 Sol', constructions formalised in Lean 4 (Hexagon 2610.00558); Manvir Jaswal, infinitely many elliptic curves over ℚ with torsion ℤ/2 × ℤ/4 and rank ≥ 6 (previous infinite-family record 5, Eroshkin), the ℤ/2 × ℤ/4 case of Dujella's Problem 2.6, Claude Opus, Codex and Lean, no human author claimed (Hexagon 2610.00586); Shihao Wang and Zhiwei Zheng, finite p-group counterexamples to the Amit–Ashurst conjecture for every prime (order p^498; Hexagon 2610.00563, no human author claimed); Roy van Rijn, the Generalized Vanishing Conjecture holds in two variables and fails in three, with Codex (Hexagon 2610.00580); Scott Kominers, a preliminary exposition of a qualitative form of OpenAI's ETH-refutation algorithm with ChatGPT and Claude Opus (Hexagon 2610.00574; see the ETH entry); Babanskyy, Sun's supercongruence for an Apéry-like sequence, Codex, understanding 'some parts' (Hexagon 2610.00578); Steve Hubbard, Chen's theorem under GRH for N ≥ exp(exp(13.375)) by re-choosing parameters in Bordignon–Starichkova (Hexagon 2610.00560); Isaac Kaimfa, reductions and barriers for Wolfram's Rule 30 Problem 1, not a solution (Hexagon 2610.00573)"],"key_numbers":[],"tags":["math","computer-science","physics","arxiv","hexagon","catalogue","chatgpt","gpt-6-astra","gpt-6-pro","gpt-6-1-sol","gpt-5-6-sol","claude","claude-opus-5-5","claude-fable-5-1","codex","gemini","axiomprover","lean"],"science":{"field":"mathematics","subfield":"multiple (graph theory, discrete geometry, topology, algebraic geometry, number theory, analysis, symplectic geometry, algorithms)","problem":"See list","result":"Catalogue of AI-disclosing papers of 29–30 Oct 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 Opus 5","Claude Fable 5.1","Claude Sonnet 5.5","Gemini","AxiomProver"],"human_role":"From proofs found by models with human write-ups (Lemmermeyer, Chaubal, Takamatsu) to human proofs with AI for gaps or exploration (Wu–Zhang, Arman et al.)","verification":{"key":"lean","label":"Lean-verified","text":"Unrefereed preprints; Lean for some (Ono via AxiomProver, Colbrook's Kroó, Numberlink)"},"status":"pending","shock":"","verified_by":["preprint","lean"],"kind":"batch"},"body_md":"## What happened\n\nThe 30 Oct sweep read the arXiv announcements of 29 and 30 Oct and scanned every maths, cs.CC, cs.DS and cs.DM PDF for an AI statement.\n374 papers mention AI. Most use it for editing, references or code. About 60 report that models found or developed proofs, constructions\nor counterexamples. We read the PDFs of the strongest 35 or so. Six got their own entries, and PNNL's study of GPT models on random\nconjectures got one too. The rest are summarised above, with the AI statement quoted where it matters.","disputed":[{"label":"Verification","text":"Unrefereed preprints; Lean for some (Ono via AxiomProver, Colbrook's Kroó, Numberlink)","sources":[]}],"related":[{"id":"2026-10-29-spectral-isometry-conjecture-c-star-algebras-gpt-6-astra","url":"https://postcutoff.com/e/2026-10-29-spectral-isometry-conjecture-c-star-algebras-gpt-6-astra/","date":"2026-10-29","date_precision":"day","short_title":"Spectral isometry conjecture for C*-algebras: GPT-6 Astra proof, Lean","deck":null,"takeaway":"Mathieu's spectral isometry conjecture asks whether every unital surjective linear map between unital C*-algebras that preserves the spectral radius is a Jordan isomorphism. Only special classes were known. On 29 Oct Matthew Colbrook and George Stepaniants (Cambridge) posted what they call 'a human digestion of a proof … found by GPT-6 Astra'. The theorem is registered in Lean on Palomar. Their AI declaration says the proof came 'after a sequence of simple prompts'. This is the second such digest from Colbrook in a week, after Smale's mean value conjecture. It is a preprint, not refereed.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":2,"official":2,"filed":"2026-10-30","updated":"2026-10-30","orgs":["OpenAI","University of Cambridge"]},{"id":"2026-10-29-online-steiner-forest-greedy-log-k-loglog-k-gpt-astra-lean","url":"https://postcutoff.com/e/2026-10-29-online-steiner-forest-greedy-log-k-loglog-k-gpt-astra-lean/","date":"2026-10-29","date_precision":"day","short_title":"Online Steiner forest: greedy claimed Θ(log k log log k), with GPT Astra","deck":null,"takeaway":"In online Steiner forest, terminal pairs arrive one by one and must be connected at once. Awerbuch, Azar and Bartal proved in 1996 that the greedy algorithm is O(log² k)-competitive and conjectured O(log k). On 29 Oct a University of Maryland group led by MohammadTaghi Hajiaghayi posted matching bounds of Θ(log k log log k). If correct, that refutes the conjecture and separates greedy from the best online algorithm by a log log k factor. Some proofs 'were developed with the help of OpenAI's GPT Astra', with Gemini Argon assisting, and Lean files for the main theorem are on GitHub. It is a preprint, not refereed.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":2,"official":2,"filed":"2026-10-30","updated":"2026-10-30","orgs":["OpenAI","Google DeepMind","University of Maryland"]},{"id":"2026-10-29-pure-semisimplicity-conjecture-counterexample-gpt-6-astra-lean","url":"https://postcutoff.com/e/2026-10-29-pure-semisimplicity-conjecture-counterexample-gpt-6-astra-lean/","date":"2026-10-29","date_precision":"day","short_title":"Pure semisimplicity conjecture: claimed counterexample, GPT-6 Astra, Lean","deck":null,"takeaway":"The pure semisimplicity conjecture says a ring over which every module is a direct sum of finitely generated ones must have finite representation type. It holds for Artin algebras (Auslander) and PI rings (Simson, Herzog). Simson reduced a counterexample to a 'generalized Artin problem' about division ring extensions. On 29 Oct Junpeng Ren posted a division ring extension that solves it. The AI declaration says GPT-6 Astra helped choose the criterion and develop the proof, 'in particular the construction of the division rings'. The main theorem is fully formalised in Lean 4 in a public repository. It is a preprint, not refereed.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":2,"filed":"2026-10-30","updated":"2026-10-30","orgs":["OpenAI","Anthropic"]},{"id":"2026-10-29-petty-equilateral-set-conjecture-dimension-five-tencent-hyprover","url":"https://postcutoff.com/e/2026-10-29-petty-equilateral-set-conjecture-dimension-five-tencent-hyprover/","date":"2026-10-29","date_precision":"day","short_title":"Petty's conjecture in dimension 5: proof by Tencent's hyprover agent","deck":null,"takeaway":"Petty conjectured that every n-dimensional normed space contains n + 1 points at equal distances. Petty proved dimension 3 and Makeev dimension 4. On 29 Oct Kaiwen Yang (Tongji University and Tencent Hunyuan) posted a proof for dimension 5. Its AI declaration says the proof 'was generated by Tencent Hunyuan's AI agent hyprover on September 29, 2026', and that the author organised, verified and rewrote it. The paper prints the full prompt, which points the agent to Lu–Yang's solution of Banach's isometric conjecture. Few research results in our dataset credit a Chinese lab's agent. It is a preprint, not refereed.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-30","updated":"2026-10-30","orgs":["Tencent","Tongji University"]},{"id":"2026-10-29-openconjecture-random-conjectures-gpt-models-pnnl","url":"https://postcutoff.com/e/2026-10-29-openconjecture-random-conjectures-gpt-models-pnnl/","date":"2026-10-29","date_precision":"day","short_title":"OpenConjecture: GPT models on 200 random arXiv conjectures","deck":null,"takeaway":"Reported AI-maths breakthroughs are hand-picked. Researchers at Pacific Northwest National Laboratory sampled 200 conjectures at random from arXiv maths papers posted since February 2026. They ran GPT-5.6 Sol, then GPT-5.6 Sol Pro, then GPT-6 Astra Pro on each, with no problem-specific guidance. The models proposed 70 counterexamples and 55 proofs, and 84% of these passed review by a fresh instance of the same model. No experts checked them. About 60% of the reviewed counterexamples were 'off-the-shelf' and the rest 'standard constructions'. Some exploited missing hypotheses, such as offering the trivial group, and a number of proofs followed closely from known results.","category":"research","category_label":"Research","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-30","updated":"2026-10-30","orgs":["Pacific Northwest National Laboratory","OpenAI"]},{"id":"2026-10-29-ai-assisted-results-october-29-listing-3","url":"https://postcutoff.com/e/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":22,"official":22,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Anthropic","Google","various researchers"]},{"id":"2026-10-28-murty-simon-conjecture-proof-gpt-5-6-sol-das-fox","url":"https://postcutoff.com/e/2026-10-28-murty-simon-conjecture-proof-gpt-5-6-sol-das-fox/","date":"2026-10-28","date_precision":"day","short_title":"Murty–Simon conjecture: proof for all n, bound found by GPT-5.6 Sol","deck":null,"takeaway":"The Murty–Simon conjecture (Plesník 1975, Murty and Simon) says a diameter-2-critical graph on n vertices has at most ⌊n²/4⌋ edges, with equality only for the balanced complete bipartite graph. Füredi proved it in 1992 only for n above a tower of 2s of height about 10¹⁴. On 28 Oct Sanjana Das and Jacob Fox (Stanford) posted a proof for every n. Their AI statement says the proof of the n²/4 bound 'was mostly found by AI, specifically GPT-5.6 Sol on August 11, 2026'. The authors simplified it and extended it to the equality case for odd n by hand. It is a preprint and has not been refereed.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":2,"official":2,"filed":"2026-10-30","updated":"2026-10-30","orgs":["OpenAI","Stanford University"]},{"id":"2026-10-28-laczkovich-lipschitz-mapping-problem-chatgpt-gaspar","url":"https://postcutoff.com/e/2026-10-28-laczkovich-lipschitz-mapping-problem-chatgpt-gaspar/","date":"2026-10-28","date_precision":"day","short_title":"Laczkovich's Lipschitz mapping problem: claimed answer, ChatGPT key step","deck":null,"takeaway":"In 1991 Miklós Laczkovich asked whether every measurable set of positive measure in ℝ^d can be mapped onto a cube by a Lipschitz map. Preiss and Matoušek answered it in the plane; dimension 3 and up stayed open. On 28 Oct Attila Gáspár posted a positive answer in every dimension. His disclosure says the proof of Theorem 1.8 'was obtained using ChatGPT on 26 October', and Proposition 2.8 with Lemma 2.7 is 'entirely due to ChatGPT'. He had known other parts and the lower bound since early 2026. It is a short preprint, not refereed.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-30","updated":"2026-10-30","orgs":["OpenAI"]},{"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":"2026-10-06-openai-borsuk-conjecture-dimension-nine-counterexample","url":"https://postcutoff.com/e/2026-10-06-openai-borsuk-conjecture-dimension-nine-counterexample/","date":"2026-10-06","date_precision":"day","short_title":"Borsuk's conjecture fails in dimension 9 (OpenAI claim, Lean-checked)","deck":null,"takeaway":"A manuscript in OpenAI's 6 Oct 2026 maths release (family 156, dated 23 Sept) claims that the compact set of rank-one projectors onto lines in ℝ⁴, a copy of real projective 3-space in a 9-dimensional space, cannot be cut into ten pieces of smaller diameter. That would make 9 the smallest known dimension in which Borsuk's 1933 conjecture fails. The record had been 63, set in May 2026 with a finite 321-point set. The main theorem has a Lean proof, which a community Comparator run accepted. Gil Kalai called it 'a major progress' and said the topological proof 'looks very beautiful', but added that it still needs careful checking. The example is infinite, so for finite sets the record is still 63. Gábor Damásdi showed that every finite subset of it can be split into eight smaller pieces.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":18,"official":10,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI"]},{"id":"2026-10-06-openai-l-equals-rl-equals-bpl-lean-claim","url":"https://postcutoff.com/e/2026-10-06-openai-l-equals-rl-equals-bpl-lean-claim/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI claims L = RL = BPL with a Lean proof","deck":null,"takeaway":"OpenAI's 6 Oct 2026 math release (family 103, manuscript dated 23 Sept) claims L = RL = BPL. That would mean randomness does not help logarithmic-space computation, a central open problem of complexity theory. The best unconditional bound was Saks and Zhou's O(log^{3/2} n) space, slightly improved by Hoza. A Lean formalization added on 7 Oct proves the equality in an explicit Turing-machine model. The community comparator run of 26 Oct accepted it. A re-check found the proof's definitions identical to the statement file's and the proof built on standard axioms only. It notes that it does not show 'that the machine model is the standard one'. No complexity theorist has assessed it publicly as of 29 Oct.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":7,"official":5,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI"]},{"id":"2026-08-23-hopf-problem-s6-complex-structure","url":"https://postcutoff.com/e/2026-08-23-hopf-problem-s6-complex-structure/","date":"2026-08-23","date_precision":"day","short_title":"Claude-assisted construction claims a complex structure on the 6-sphere, answering Hopf's 1947 problem (pending verification)","deck":null,"takeaway":"The existence of a complex structure on S⁶ is one of the best-known open problems in geometry.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":5,"official":3,"filed":"2026-09-29","updated":"2026-10-30","orgs":["Anthropic"]}],"people":[{"id":"jensen-huang","name":"Jensen Huang","url":"https://postcutoff.com/person/jensen-huang/"},{"id":"levent-alpoge","name":"Levent Alpöge","url":"https://postcutoff.com/person/levent-alpoge/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-30","type":"filed","text":"Created (science agent; arXiv API metadata and PDFs, Hexagon API, GitHub commit API)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-10-30","run":null,"sources_read":null,"updated":"2026-10-30","human_review":null,"version":{"date":"2026-10-30"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":183,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":122,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":213,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":152,"in_training_data":false}],"short_url":null}