{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/","md":"https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/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":"2026-09-30-ai-assisted-conjecture-wave-summer-2026","date":"2026-09-30","date_precision":"day","short_title":"Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help","deck":null,"takeaway":"This entry catalogues about 50 of them, with the AI role as the authors state it.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2608.24961: The Gold Rush in AI4Math: Where Are We Now?","url":"https://arxiv.org/abs/2608.24961","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"arXiv 2609.40324: Cogentic, multi-agent orchestration for automated proof discovery (Google, Gemini)","url":"https://arxiv.org/abs/2609.40324","type":"paper","group":"primary","domain":"arxiv.org"},{"n":3,"title":"arXiv 2609.39959: Haah's 3D cubic code thermalizes rapidly","url":"https://arxiv.org/abs/2609.39959","type":"paper","group":"primary","domain":"arxiv.org"},{"n":4,"title":"GitHub: MColbrook/AIM (open applied problems, statuses and reviewed solutions)","url":"https://github.com/MColbrook/AIM","type":"code","group":"primary","domain":"github.com"},{"n":5,"title":"arXiv 2607.23307: Chen & Klartag, sharp thin-shell inequality (proof found by GPT-5.6 Pro; own entry)","url":"https://arxiv.org/abs/2607.23307","type":"paper","group":"primary","domain":"arxiv.org"},{"n":6,"title":"VibeMathed: tracker of AI-involved math problems","url":"https://vibemathed.com/","type":"discussion","group":"reactions","domain":"vibemathed.com"},{"n":7,"title":"Wikipedia: List of mathematical discoveries by artificial intelligence","url":"https://en.wikipedia.org/wiki/List_of_mathematical_discoveries_by_artificial_intelligence","type":"discussion","group":"reactions","domain":"en.wikipedia.org"},{"n":8,"title":"Kingy AI: Mathematics & Science Breakthrough Tracker","url":"https://kingy.ai/mathematics-science-breakthrough-tracker/","type":"discussion","group":"reactions","domain":"kingy.ai"},{"n":9,"title":"GitHub: ai4math-chronicle (provenance tracker)","url":"https://github.com/Charlie-Wang-03/ai4math-chronicle","type":"discussion","group":"reactions","domain":"github.com"},{"n":10,"title":"Terence Tao's blog (guest post by Matthew Colbrook): AIM, an invitation to explore mathematics together (Oct 2, 2026)","url":"https://terrytao.wordpress.com/2026/10/02/aim-an-invitation-to-explore-mathematics-together/","type":"discussion","group":"reactions","domain":"terrytao.wordpress.com"},{"n":11,"title":"MathOverflow: Alexandre Eremenko's answer, 'In August 2026, at least 7 of them were solved using AI'","url":"https://mathoverflow.net/a/515515","type":"discussion","group":"reactions","domain":"mathoverflow.net"}],"official":5,"filed":"2026-09-30","updated":"2026-10-19","orgs":["OpenAI","Anthropic","Google DeepMind","various mathematicians"],"title":"Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help (July–September catalogue)","summary":"Between July and September 2026 arXiv saw a steady stream of papers that resolve a named conjecture or open question and disclose that a frontier model (mostly GPT-5.6 Sol/Pro and GPT-6 Astra, also Claude Fable 5/5.1, Opus 5/5.5, Gemini) found the key idea, the counterexample or the whole proof. This entry catalogues about 50 of them, with the AI role as the authors state it. Most are preprints without peer review. The most important ones have their own entries.","key_facts":["Scale: the 'Gold Rush in AI4Math' survey counted 1,712 arXiv math papers with substantive AI contributions from 1 Mar to 20 Aug 2026 (14% of submissions by August). The VibeMathed tracker listed 748 AI-involved problems (511 marked resolved, 158 Lean-verified) when checked on 30 Sep 2026","Typical disclosure pattern: GPT-5.6 Sol/Pro dominates July–August; GPT-6 Astra dominates September after its early-September release; Anthropic models appear mostly as Claude Code agents, for Lean formalisation or for review","Fully AI-generated, per the authors: Talagrand's Conjecture 9.1 (Park & Talagrand, 'generated entirely by the AI model GPT-6 Astra'); the dominating Hadwiger conjecture disproof (found by ChatGPT 6 Astra Ultra); the Partial List Colouring Conjecture disproof ('discovered and fully verified by ChatGPT 6 Astra Ultra'); Daykin–Frankl ('LLM-generated proof'); Yau's scalar-curvature integral bound refuted ('ChatGPT generated the main theorems and their proofs'); optimal shallow circuits for Majority ('originally found by GPT-6 Astra')","Key idea from AI, human completion: the stable forking conjecture (Hart–Kim–Pillay 1996) refuted with GPT-5.6 Sol; a smooth random fast dynamo on T³ ('central proof idea was generated autonomously by ChatGPT 5.6 Sol Ultra'); Kahn–Saks conjecture on linear extensions (ChatGPT 6 Astra 'used primarily to aid in the discovery'); Talagrand's operator cotype problem ('discovered by ChatGPT (GPT-5.6)'); Khachiyan's ellipsoid conjecture ('An AI language model discovered the proof'; Lean-checked)","Counterexamples found by chatbots on the first or second prompt: Schubitopes are not Ehrhart positive (GPT-5.6 Sol Pro, first prompt, 38 min); claw-free graphs' chromatic symmetric functions are not Schur positive (ChatGPT-5.6 Sol Pro); a very ample polytope with non-unimodal h*-vector (ChatGPT 5.6 Sol); the Hinrichs–Vybíral conjecture ('found in a single prompt' with ChatGPT 6)","Agent systems: Kazhdan–Lusztig polynomials of matroids need not be unimodal (Rethlas agent on GPT-5.6 Sol, 4 h 59 min, where the GPT-5.6 Sol Ultra web interface failed); Ehrhart volume conjecture equality case (GPT-5.6 Sol, Fable 5 and Danus); the Fröberg conjecture for quintics and septics in four variables (GPT-5.6 Sol, Claude Fable 5 and Grok 4.6)","Contrasting disclosures: Reed & Stein's dense-case Erdős–Sós proof was found 'without any use of AI'; Kielak et al. solved the uniform Turán tetrahedron problem with no AI-derived arguments, while a competing author completed an alternative proof with ChatGPT-6; Cairo's Ehlers–Kundt counterexample states 'All ideas in this paper are of human origin'","Priority and credibility problems: the inhomogeneous Duffin–Schaeffer counterexample (GPT-5.6 Sol) had been announced by Pollington a year earlier; Kumar & Volk 'were unable to follow the details and verify' Sheshadri's AI-assisted determinantal-complexity proof and gave their own short quadratic lower bound; the 'Liouville Goldbach' proof was misreported as a Goldbach breakthrough","A specialist's own count: Alexandre Eremenko (Purdue, retired) wrote on MathOverflow that of about 40 unsolved problems he had collected on his web page, 'In August 2026, at least 7 of them were solved using AI. Some of these solutions are truly exciting, and contain completely new ideas.'"],"key_numbers":[],"tags":["math","physics","computer-science","meta-science","arxiv","ai-for-math","catalogue","gpt-5-6","gpt-6-astra","claude"],"science":{"field":"mathematics","subfield":"multiple (combinatorics, analysis, algebra, logic, TCS, mathematical physics)","problem":"Dozens of named conjectures and open questions (see list in body)","result":"Catalogue (roundup entry): about 50 claimed resolutions from July to September 2026 in which authors disclose a substantive AI contribution.","open_since":"","ai_system":["GPT-5.6 Sol","GPT-5.6 Pro","GPT-6 Astra","Claude Fable 5","Claude Fable 5.1","Claude Opus 5","Claude Opus 5.5","Gemini 3.1 Pro","Aristotle"],"human_role":"Varies from fully AI-generated proofs to human-led work with AI checking; see each item","verification":{"key":"preprint","label":"Preprint only","text":"Mostly unrefereed preprints; some Lean-verified; AI role self-reported by authors"},"status":"pending","shock":"","verified_by":["preprint"],"kind":"batch"},"body_md":"## What happened\n\nThis catalogue comes from a systematic pass over arXiv. It combined API queries for math, physics and theoretical-CS papers from 1 Jul to 30 Sep 2026 that mention a model name, \"conjecture\" or \"open problem\", with the AI-disclosure section of the project sweep and the public trackers. For each paper below, the PDF's AI statement was read. Quotes are from the papers, and nothing here was independently checked unless noted.\n\n### Combinatorics and discrete geometry\n- **Kahn–Saks conjecture** (balance in posets) proved. Aires, [arXiv 2609.30895](https://arxiv.org/abs/2609.30895). ChatGPT 6 Astra \"used primarily to aid in the discovery\".\n- **Talagrand's Conjecture 9.1**. Park & Talagrand, [arXiv 2609.33644](https://arxiv.org/abs/2609.33644). \"The proofs presented in this document were generated entirely by the AI model GPT-6 Astra, and none of the authors claim any credit for them.\"\n- **Dominating Hadwiger conjecture** disproved. Illingworth & Steiner, [arXiv 2609.35361](https://arxiv.org/abs/2609.35361). Found by ChatGPT 6 Astra Ultra; the humans wrote the exposition.\n- **Partial List Colouring Conjecture** (Albertson–Grossman–Haas) false. Noel, [arXiv 2609.23291](https://arxiv.org/abs/2609.23291). Counterexample \"discovered and fully verified by ChatGPT 6 Astra Ultra after some persistent prompting\".\n- **Daykin–Frankl conjecture** confirmed. Williams, [arXiv 2609.03087](https://arxiv.org/abs/2609.03087). \"We verify and communicate an LLM-generated proof\" (ChatGPT 5.6 Sol Pro).\n- **Teschner's bondage-number conjecture** counterexample. Yavari, [arXiv 2609.04257](https://arxiv.org/abs/2609.04257). Generated by GPT-5.6 Sol Max.\n- **Anstee–Sali conjecture** counterexample. Wu, [arXiv 2608.07646](https://arxiv.org/abs/2608.07646). GPT-5.6 Sol helped identify the example.\n- **Stanley's rankwise lower-bound conjecture for differential posets** (1988) disproved. Dai, [arXiv 2607.22988](https://arxiv.org/abs/2607.22988) (25 Jul). Counterexample (for r=3, rank sequence 1,3,9,22,50 instead of 1,3,9,22,51) found by the TARS agent system in an autonomous search; Xinan Dai reconstructed and checked the proof by hand.\n- **Bernhart–Kainen dispersability conjecture** (1979): a new smallest counterexample, a 5-regular two-orbit graph on 16 vertices (the previous smallest was the 20-vertex Folkman graph), given an explicit algebraic construction by an AI agent. [arXiv 2608.08118](https://arxiv.org/abs/2608.08118) (NeSy 2026); the Gold Rush survey's Table 3 lists GPT-5.5, Claude Opus 4.7, Gemini 3 Flash, Gemini 3.1 Pro and Claude Sonnet 4.6 as the models used.\n- **Chromatic symmetric functions of claw-free graphs are not Schur positive**. Matherne & Morales, [arXiv 2607.21508](https://arxiv.org/abs/2607.21508). Found with ChatGPT-5.6 Sol Pro; independently found by Prajapati.\n- **Schubitopes are not Ehrhart positive**. Li & St. Dizier, [arXiv 2608.00377](https://arxiv.org/abs/2608.00377). GPT-5.6 Sol Pro, first prompt, 38 minutes; verified in SageMath.\n- **Very ample lattice polytope with non-unimodal h\\*-vector**. Hofscheier, Kurylenko & Nill, [arXiv 2608.21507](https://arxiv.org/abs/2608.21507). Found with ChatGPT 5.6 Sol; answers a question of Ferroni–Higashitani.\n- **Equality case of Ehrhart's volume conjecture**. J. Liu, [arXiv 2608.01040](https://arxiv.org/abs/2608.01040). Complements OpenAI's inequality proof; \"obtained by generative AI\" (GPT-5.6 Sol, Fable 5, Danus).\n- **Kazhdan–Lusztig polynomials of matroids need not be unimodal**. Cheng et al., [arXiv 2607.24186](https://arxiv.org/abs/2607.24186). The Rethlas agent on GPT-5.6 Sol found it in 4 h 59 min.\n- **Laplacian S_{n,n} conjecture**. Johnston, [arXiv 2609.26895](https://arxiv.org/abs/2609.26895). \"Significant amount of help\" from ChatGPT 5.5, 5.6 Sol and 6 Astra.\n- **Comon's conjecture**, 27×27×27 counterexample. Lovitz, [arXiv 2609.28292](https://arxiv.org/abs/2609.28292). GPT-6 Astra gave \"an initial proof of the main result\".\n- **Topological Bárány–Larman conjecture** proved for prime r; the optimal colorful Tverberg theorem of Blagojević–Matschke–Ziegler cannot extend to prime powers. Soberón, [arXiv 2609.37876](https://arxiv.org/abs/2609.37876). \"An LLM was used to simplify the proof of the main result and to construct the counterexample\" (a 13-point example in R³, \"found with the use of an LLM\"; model not named).\n- **Nagamochi's scoring lemma** (unit-square packing, 2005) counterexample, showing the published proof of his rectangle bound is incomplete. Karakuş, [arXiv 2609.37410](https://arxiv.org/abs/2609.37410). \"AI tools were used during exploratory work, for symbolic and numerical checks, and for language and typesetting assistance.\"\n- **Quantum percolation on regular trees**: infinite clusters appear strictly before absolutely continuous spectrum (p_c < p_ac < 1). Becker & Oltman, [arXiv 2609.38017](https://arxiv.org/abs/2609.38017). ChatGPT used \"as a research and writing aid\".\n- **Kaplansky's conjecture** (semifields) counterexamples. Nagy & Zhou, [arXiv 2609.32651](https://arxiv.org/abs/2609.32651). Developed with ChatGPT 6 Pro; formalised by Harmonic's Aristotle in Lean 4.\n- **Generalized packing–covering conjecture**. Alfarano, Marino, Neri & Trombetti, [arXiv 2609.34910](https://arxiv.org/abs/2609.34910). ChatGPT 6 Astra turned the authors' strategy into a complete argument.\n- **Conway's subprime closure grows by the golden ratio** (conjecture of Caragiu–Vicol–Zaki). Popescu, [arXiv 2609.14188](https://arxiv.org/abs/2609.14188). GPT-6 Astra assisted; Lean-verified.\n- **Kalai's conjecture for tight trees** and **Erdős–Sós for digraphs**: see the Erdős–Sós entry.\n- **Strongly aperiodic monotile in 3D** (\"Chair44\"). Tsiokos, [arXiv 2609.19214](https://arxiv.org/abs/2609.19214). Found by \"an OpenAI reasoning model (ChatGPT, Astra)\"; the text was largely written by Claude Fable 5.1 and reviewed by agents. Follow-ups: [arXiv 2609.24779](https://arxiv.org/abs/2609.24779) (notes) and [arXiv 2609.23783](https://arxiv.org/abs/2609.23783) (matching rules). A guest post on Terence Tao's blog (Kate Stange and Edmund Harriss, [11 Oct 2026](https://terrytao.wordpress.com/2026/10/11/illustration-beyond-proof/)) says Tsiokos shared a 61-page paper and \"understood the intuitive geometric argument but not the mathematics\", and that Chaim Goodman-Strauss then distilled it into eight pages built around a diagram of matching arrows, \"giving a classical hierarchical proof of aperiodicity\".\n\n- **Chvátal's conjecture** (1972) proved. Chang, Liu & Liu, [arXiv 2609.19123](https://arxiv.org/abs/2609.19123): ChatGPT proved a guiding special case. Short spectral \"Book proof\" by GPT-6 Astra in Ellis–Filmus–Friedgut, [arXiv 2609.28404](https://arxiv.org/abs/2609.28404). Lean formalization via Codex. Own entry: `2026-09-16-chvatal-conjecture-proved`.\n- **Diagonal bipartite Ramsey b(t,t) = O(2^t)**. Mubayi, [arXiv 2609.32937](https://arxiv.org/abs/2609.32937). \"The proof was found by GPT-6 Astra.\" Own entry: `2026-09-26-mubayi-zarankiewicz-astra`.\n- **1/3–2/3 conjecture**: first general improvement of the Brightwell–Felsner–Trotter balance constant in 30 years. Aires, Chan, Pak & Panova, [arXiv 2609.30888](https://arxiv.org/abs/2609.30888). Minor AI role: \"we directed an AI assistant to explore the underlying algebraic optimization problem\" for one lemma's inequalities.\n- **List Total Colouring Conjecture** (Borodin–Kostochka–Woodall 1997; Juvan–Mohar–Škrekovski; Hilton–Johnson) false: a 20-vertex cubic graph with total chromatic number 4 and list total chromatic number 5. Noel, [arXiv 2609.38417](https://arxiv.org/abs/2609.38417) (29 Sep). \"ChatGPT 6 Astra Ultra discovered the counterexample with little input from the author\" (prompted on Sept 24). Own entry: `2026-09-29-list-total-colouring-conjecture-false-astra`.\n- **Fishburn's latent-subset conjecture** (1987) proved. Dong & Mao, [arXiv 2609.35920](https://arxiv.org/abs/2609.35920) (28 Sep). \"This proof was found by GPT-6 Astra, following an approach suggested by the author and using the weighted star inequality of Chang, Liu, and Liu\" (the inequality from the Chvátal proof).\n- **Burr–Erdős–Graham–Sós conjecture for the seven-cycle**, the remaining case k=3 after Bucić–Chen–Ma: f(n, ⌊n²/4⌋+1, C₇) = (1/8+o(1))n². Shahab, [arXiv 2609.38286](https://arxiv.org/abs/2609.38286) (29 Sep). \"Made extensive use of AI systems, principally agents built on OpenAI's Codex and Anthropic's Claude\" for the proof search, the exact rational certificate, the Lean formalisation and the manuscript; one counting lemma proved with Harmonic's Aristotle; main results Lean-checked.\n- **Aigner's majorization conjecture** (adaptive group testing on star forests) false: an explicit six-test counterexample and a family for every k ≥ 6; the converse holds for k ≤ 5. Karpelevitch, [arXiv 2609.38284](https://arxiv.org/abs/2609.38284) (29 Sep). \"Generative-AI assistants, primarily OpenAI Codex and, to a lesser extent, Anthropic Claude\" were used for arguments, software, experiments and writing.\n- **Erdős–Ulam conjectures on monochromatic union-closed families**, both claimed: every 2-colouring of subsets of [n] has a monochromatic union-closed family of super-polynomial size, but not necessarily of exponential size; Lean-verified. Bhattacharjee, Mandal & Bhattacharya, [arXiv 2610.02833](https://arxiv.org/abs/2610.02833) (2 Oct). Minor AI role: \"Claude (Anthropic) assisted with the coding\" of the Lean formalisation.\n\n### Analysis, PDE and geometry\n- **Landis conjecture** fails in dimensions ≥ 3 (real potentials). Frank & Ivanisvili, [arXiv 2608.00802](https://arxiv.org/abs/2608.00802). \"The authors acknowledge the use of AI tools\"; no detail.\n- **Pólya's conjecture for higher-dimensional Neumann balls**. Filonov, Levitin, Polterovich & Sher, [arXiv 2607.29305](https://arxiv.org/abs/2607.29305). ChatGPT and Claude \"contributed to the development of several technical lemmas\" and the rigorous computer-assisted algorithm.\n- **Yau's conjectured scalar-curvature integral bound** refuted. Hao & Zhu, [arXiv 2609.06533](https://arxiv.org/abs/2609.06533). \"ChatGPT generated the main theorems and their proofs\" (GPT-5.6 Pro).\n- **AI-discovered smooth random fast dynamo on T³**. Rowan, [arXiv 2608.20105](https://arxiv.org/abs/2608.20105). Central idea \"generated essentially autonomously by ChatGPT 5.6 Sol Ultra\"; the original AI manuscript is in the arXiv source.\n- **Nevanlinna's century-old half-plane problem** counterexample. He & Zhang, [arXiv 2608.24829](https://arxiv.org/abs/2608.24829). \"AI-assisted exploration\" (model not named).\n- **Fuchs's conjecture** counterexample. Eremenko & Zhang, [arXiv 2609.28443](https://arxiv.org/abs/2609.28443). ChatGPT as an \"exploratory tool\" and for editing.\n- **Forsythe's conjecture for restarted conjugate gradients**. Colbrook, Stepaniants & Townsend, [arXiv 2609.04659](https://arxiv.org/abs/2609.04659). Framed as an experiment in \"how far a frontier language model could be pushed\" (GPT-5.6, GPT-6).\n- **Rockafellar's sum conjecture** fails. Boţ, [arXiv 2609.13906](https://arxiv.org/abs/2609.13906). GPT-6 Astra assisted with the development.\n- **Hinrichs–Vybíral conjecture** counterexample. Vybíral, [arXiv 2609.21733](https://arxiv.org/abs/2609.21733). Found by a colleague \"in a single prompt try\" with ChatGPT 6.\n- **Talagrand's operator cotype problem**. Wu, [arXiv 2609.19731](https://arxiv.org/abs/2609.19731). \"The counterexample was discovered by ChatGPT (GPT-5.6).\"\n- **Khachiyan's ellipsoid conjecture**. Zhou, Zou & Liu, [arXiv 2609.28447](https://arxiv.org/abs/2609.28447). \"An AI language model discovered the proof\"; main theorem Lean-verified.\n- **Smooth Hamiltonian diffeomorphism with two fixed points on S²×S²**. Jiao, [arXiv 2609.33626](https://arxiv.org/abs/2609.33626). \"GPT suggested a key idea … most of the computation is done by GPT.\"\n- **Explicit mono-monostatic polyhedron** (a certified polyhedral Gömböc). Schettini Gherardini, [arXiv 2609.07827](https://arxiv.org/abs/2609.07827). A Claude Opus 4.8 / Fable 5 agent designed and ran the experiments; exact certificates.\n- **Lukic conjecture** counterexample. Yan, [arXiv 2607.26419](https://arxiv.org/abs/2607.26419). \"This example was generated by GPT-5.6.\"\n- **Feige's conjecture**. Nie & Wei, [arXiv 2607.24528](https://arxiv.org/abs/2607.24528). Proof \"obtained with the assistance of GPT-5.6 Sol\".\n- **Pólya–Szegő logarithmic vs Newtonian capacity conjecture** (1945): only a conditional reduction, the conjecture \"remains open\". Clark & Laugesen, [arXiv 2609.35438](https://arxiv.org/abs/2609.35438) (28 Sep). Review role only: ChatGPT/Codex with GPT-5.6 Sol \"assisted with a detailed critical review\" of calculations, logic and citations.\n\n### Algebra, number theory, topology and logic\n- **Stable forking conjecture** (Hart–Kim–Pillay 1996) refuted. Freitag & Mutchnik, [arXiv 2609.00436](https://arxiv.org/abs/2609.00436). \"This is an AI-generated result proven with the help of GPT-5.6 Sol.\"\n- **Huneke–Wiegand conjecture** counterexample. Pham, [arXiv 2609.07615](https://arxiv.org/abs/2609.07615). AI-assisted search with GPT-5.6 Pro; Craig Huneke independently recomputed the data.\n- **Sato's weak F-equivalence conjecture** counterexamples. Chakravarty, Choi & Xu, [arXiv 2608.18054](https://arxiv.org/abs/2608.18054). GPT-5.6 Sol \"produced the key construction\".\n- **Qin's quasimodularity conjecture** for Hilbert schemes of points. Alekseev et al., [arXiv 2609.33884](https://arxiv.org/abs/2609.33884). \"Most of the formal arguments … were initially generated by GPT-5.6 Sol.\"\n- **Fröberg's conjecture** for quintics and septics in four variables. Wang & Zhang, [arXiv 2608.24797](https://arxiv.org/abs/2608.24797). GPT-5.6 Sol, Claude Fable 5 and Grok 4.6 workflow.\n- **Mod 4 Kawauchi conjecture**. Conant, [arXiv 2607.18655](https://arxiv.org/abs/2607.18655). Claude Fable 5 \"proposed the quotient-tower strategy\" and drafted the first version.\n- **HZ/4 is not an E2-Thom spectrum** (the remaining case). Ji, [arXiv 2609.19446](https://arxiv.org/abs/2609.19446). GPT-5.6 Sol and GPT-6 Astra; reviewed with Claude Fable 5.1.\n- **Yang's conjecture** (tempered xi function) disproved. Kazin & Kadyrov, [arXiv 2609.29898](https://arxiv.org/abs/2609.29898). GPT-6 Astra identified the key sine-transform formulation.\n- **Inhomogeneous Duffin–Schaeffer conjecture** counterexamples. He & Liao, [arXiv 2609.30870](https://arxiv.org/abs/2609.30870). Found with GPT-5.6 Sol; the authors later learned that Pollington had announced a counterexample more than a year earlier.\n- **Fraenkel's conjecture** (Beatty sequences). Tan & Zhang, [arXiv 2609.01570](https://arxiv.org/abs/2609.01570). GPT-5.6 Sol resolved the cases m = 8–11, which inspired the proof strategy; Codex helped with the finite-case verification code.\n- **Separable Jacobian conjecture in characteristic two**, dimension-2 counterexample. Mondello, [arXiv 2608.02634](https://arxiv.org/abs/2608.02634). Lean-checked; ChatGPT/Codex used for organisation; Aristotle replay.\n- **Colombo's determinant problem**. [arXiv 2609.00101](https://arxiv.org/abs/2609.00101). The WuJie agent, DeepSeek, Qwen, Kimi and GPT played \"a substantial role in identifying the proof strategy\"; Lean 4.\n- **Hirose's duality conjecture** (q-discretised iterated integrals on the four-punctured line). Seki, [arXiv 2609.40213](https://arxiv.org/abs/2609.40213). \"ChatGPT, powered by GPT-6 Astra Pro, was used for mathematical discussions and to refine the English prose\" (minor role).\n- **Stuck–Zimmer conjecture**, two new cases (ergodic actions of irreducible higher-rank lattices; irreducible actions with an SL₂(ℝ) factor). Machado & Yifrach, [arXiv 2609.39424](https://arxiv.org/abs/2609.39424). \"GPT6 Astra was used to help with the literature review, explore research leads, carry out some computations and proofread\" (supporting role).\n- **De Bruijn–Erdős consecutive-gap problem**. Korsky, [arXiv 2609.07196](https://arxiv.org/abs/2609.07196). GPT Astra used \"for completing the mathematical argument\".\n\n- **Lehmer's permutation conjecture** (1965; a research problem in Knuth's TAOCP). Verhoeff, [arXiv 2610.01240](https://arxiv.org/abs/2610.01240). \"The hypercube proof at the heart of this article was found and developed by Claude Opus 5.5 in a multi-agent proof effort\"; Lean formalization by Aristotle (own entry: 2026-10-01-lehmer-permutation-conjecture-opus-5-5).\n- **Amenable actions of free groups on unital simple AF-algebras** (the last open case, for free groups, of the existence problem for amenable actions of non-amenable groups on classifiable simple C*-algebras). Suzuki, [arXiv 2610.01460](https://arxiv.org/abs/2610.01460). \"GPT-6 Astra (OpenAI) proposed a proof, including the idea of using [5], a key reference of which the author had previously been unaware.\"\n- **Erdős–Graham square products of factorials** (Erdős Problem #374): order of growth of D_k(X) settled for every k, including D_5 ≍ D_6 ≍ X. Yudin, [arXiv 2610.01899](https://arxiv.org/abs/2610.01899). \"Large language models (ChatGPT and Claude) were used in developing and checking arguments, locating references, and editing the exposition.\"\n- **Explicit polynomial counterexample to Connes' embedding conjecture** (degree 12 in 65 variables; the conjecture was already known to be false via MIP* = RE, but no explicit polynomial was known). Wang & Zhi, [arXiv 2610.01536](https://arxiv.org/abs/2610.01536). \"Generative AI tools assisted with exploring proof strategies, checking calculations, and revising the exposition.\"\n- **Pappas's conjecture on ramified unitary local models**, case r>s at self-dual level for p ≥ 2s−1 (flatness of the wedge local model). Luo, [arXiv 2610.02602](https://arxiv.org/abs/2610.02602) (1 Oct). Minor AI role: \"The author used ChatGPT and Claude for general research assistance\".\n- **Cyclic steepest descent is not universally R-superlinear** (disproves the form stated in Dai's ICM 2022 survey). Li & Wang, [arXiv 2610.00939](https://arxiv.org/abs/2610.00939). \"The main results of this paper were obtained through a generative-AI workflow using OpenAI GPT-5.6 Sol, Anthropic Claude Fable 5, and OpenAI GPT-6 Astra.\"\n- **Borg's conjecture on intersecting integer partitions**: counterexamples at every scale. Person & Schweser, [arXiv 2610.01747](https://arxiv.org/abs/2610.01747). \"ChatGPT (5.6 Sol and later GPT-6 Astra) also performed the asymptotic calculations based on Szekeres' formula and assisted with the exposition.\"\n- Also on Oct 1, with AI disclosures but smaller or unstated AI roles: Borcea's 2-variance conjecture and Baernstein's quasi-norm monotonicity conjecture (Zhang, [2610.02035](https://arxiv.org/abs/2610.02035), [2610.02009](https://arxiv.org/abs/2610.02009); Lean 4 for Borcea), the Bryant conjecture for minimal hypersurfaces in S⁴ (Qian & Tao, [2610.00886](https://arxiv.org/abs/2610.00886); \"ChatGPT … was used in the preparation\"), and higher-dimensional Morley simplices (Tran, [2610.01216](https://arxiv.org/abs/2610.01216)).\n### Theoretical CS, information theory, quantum\n- **Optimal shallow circuits for Majority**. Lecomte & Ramakrishnan, [arXiv 2609.34029](https://arxiv.org/abs/2609.34029). Constructions \"originally found by GPT-6 Astra\"; the authors rebuilt the proofs from high-level ideas.\n- **Quadratic lower bound on determinantal complexity**. Kumar & Volk, [arXiv 2609.34462](https://arxiv.org/abs/2609.34462). Came out of using ChatGPT Astra to parse Sheshadri's AI-assisted proof, whose details they were 'unable to follow' and verify.\n- **Strong secretary conjecture for linear matroids**. Bérczi, Dughmi, Livanos & Soto, [arXiv 2609.20797](https://arxiv.org/abs/2609.20797). Astra \"identified the supermodularity … and proposed the uncrossing argument\" on 15 Sep; concurrent-discovery note.\n- **Nelson–Nguyen conjecture**. Mai & Rao, [arXiv 2609.22548](https://arxiv.org/abs/2609.22548). ChatGPT-5.6 Pro \"used in proving and writing\".\n- **Markovity conjecture for two-receiver broadcast channels** refuted. Liu & Huang, [arXiv 2608.13170](https://arxiv.org/abs/2608.13170). GPT-5.6 Sol; Chandra Nair suggested the AI search and checked the result.\n- **Shor's orthogonal-measurement conjecture**. [arXiv 2609.27992](https://arxiv.org/abs/2609.27992). Codex and GPT-5.6 Sol for exploration and error checking only.\n- **Distributional variants of the Aaronson–Ambainis conjecture**. [arXiv 2609.35327](https://arxiv.org/abs/2609.35327). \"Google Gemini suggested the core idea underlying the inner-gadget construction.\"\n\n- **Haah's 3D cubic code thermalizes rapidly** (settles whether it is a self-correcting quantum memory: it is not, at any positive temperature; first analytic rapid-mixing proof for a fracton code). Stengele, Caha, Capel & Warzel, [arXiv 2609.39959](https://arxiv.org/abs/2609.39959). \"We acknowledge the use of LLMs for a proof of Lemma 4.1\" and for testing proof ideas (model not named).\n- **Generalized semi-Clifford conjecture** (Zeng et al. 2007) at level k ≤ 4, any prime dimension. Marcus, Subramanian & Dall'Agnol, [arXiv 2609.38751](https://arxiv.org/abs/2609.38751). OpenAI Codex helped develop proof strategies and check algebra; Claude Code for literature and drafting.\n- **Edit-distance codes over a four-letter alphabet** (DNA barcodes): E₄(6,3) ≥ 120 (was 114) plus 12 further improved lower bounds at lengths 6–9. Yeung, [arXiv 2609.39081](https://arxiv.org/abs/2609.39081). An LLM coding agent wrote the search and verifier code over five weeks; the paper documents failures in which unchecked intermediate results stopped the search early.\n- **Cogentic** (Google Research multi-agent prover on Gemini): novel results on five open problems in online learning, auction theory and mechanism design, each checked by domain experts. Cai, Gupta, Jiang, Liaw, Mehta, Velegkas & Wang, [arXiv 2609.40324](https://arxiv.org/abs/2609.40324); results listed at [sites.google.com/view/cogentic](https://sites.google.com/view/cogentic).\n\n### Sept 30 – Oct 2 additions (found Oct 5)\n- **Erdős #108 (Erdős–Hajnal high-girth problem)** disproved through a Lean bounty (Kohlmeyer–Kruer, ChatGPT/Codex). The 3-colour sharpening by Nguyen & Walczak, [arXiv 2609.40192](https://arxiv.org/abs/2609.40192), has \"ChatGPT-6 Astra discovered a proof of Theorem 2.1\". Own entry: `2026-09-15-erdos-108-high-girth-problem-disproved-conjectures-io`.\n- **ε-Dvoretzky conjecture** proved. Klartag & Moshe, [arXiv 2610.03204](https://arxiv.org/abs/2610.03204). The key idea \"stemmed from a discussion between ChatGPT and the second named author\". Own entry.\n- **Barvinok's log-concavity question (line version)**. Leake & Mohammadi Yekta, [arXiv 2609.39917](https://arxiv.org/abs/2609.39917): \"proven using ChatGPT 6 Astra\". Own entry.\n- **Triangle-free box graphs beating Burling (1965)**. Tomon, [arXiv 2610.03517](https://arxiv.org/abs/2610.03517): \"found by ChatGPT Astra after guidance from the author\". Own entry.\n- **Friedgut's continuous-cube coalition conjecture**: a simplified proof of Chattopadhyay–Gurumukhani's result. Friedgut, [arXiv 2610.03086](https://arxiv.org/abs/2610.03086): \"discovered with the aid of ChatGPT-6 Astra … my mathematical contribution to this current project was limited to my two suggestions to the bot\".\n- **Mond's conjecture** for corank-one germs C³→C⁴. Rimányi, [arXiv 2610.03331](https://arxiv.org/abs/2610.03331). Experiments, first drafts of several proofs and audits came \"with substantial help from AI (Anthropic's Claude; OpenAI's ChatGPT)\".\n- **Simpson's closedness conjecture** in arbitrary rank. Hu, [arXiv 2610.03542](https://arxiv.org/abs/2610.03542). \"ChatGPT was used for calculations, proving intermediate results, and polishing the writing.\"\n- **Lam–Schilling–Shimozono conjecture**: K-k-Schur functions are k-Schur positive. Bai & Guo, [arXiv 2610.01708](https://arxiv.org/abs/2610.01708). The proof is human; \"the counterexample given in Section 5 was found by ChatGPT-6 Astra\".\n- **Strong Roberson conjecture** (homomorphism distinguishing power) refuted. Kristjánsson, [arXiv 2610.03550](https://arxiv.org/abs/2610.03550): \"developed through substantial interaction with an AI agent\".\n- **Exact eight-point angular-energy conjecture** (Hiriart-Urruty's list) counterexample. Zhao, [arXiv 2610.03207](https://arxiv.org/abs/2610.03207): \"produced by OpenAI's GPT-5.6 Sol Ultra through Codex\".\n- **Hegselmann–Krause models**: the proximity digraph need not freeze. Hegarty, Ognissanti & Wedin, [arXiv 2610.03229](https://arxiv.org/abs/2610.03229): \"All of the examples above were found by Claude Opus 5.5\".\n- **Delooping level is not additive under tensor products**. Lam, [arXiv 2609.39745](https://arxiv.org/abs/2609.39745). The counterexample was found by \"the newest publicly available (Pro Subscription) model of ChatGPT\" (Oct 1).\n- **Quantum random self-reduction for linear problems**. Asadi, Hirahara & Shimizu, [arXiv 2609.39823](https://arxiv.org/abs/2609.39823): \"The algorithm and proof strategy underlying the main theorem were suggested by ChatGPT 5.5.\"\n- **Nearest stabilizer product state hardness**. Grier, Pashayan & Schaeffer, [arXiv 2610.02037](https://arxiv.org/abs/2610.02037): \"Significant parts of the hardness proofs … were found by an interactive prompting of Gemini 3.1 Pro.\"\n- **Disjoint-data inverse problem** sharp spectral threshold. Ylinen, [arXiv 2610.00871](https://arxiv.org/abs/2610.00871): \"GPT-5.6-sol produced the initial nonuniqueness construction\".\n- **Ramanujan–Sato series of level 11** (open since Cooper et al. 2015). Campbell, [arXiv 2610.00551](https://arxiv.org/abs/2610.00551). Built on \"a construction described by GPT-5.6 Sol Pro\".\n- **Prime labelings of trees**. Ho, [arXiv 2610.02271](https://arxiv.org/abs/2610.02271): \"Most of the proof development, computational verification, and drafting … were carried out by generative AI systems, principally GPT Astra and Claude Opus\".\n- **Standard conjecture of Hodge type**, explicit form for Hermitian varieties. Harashita, [arXiv 2610.01731](https://arxiv.org/abs/2610.01731), with \"extensive use of Claude Opus 5 and Claude Opus 5.5 for formulating assertions, proving results, drafting\".\n- Smaller or mostly human: Quillen's finiteness conjecture for the cotangent complex in characteristic 2 (Schürg, [2610.03208](https://arxiv.org/abs/2610.03208); ChatGPT as \"somebody to talk to\"); irrationality exponent of ζ(2) below 5.0193784 (Niedbala Giraudin, [2610.02912](https://arxiv.org/abs/2610.02912); \"Technical assistance: Claude\"); typical intersecting families at n=2k+1, 2k+2 (Li, [2610.02119](https://arxiv.org/abs/2610.02119); ChatGPT 5.6 Sol helped with technical lemmas); Matsumura's extension problem, smooth case, confirming Siu's plurigenera conjecture in that setting (Chen, Rao & Wang, [2609.40040](https://arxiv.org/abs/2609.40040); ChatGPT 5.6 and 6 Pro as auxiliary tools).\n\n### Late-September disclosures the sweep missed (PDF scan, Oct 5 evening)\n- **Lovász conjecture (1969)**, long cycles in vertex-transitive graphs: n^(1−o(1)), up from n^(2/3−o(1)). Li & Methuku, [arXiv 2609.38135](https://arxiv.org/abs/2609.38135) (29 Sep). GPT-5.6 Sol pointed the authors to the Tessera–Tointon structure theorem and Babai's contraction lemma, and \"supplied the required group-theoretic arguments\" for the key remaining Lemma 6.1. Own entry: `2026-09-29-lovasz-conjecture-nearly-linear-bound-gpt-5-6-sol`.\n- **Tight convergence of Nesterov's fast gradient method**: Peppy, an AI workflow built on performance-estimation problems (PEP), closes Conjectures 4–5 of Taylor et al. (2017) for FGM and OGM and the FGM/FISTA rational-coefficient conjectures. The authors call these the first analytic proofs of the tight FGM bounds, open \"roughly a decade\". Suh, Yoon, Nguyen, Ying & Ma, [arXiv 2609.35762](https://arxiv.org/abs/2609.35762) (28 Sep). Proofs generated by Codex with GPT-6 Astra (Ultra reasoning) and checked symbolically in SymPy; \"the Codex-generated drafts required human editing\". Code: [PEPFlow peppy-v1](https://github.com/pepflow-lib/PEPFlow/tree/peppy-v1).\n- **Watkins's conjecture holds for all infinite groups** (graphical regular representations; the Cayley index of every infinite group is 1, 2 or 8). Sutherland, [arXiv 2610.01049](https://arxiv.org/abs/2610.01049) (1 Oct). \"OpenAI's ChatGPT provided substantial assistance with developing arguments, locating references, and preparing the checking programs\"; the checks \"do not constitute formal verification\".\n- **Rational points near the moment curve**: counterexamples showing the Hickman–Srivastava range is nearly sharp, against the belief that an O(n⁻¹) improvement was possible. Chen, Srivastava & Technau, [arXiv 2610.02443](https://arxiv.org/abs/2610.02443) (1 Oct). A self-contained argument (the recursive identity (2.5)) \"was later suggested to us by Chat G.P.T. 6 Astra\"; written and verified by the authors.\n- **Chen's conjecture for flat n-tori** confirmed (sharp Willmore lower bound, Clifford torus the unique minimiser), but it fails for the total mean curvature of general n-tori when n ≥ 3. Ni, Wang & Xie, [arXiv 2609.36491](https://arxiv.org/abs/2609.36491) (29 Sep). \"ChatGPT 5.6 Sol was used to generate preliminary versions of certain arguments in Lemma 3.2, Remark 4.6, and Proposition 5.5\"; the authors substantially revised them.\n- **Flat normal bundles are not preserved by mean curvature flow** (an embedded torus and an entire graph in R⁴). Kunikawa, [arXiv 2609.34291](https://arxiv.org/abs/2609.34291) (28 Sep). ChatGPT 5.6 \"was used to suggest suitable ansatzes and to explore examples\".\n- Smaller AI roles: union-closed sets conjecture bound raised past Liu's conjectured 0.382709 to 0.38288 (Costa & Sadhu, [2610.02295](https://arxiv.org/abs/2610.02295); ChatGPT for \"exploratory symbolic calculations, proof checking\" and code); Fang–Lin spectral Turán conjecture counterexample (Wu & Lu, [2609.37208](https://arxiv.org/abs/2609.37208); ChatGPT \"to discuss proof strategies, check intermediate arguments\"); Boston's unramified conjecture for odd GL₂ over Q and McLeman's (3,3)-conjecture for p > 3 (Luo, [2609.37252](https://arxiv.org/abs/2609.37252); ChatGPT 6 for proofreading and \"verifying the logical consistency\"); Cordero-Erausquin–Eskenazis question on Talagrand type of S₁ (Luo, Wang & Zhou, [2610.03407](https://arxiv.org/abs/2610.03407); Codex for literature and editing); FPT-size resolution refutations (Cai & Li, [2610.02047](https://arxiv.org/abs/2610.02047); one construction from a ChatGPT-found gap).\n\n### October 2026 listings (moved)\nThe blocks that used to follow here (the Oct 2–5, Oct 5–6, early-October, 6–8 Oct, 8–9 Oct, 5–8 Oct and 6–9 Oct arXiv listings) were moved unchanged on 13 Oct 2026 to a catalogue of their own: [AI-assisted results on arXiv, October 2026](/e/2026-10-13-ai-assisted-results-october-2026/). The smaller 5–9 Oct batch is in [a separate entry](/e/2026-10-09-arxiv-ai-disclosed-results-early-october-2026/).\n\n### Outside arXiv (claims with weaker provenance)\n- **Conway's refinement conjecture for omnific integers** (1976): Dan Abramov's \"I vibed a proof of Conway's conjecture\" (18 Sep; Claude, ChatGPT/Sol and Codex agents; Lean proof passing Palomar checks; not reviewed by mathematicians). [overreacted.io](https://overreacted.io/how-i-vibed-a-proof-of-conways-conjecture/)\n- **Theo-Conjecture** (FirstPrinciples) on a 35-year-old question about common-divisor graphs ([arXiv 2608.04040](https://arxiv.org/abs/2608.04040); \"not yet completed peer review\").\n- **Star Fleet Math**: 20 parallel Codex/GPT \"starships\" claiming 13 Lean-verified Erdős-problem solutions (July 2026). [starfleetmath.com](https://www.starfleetmath.com/)\n\n### Community response: AIM problem list (Oct 2, 2026)\nIn a guest post on Terence Tao's blog, Matthew Colbrook announced **AIM**, organised with Steve Brunton, Maarten V. de Hoop, George Stepaniants, Alex Townsend and Rachel Ward. It is a community-curated GitHub list of precise open problems in applied mathematics, spectral theory and related fields, each with a dated literature-status review. On Oct 2 the repo listed 642 open targets (531 open, 111 partial), 23 solved entries, 0 Lean-verified. Contributions with or without AI are welcome. The organisers say the list is \"rather than using a set of problems to benchmark AI systems\" and is meant to give mathematicians, especially early-career researchers, credit for understanding and explaining proofs. A companion site, [AIM, explained](https://mathematics-explained.com/), runs a competition for explanatory papers and videos of up to 10 minutes (entries close 2027-01-01). [Tao's blog](https://terrytao.wordpress.com/2026/10/02/aim-an-invitation-to-explore-mathematics-together/) · [GitHub](https://github.com/MColbrook/AIM)\n\n## Why it matters\n\nBy September 2026, \"settled with AI help\" had stopped being news in itself: several named conjectures a week, across most of mathematics, with disclosures ranging from \"fully generated by the model\" to \"used for proofreading\". For a model with an older cutoff, the practical lesson is to check the current status of any conjecture before calling it open. Many that were open in early 2026 have claimed resolutions, but most are still unrefereed.","disputed":[{"label":"Verification","text":"Mostly unrefereed preprints; some Lean-verified; AI role self-reported by authors","sources":[]}],"related":[{"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":"2026-10-06-openai-math-release-722-manuscripts","url":"https://postcutoff.com/e/2026-10-06-openai-math-release-722-manuscripts/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI releases 722 AI-written math manuscripts claiming hundreds of open problems","deck":"Including quasi-Riemann, Unique Games, Hodge for CM abelian varieties and free group factors","takeaway":"If even a fraction of these results hold up, this is the largest single jump in mathematical knowledge on record, produced by an AI system in about six weeks.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":79,"official":13,"filed":"2026-10-07","updated":"2026-10-29","orgs":["OpenAI"]},{"id":"2026-10-02-kls-conjecture-proved-ai-assisted","url":"https://postcutoff.com/e/2026-10-02-kls-conjecture-proved-ai-assisted/","date":"2026-10-02","date_precision":"day","short_title":"Kannan–Lovász–Simonovits conjecture proved in two AI-assisted preprints","deck":"Song–Zhang's O(1) bound, then Bizeul–Klartag–Lehec ('most proofs … found by ChatGPT')","takeaway":"KLS was among the best-known open problems in high-dimensional geometry, with consequences for sampling algorithms on convex bodies.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":2,"filed":"2026-10-06","updated":"2026-10-13","orgs":["Microsoft Research","Weizmann Institute of Science","OpenAI","Anthropic"]},{"id":"2026-10-02-epsilon-dvoretzky-conjecture-klartag-moshe","url":"https://postcutoff.com/e/2026-10-02-epsilon-dvoretzky-conjecture-klartag-moshe/","date":"2026-10-02","date_precision":"day","short_title":"Klartag and Moshe prove the ε-Dvoretzky conjecture","deck":"The key probabilistic idea came from a ChatGPT discussion","takeaway":"This is a classical problem in asymptotic geometric analysis, and the preprint comes from Boaz Klartag (Tel Aviv University and Weizmann Institute), a leading researcher in the field.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-05","updated":"2026-10-05","orgs":["Tel Aviv University","Weizmann Institute of Science","OpenAI"]},{"id":"2026-10-02-tomon-triangle-free-box-graphs-astra","url":"https://postcutoff.com/e/2026-10-02-tomon-triangle-free-box-graphs-astra/","date":"2026-10-02","date_precision":"day","short_title":"ChatGPT Astra finds geometric triangle-free graphs with near-optimal chromatic number, the first improvement on Burling's 1965 box bound","deck":null,"takeaway":"This is an exponential improvement on a 60-year-old bound in geometric graph colouring, and it is another case where the model supplied the constructions rather than routine checks.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-05","updated":"2026-10-05","orgs":["Umeå University","OpenAI"]},{"id":"2026-10-01-lehmer-permutation-conjecture-opus-5-5","url":"https://postcutoff.com/e/2026-10-01-lehmer-permutation-conjecture-opus-5-5/","date":"2026-10-01","date_precision":"day","short_title":"Lehmer's 1965 permutation conjecture proved","deck":"Claude Opus 5.5 found the short hypercube proof","takeaway":"This is a famous, decades-old combinatorics problem named in Knuth's TAOCP, and the paper credits the key proof idea directly to Claude Opus 5.5.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":1,"filed":"2026-10-02","updated":"2026-10-09","orgs":["Eindhoven University of Technology","Anthropic","Harmonic"]},{"id":"2026-09-30-barvinok-log-concavity-totally-unimodular-astra","url":"https://postcutoff.com/e/2026-09-30-barvinok-log-concavity-totally-unimodular-astra/","date":"2026-09-30","date_precision":"day","short_title":"GPT-6 Astra proves Barvinok's log-concavity question for contingency tables on lines, giving lattice-point bounds for all totally unimodular polytopes","deck":null,"takeaway":"It is a named question in a central area of combinatorial counting, with the core proof credited to the model.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-05","updated":"2026-10-05","orgs":["OpenAI"]},{"id":"2026-09-29-list-total-colouring-conjecture-false-astra","url":"https://postcutoff.com/e/2026-09-29-list-total-colouring-conjecture-false-astra/","date":"2026-09-29","date_precision":"day","short_title":"List Total Colouring Conjecture (late 1990s) disproved","deck":"Counterexample found by ChatGPT 6 Astra Ultra 'with little input'","takeaway":"This is a named conjecture from the late 1990s, listed on Open Problem Garden, falling to a prompted AI search, with a counterexample small enough to verify by hand.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":2,"filed":"2026-10-05","updated":"2026-10-07","orgs":["OpenAI","University of Victoria"]},{"id":"2026-09-29-lovasz-conjecture-nearly-linear-bound-gpt-5-6-sol","url":"https://postcutoff.com/e/2026-09-29-lovasz-conjecture-nearly-linear-bound-gpt-5-6-sol/","date":"2026-09-29","date_precision":"day","short_title":"GPT-5.6 Sol supplies key steps in a nearly linear bound for the Lovász path conjecture","deck":null,"takeaway":"This is a large quantitative step on a famous 57-year-old problem in graph theory.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-05","updated":"2026-10-05","orgs":["OpenAI"]},{"id":"2026-09-28-schiffer-pompeiu-convex-higher-dimensions","url":"https://postcutoff.com/e/2026-09-28-schiffer-pompeiu-convex-higher-dimensions/","date":"2026-09-28","date_precision":"day","short_title":"Convex counterexamples to Schiffer and Pompeiu in dimensions 3, 4, 6, 8, 10 and 14, made with Claude Opus 5.5 and GPT-6 Astra/Sol","deck":null,"takeaway":"If it holds up, the Schiffer and Pompeiu conjectures fail even for convex domains, which was one of the natural fallback forms of the conjectures.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":3,"filed":"2026-09-30","updated":"2026-09-30","orgs":["Jizhou Guo"]},{"id":"2026-09-28-four-body-convex-central-configurations-unique-tomar","url":"https://postcutoff.com/e/2026-09-28-four-body-convex-central-configurations-unique-tomar/","date":"2026-09-28","date_precision":"day","short_title":"Four-body problem: uniqueness of convex central configurations for all masses claimed (Simó–Yoccoz conjecture), AI-found and formalized in Lean (Tomar)","deck":null,"takeaway":"The problem is less famous than Smale's sixth, but it sat on the standard list of open problems in the field for 14 years and had attracted steady partial results.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-13","updated":"2026-10-19","orgs":["independent"]},{"id":"2026-09-27-poincare-conjecture-lean-formalization","url":"https://postcutoff.com/e/2026-09-27-poincare-conjecture-lean-formalization/","date":"2026-09-27","date_precision":"day","short_title":"Perelman's proof of the Poincaré conjecture formalised in Lean, with AI-generated code","deck":null,"takeaway":"After Fermat's Last Theorem (Claude, Sept 2026), this is the second landmark formalization of a famous proof in a month.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":8,"official":6,"filed":"2026-10-01","updated":"2026-10-19","orgs":["UC San Diego","Cornell University","Princeton University"]},{"id":"2026-09-22-mumford-shah-conjecture-astra-claim","url":"https://postcutoff.com/e/2026-09-22-mumford-shah-conjecture-astra-claim/","date":"2026-09-22","date_precision":"day","short_title":"Mathematician posts an unchecked ChatGPT Astra proof of the planar Mumford–Shah conjecture (1989), citing OpenAI's '100 open problems' claim","deck":null,"takeaway":"If correct, it would settle one of the best-known open problems in the calculus of variations.","category":"science","category_label":"Science & math","importance":4,"confidence":"low","status":{"key":"pending","labels":["Awaiting review"]},"sources":1,"official":1,"filed":"2026-09-30","updated":"2026-10-19","orgs":["Francesco Deangelis","University of Münster","OpenAI"]},{"id":"2026-09-22-odlyzko-poonen-conjecture-proved","url":"https://postcutoff.com/e/2026-09-22-odlyzko-poonen-conjecture-proved/","date":"2026-09-22","date_precision":"day","short_title":"Odlyzko–Poonen conjecture (1993) proved unconditionally","deck":"'The proofs are due to GPT-6 Astra', which also wrote a 22,000-line Lean formalisation","takeaway":"The unconditional case had stayed open after Breuillard and Varjú's conditional proof in 2019.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":2,"official":2,"filed":"2026-09-30","updated":"2026-10-07","orgs":["Constantin Kogler","OpenAI"]},{"id":"2026-09-21-openai-100-open-problems-claim","url":"https://postcutoff.com/e/2026-09-21-openai-100-open-problems-claim/","date":"2026-09-21","date_precision":"day","short_title":"OpenAI says an internal model resolved 100+ long-standing open problems in 24 days of training (list released 6 Oct: 722 manuscripts)","deck":null,"takeaway":"If substantiated, it would mean open problems are being resolved at industrial scale.","category":"science","category_label":"Science & math","importance":3,"confidence":"low","status":{"key":"pending","labels":["Awaiting review"]},"sources":11,"official":5,"filed":"2026-09-29","updated":"2026-10-10","orgs":["OpenAI"]},{"id":"2026-09-16-liouville-goldbach-lean-proof","url":"https://postcutoff.com/e/2026-09-16-liouville-goldbach-lean-proof/","date":"2026-09-16","date_precision":"day","short_title":"Lean-verified 'Liouville Goldbach' theorem goes viral as a GPT-6 Astra 'Goldbach breakthrough'; the AI role is unconfirmed and it is not the Goldbach conjecture","deck":null,"takeaway":"The mathematics is formally verified and does answer a small open question.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":7,"official":2,"filed":"2026-09-30","updated":"2026-10-19","orgs":["Captain Sude (pseudonymous)"]},{"id":"2026-09-15-erdos-108-high-girth-problem-disproved-conjectures-io","url":"https://postcutoff.com/e/2026-09-15-erdos-108-high-girth-problem-disproved-conjectures-io/","date":"2026-09-15","date_precision":"day","short_title":"Erdős–Hajnal high-girth problem (Erdős #108) disproved with ChatGPT/Codex help and a Lean proof, via the Conjectures.io bounty; experts sharpen it with GPT-6 Astra","deck":null,"takeaway":"This is a well-known problem from Erdős's list, and the counterexample comes with a machine-checked proof.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":7,"official":7,"filed":"2026-10-05","updated":"2026-10-07","orgs":["Conjectures.io","Purdue University","OpenAI"]},{"id":"2026-09-14-k-server-conjecture-proved","url":"https://postcutoff.com/e/2026-09-14-k-server-conjecture-proved/","date":"2026-09-14","date_precision":"day","short_title":"The k-server conjecture, the 'holy grail' of online algorithms, is proved at Oxford","deck":"ChatGPT 6 Astra generalised the authors' k = 3 proof to all k","takeaway":"The k-server conjecture is one of the best-known open problems in algorithms, and Koutsoupias co-proved the previous best bound in 1995.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":1,"filed":"2026-09-30","updated":"2026-09-30","orgs":["University of Oxford","Christian Coester","Elias Koutsoupias","Marek Zbysiński","OpenAI"]},{"id":"2026-09-11-medvedev-logic-undecidable","url":"https://postcutoff.com/e/2026-09-11-medvedev-logic-undecidable/","date":"2026-09-11","date_precision":"day","short_title":"Medvedev's logic of finite problems (1962) shown undecidable","deck":"Key idea from ChatGPT Sol 5.6, central argument checked in Lean by Claude Opus 5","takeaway":"It answers a well-known question in non-classical logic, and other logicians already build on it: on 30 September Han Xiao derived the undecidability of the logic Cheq from it, citing \"the AI-generated proof\".","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":2,"official":2,"filed":"2026-09-30","updated":"2026-10-29","orgs":["Rodrigo Nicolau Almeida","Søren Brinck Knudstorp","OpenAI","Anthropic"]},{"id":"2026-09-09-pierce-birkhoff-conjecture-disproved","url":"https://postcutoff.com/e/2026-09-09-pierce-birkhoff-conjecture-disproved/","date":"2026-09-09","date_precision":"day","short_title":"Pierce–Birkhoff conjecture disproved by a multi-agent GPT + Claude harness","deck":"Counterexamples Lean-verified","takeaway":"Pierce–Birkhoff is a classic problem in real algebraic geometry and ordered rings, open for 70 years.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":2,"official":2,"filed":"2026-09-30","updated":"2026-10-19","orgs":["University of Chicago","Lek-Heng Lim","Zehua Lai","Junyu Ren","OpenAI","Anthropic"]},{"id":"2026-09-05-i3322-bell-inequality-infinite-dimensions","url":"https://postcutoff.com/e/2026-09-05-i3322-bell-inequality-infinite-dimensions/","date":"2026-09-05","date_precision":"day","short_title":"The I3322 Bell inequality needs infinite dimensions","deck":"Pál–Vértesi conjecture (2010) proved from an approximate proof by GPT-5.5 Pro","takeaway":"It settles a basic question about how much entanglement quantum correlations can require, in the smallest possible Bell scenario.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-09-30","updated":"2026-09-30","orgs":["Andrea Coladangelo","University of Washington","OpenAI"]},{"id":"2026-09-04-reed-solomon-list-decoding-capacity-ai","url":"https://postcutoff.com/e/2026-09-04-reed-solomon-list-decoding-capacity-ai/","date":"2026-09-04","date_precision":"day","short_title":"Reed–Solomon codes list-decoded up to capacity and proximity gaps settled, with GPT-5.6 Sol and ChatGPT 5.6 Pro (Brakensiek–Chen–Putterman–Zhang–Zheng; Jeronimo)","deck":null,"takeaway":"In early September 2026 two preprints settled long-standing problems about Reed–Solomon codes, the most widely used error-correcting codes.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":8,"official":8,"filed":"2026-10-07","updated":"2026-10-29","orgs":["Simons Institute","OpenAI","Ethereum Foundation"]},{"id":"2026-09-03-frontiermath-erdos-astra-disproves-erdos-problem-1","url":"https://postcutoff.com/e/2026-09-03-frontiermath-erdos-astra-disproves-erdos-problem-1/","date":"2026-09-03","date_precision":"day","short_title":"Pre-release GPT-6 Astra disproves Erdős's 'first serious problem' (1931, $500) and proves the rational-exponents conjecture, all Lean-verified, in Epoch's FrontierMath Erdős runs","deck":null,"takeaway":"Problem #1 is probably the longest-standing open Erdős problem.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":10,"official":7,"filed":"2026-09-30","updated":"2026-10-16","orgs":["OpenAI","Epoch AI"]},{"id":"2026-09-03-erdos-sos-conjecture-proved-gpt-6-astra","url":"https://postcutoff.com/e/2026-09-03-erdos-sos-conjecture-proved-gpt-6-astra/","date":"2026-09-03","date_precision":"day","short_title":"GPT-6 Astra proves the Erdős–Sós conjecture with a short counting argument","deck":"Mathematicians race to simplify and extend it","takeaway":"Erdős–Sós is one of the best-known conjectures in extremal graph theory, and this is among the clearest cases of an AI finding a genuinely new, short idea that experts call \"ingenious\" and \"surprising\".","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":10,"official":9,"filed":"2026-09-30","updated":"2026-09-30","orgs":["OpenAI","Epoch AI"]},{"id":"2026-08-28-matrix-spencer-conjecture-proved","url":"https://postcutoff.com/e/2026-08-28-matrix-spencer-conjecture-proved/","date":"2026-08-28","date_precision":"day","short_title":"Matrix Spencer conjecture proved","deck":"Authors credit GPT-5.6 Sol Pro with 'the heavy-lifting' for the key lemma","takeaway":"Matrix Spencer was one of the headline open problems in discrepancy theory.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":2,"filed":"2026-09-30","updated":"2026-09-30","orgs":["Emrullah Akbas","Suvrit Sra","OpenAI"]},{"id":"2026-08-25-gold-rush-ai4math-survey","url":"https://postcutoff.com/e/2026-08-25-gold-rush-ai4math-survey/","date":"2026-08-25","date_precision":"day","short_title":"Substantive AI use in arXiv math papers rises from 1.4% to 14% in five months","deck":"From the survey 'The Gold Rush in AI4Math'.","takeaway":"It is one of the first quantitative measures of how fast AI entered research mathematics in 2026: roughly a tenfold rise in substantive use within one semester.","category":"research","category_label":"Research","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":1,"official":1,"filed":"2026-09-29","updated":"2026-09-30","orgs":["Jiashun Jin","Zheng Tracy Ke","Bingcheng Sui"]},{"id":"2026-08-19-yau-tian-donaldson-cscK-disproof-claim","url":"https://postcutoff.com/e/2026-08-19-yau-tian-donaldson-cscK-disproof-claim/","date":"2026-08-19","date_precision":"day","short_title":"Peking University preprint claims an AI-found disproof of the Yau–Tian–Donaldson conjecture for constant scalar curvature metrics","deck":null,"takeaway":"The Yau–Tian–Donaldson programme is central to modern complex geometry, and the paper is explicit that its main result is AI-generated.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":2,"filed":"2026-09-30","updated":"2026-10-07","orgs":["Peking University","Jihao Liu","Anthropic","OpenAI"]},{"id":"2026-08-13-banach-isometric-conjecture-solved","url":"https://postcutoff.com/e/2026-08-13-banach-isometric-conjecture-solved/","date":"2026-08-13","date_precision":"day","short_title":"Banach's isometric conjecture (1932) completed in the real case with key steps from ChatGPT 5.5/5.6 Pro; complex and quaternionic cases follow five days later","deck":null,"takeaway":"Banach's conjecture is one of the oldest questions in the geometry of normed spaces, and Gromov's even-dimensional solution had left the remaining odd cases open.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":2,"filed":"2026-09-30","updated":"2026-09-30","orgs":["Xinbao Lu","Kaiwen Yang","Antonio Acuaviva","Tomasz Kania","OpenAI"]},{"id":"2026-08-04-period-index-conjecture-false","url":"https://postcutoff.com/e/2026-08-04-period-index-conjecture-false/","date":"2026-08-04","date_precision":"day","short_title":"Alexander Perry disproves the period-index conjecture","deck":"A flawed ChatGPT example was the starting point","takeaway":"The period-index conjecture was a central open question on Brauer groups of function fields.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-09-30","updated":"2026-09-30","orgs":["Alexander Perry","OpenAI"]},{"id":"2026-08-03-schiffer-pompeiu-conjectures-disproved","url":"https://postcutoff.com/e/2026-08-03-schiffer-pompeiu-conjectures-disproved/","date":"2026-08-03","date_precision":"day","short_title":"Planar Schiffer and Pompeiu conjectures disproved by two independent groups","deck":"One proof has a Lean certificate written by GPT-5.6","takeaway":"Schiffer's conjecture is a classic rigidity question and appears on Yau's list of open problems.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":7,"official":5,"filed":"2026-09-30","updated":"2026-09-30","orgs":["Matthew Colbrook","George Stepaniants","Gonzalo Cao-Labora","Jaume de Dios Pont"]},{"id":"2026-07-29-maxwell-point-charge-conjecture-false","url":"https://postcutoff.com/e/2026-07-29-maxwell-point-charge-conjecture-false/","date":"2026-07-29","date_precision":"day","short_title":"Maxwell's conjecture on equilibria of point charges is false","deck":"Five charges with at least 24 critical points, construction idea from GPT-5.6 Sol","takeaway":"It is a long-standing question at the boundary of physics and real algebraic geometry, and one of the few 2026 AI-assisted results in classical physics.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-09-30","updated":"2026-09-30","orgs":["Philip Arathoon","Gavin Ball","Matthew D. Kvalheim","OpenAI"]},{"id":"2026-07-25-sharp-thin-shell-inequality-gpt-5-6-pro","url":"https://postcutoff.com/e/2026-07-25-sharp-thin-shell-inequality-gpt-5-6-pro/","date":"2026-07-25","date_precision":"day","short_title":"Sharp thin-shell inequality","deck":"Var(|X|²) ≤ 8n for isotropic log-concave vectors, with a proof 'found by GPT-5.6 Pro' (Chen & Klartag)","takeaway":"This is a sharp result in a mature area, signed by people who built that area, with the model credited for the proof in the abstract.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":2,"filed":"2026-10-13","updated":"2026-10-13","orgs":["ETH Zurich","Weizmann Institute of Science","OpenAI"]}],"people":[{"id":"terence-tao","name":"Terence Tao","url":"https://postcutoff.com/person/terence-tao/"},{"id":"scott-aaronson","name":"Scott Aaronson","url":"https://postcutoff.com/person/scott-aaronson/"}],"posts":[{"id":"2026-10-03-szegedy-quo-vadis-mathematics","title":"Christian Szegedy, \"Quo Vadis, Mathematics?\": 'Mathematics is about to graduate'","url":"https://postcutoff.com/p/2026-10-03-szegedy-quo-vadis-mathematics/"},{"id":"2026-09-24-eremenko-mathoverflow-seven-of-my-open-problems-solved-by-ai","title":"Alexandre Eremenko on MathOverflow: 'In August 2026, at least 7' of his ~40 collected open problems 'were solved using AI'","url":"https://postcutoff.com/p/2026-09-24-eremenko-mathoverflow-seven-of-my-open-problems-solved-by-ai/"},{"id":"2026-09-22-kalai-be-a-grothendieck-ai-mathematics","title":"Gil Kalai: '“Be a Grothendieck!”—On AI and Mathematics'","url":"https://postcutoff.com/p/2026-09-22-kalai-be-a-grothendieck-ai-mathematics/"},{"id":"2026-10-11-stange-harriss-illustration-beyond-proof-tao-blog","title":"Illustration beyond Proof","url":"https://postcutoff.com/p/2026-10-11-stange-harriss-illustration-beyond-proof-tao-blog/"},{"id":"2026-10-03-taback-tao-blog-ai-mathematicians-like-me","title":"What does the advent of powerful AI models mean for mathematicians like me?","url":"https://postcutoff.com/p/2026-10-03-taback-tao-blog-ai-mathematicians-like-me/"},{"id":"2026-09-29-rachel-webb-tao-blog-ai-math","title":"How AI does, and does not, change the way I do math","url":"https://postcutoff.com/p/2026-09-29-rachel-webb-tao-blog-ai-math/"},{"id":"2026-09-26-corwin-value-based-approach-mathematics-tao-blog","title":"A value-based approach to mathematics","url":"https://postcutoff.com/p/2026-09-26-corwin-value-based-approach-mathematics-tao-blog/"}],"videos":[],"models":[],"changes":[{"date":"2026-10-19","type":"edit","text":"Result field labelled as a catalogue (roundup), since this id does not contain 'ai-assisted-results'"},{"date":"2026-10-13","type":"edit","text":"Added Eremenko's MathOverflow count (7 of his ~40 collected problems solved with AI in August) with a post file; linked two results that now have their own entries: the sharp thin-shell inequality (Chen & Klartag, 25 July, GPT-5.6 Pro; [Sharp thin-shell inequality](https://postcutoff.com/e/2026-07-25-sharp-thin-shell-inequality-gpt-5-6-pro/)) and four-body convex central configurations (Tomar, 28 Sept; [Four-body problem: uniqueness of convex central configurations for all masses claimed (Simó–Yoccoz conjecture), AI-found and formalized in Lean (Tomar)](https://postcutoff.com/e/2026-09-28-four-body-convex-central-configurations-unique-tomar/))"},{"date":"2026-10-13","type":"edit","text":"Split: the October arXiv listings (Oct 2–5, Oct 5–6, early October, 6–8, 8–9, 5–8 and 6–9 Oct blocks, about 36 KB) moved unchanged to [October 2026: the arXiv stream of conjectures settled with disclosed AI help continues](https://postcutoff.com/e/2026-10-13-ai-assisted-results-october-2026/) to keep this page light; this entry now covers July to 2 October. The `related` list keeps the summer entries and drops 8 October entries that are now linked from the new catalogue"},{"date":"2026-10-13","type":"edit","text":"Added the 6–9 Oct block (3D-cube isoperimetry, László's Toeplitz conjecture refuted with Lean, SK-model sampling, Codex Astra's Proposition 5.4, Deb–Sokal, Hurwitz fields, three papers building on OpenAI manuscripts, smaller roles); no new own entries"},{"date":"2026-10-13","type":"edit","text":"Added the 5–8 Oct batch lead: five own entries (Erdős #993, Toms–Winter, Bolzano, multiplier associativity, decreasing diagrams), Jackson–Ordaz, Colonel Blotto, IPM blowup, and four papers that build on OpenAI's unrefereed manuscripts"},{"date":"2026-10-12","type":"edit","text":"Manual arXiv scan of the 8–9 Oct listing found results our automated search query missed (five new own entries: kinetic Krylov–Safonov/Pucci, Smale's sixth for five bodies, 3×3 matrix multiplication rank, Erdős #522, PPT distillation); added Forcade–Pollington, Shamir leakage, Burdzy hot spots, quasi-RH constants, Vasc inequality and related human work"},{"date":"2026-10-12","type":"edit","text":"Chair44: added the Stange–Harriss guest post on Tao's blog (Goodman-Strauss's 8-page distillation of the 61-page AI-found proof)"},{"date":"2026-10-10","type":"edit","text":"The cyclicity conjecture (Dobrick, 2610.10093) moved to its own entry; also lists the Galt–Tyutyanov, Pappas, Vaught, Arveson–Douglas, parking-function and Hedetniemi items from this sweep, all already catalogued"},{"date":"2026-10-09","type":"edit","text":"Five new own entries (treeability, Dualization, Hilbert number, hyperkähler SYZ, and the September Courtade–Kumar proofs found late); added Erdős–Sós bipartite links, Mongardi, Brudnyi, Bermond–Thomassen, Smith, minor disclosures and the Viva La Vida prover study"},{"date":"2026-10-08","type":"edit","text":"Early-October additions from the 7 Oct arXiv (explicit Tsirelson counterexample with GPT-6 Astra + Fable 5.1 and Lean, Lê's conjecture reduction with ChatGPT finishing the remaining cases in a forthcoming paper, Polishchuk–Van den Bergh, centroaffine Bernstein, HNS Euler conductors, CheapGPT, AxiomProver BSD statistics, minor disclosures); links to three new own entries"},{"date":"2026-10-07","type":"edit","text":"Science block: kind: batch (many results in one entry) (not a long-open problem; listed with other AI science results, not in the open-problems count); verified_by: preprint (most results are unrefereed preprints)"},{"date":"2026-10-07","type":"edit","text":"Four new own entries (Artin–Davenport, Woodin's GCH question, polynomial Littlewood–Offord, Reed–Solomon capacity); added Erdős–Gallai (Kim; also OpenAI family 181), Mumford–Tate for hyper-Kähler, simplex-cluster, continuous Aldous–Lyons, McLeod, Dirac Faber–Krahn, random-oracle unitary synthesis, Strang splines, Adámek–Rosický, Carlet/Kasami, Makar-Limanov, mad partition and ~20 smaller disclosures"},{"date":"2026-10-06","type":"edit","text":"Manual arXiv scan of the Oct 2–5 listing: 3SUM/APSP, linear Hadwiger and KLS got own entries; added Golod–Shafarevich (Aletheia + Fable), amicable numbers, matroid common-bases FPRAS, simple nil ring, Benson–Etingof–Ostrik, LeBrun–Salamon and ~20 more disclosures"},{"date":"2026-10-05","type":"edit","text":"PDF scan of our automated search's 43 'no AI disclosure' conjecture papers found 13 with AI statements; added Lovász (own entry), Peppy/Nesterov FGM, Watkins, rational points near curves, Chen's conjecture for n-tori, MCF flat normal bundles and five minor ones"},{"date":"2026-10-05","type":"edit","text":"Added late-September items our automated search's 6-day arXiv window surfaced (List Total Colouring, Fishburn, Burr–Erdős–Graham–Sós for C₇, Aigner, Erdős–Ulam, Pappas, Pólya–Szegő); PDF disclosures read"},{"date":"2026-10-05","type":"edit","text":"Added 18 Sept 30–Oct 2 disclosures (Erdős #108, Dvoretzky, Barvinok and Tomon have own entries), found by a manual arXiv scan after our automated search's date window missed them"},{"date":"2026-10-02","type":"edit","text":"Added the AIM open-problem list (Colbrook et al., guest post on Tao's blog, Oct 2)"},{"date":"2026-10-02","type":"edit","text":"Added Lehmer (own entry), Suzuki AF-algebras (GPT-6 Astra), Erdős #374 (Yudin), explicit Connes counterexample, cyclic steepest descent, Borg partitions and four minor Oct 1 disclosures"},{"date":"2026-10-01","type":"edit","text":"Added Chvátal (own entry), Mubayi b(t,t) (own entry) and the 1/3–2/3 balance-constant paper"},{"date":"2026-10-01","type":"edit","text":"Added Stanley rankwise conjecture (TARS agent, arXiv 2607.22988) and Bernhart–Kainen smaller counterexample (arXiv 2608.08118)"},{"date":"2026-10-01","type":"edit","text":"Added Hirose duality (Seki), Stuck–Zimmer cases (Machado–Yifrach), Haah cubic code (LLM-proved Lemma 4.1), semi-Clifford level 4 (Codex), edit-distance codes (Yeung) and Google's Cogentic"},{"date":"2026-09-30","type":"edit","text":"Added Bárány–Larman (Soberón), Nagamochi scoring lemma (Karakuş) and quantum percolation (Becker–Oltman) disclosures"},{"date":"2026-09-30","type":"filed","text":"Created from a systematic arXiv/tracker review (AI disclosures read in each PDF)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-30","run":null,"sources_read":"A systematic arXiv/tracker review (AI disclosures read in each PDF)","updated":"2026-10-19","human_review":null,"version":{"date":"2026-10-19"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":153,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":92,"in_training_data":false},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":183,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":122,"in_training_data":false}],"short_url":"https://postcutoff.com/s/summer-2026-flood-dozens"}