{"schema":"postcutoff/event@1","as_of":"2026-10-19T09:28:00+02:00","url":"https://postcutoff.com/e/2026-10-19-ai-assisted-results-october-19-listing/","md":"https://postcutoff.com/e/2026-10-19-ai-assisted-results-october-19-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":"2026-10-19-ai-assisted-results-october-19-listing","date":"2026-10-19","date_precision":"day","short_title":"AI-assisted results in the 19 Oct 2026 arXiv listing","deck":"Experts rework OpenAI's release papers (Deligne–Drinfeld, Hénon–Lane–Emden, Navier–Stokes), Wright's harmonic-analysis problems disproved with Codex, an Aaronson–Ambainis lower bound, and DeepMind's Busy Beaver agent","takeaway":"Monday's arXiv announcement brought the first wave of human follow-up papers on OpenAI's October maths release, alongside a dozen routine AI disclosures. The strongest items have their own entries: Brennan, Smith–Toda, lonely runner and tournament Hamiltonian cycles.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2610.23719: Confluence relations, Hoffman basis over Z(2), and the Deligne–Drinfeld conjecture (Hirose)","url":"https://arxiv.org/abs/2610.23719","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"arXiv 2610.22802: The fractional Hénon–Lane–Emden conjecture (Li, Lu, Zhang)","url":"https://arxiv.org/abs/2610.22802","type":"paper","group":"primary","domain":"arxiv.org"},{"n":3,"title":"arXiv 2610.22510: Magnetic flux ring splitting near a Navier–Stokes singularity (Niemi)","url":"https://arxiv.org/abs/2610.22510","type":"paper","group":"primary","domain":"arxiv.org"},{"n":4,"title":"arXiv 2610.23563: Disproof of Wright's Problems 14 and 15 on lacunary maximal functions","url":"https://arxiv.org/abs/2610.23563","type":"paper","group":"primary","domain":"arxiv.org"},{"n":5,"title":"arXiv 2610.23560: Electrostatic Limits on Quantum Spatial Search (Weikang Li)","url":"https://arxiv.org/abs/2610.23560","type":"paper","group":"primary","domain":"arxiv.org"},{"n":6,"title":"arXiv 2610.22603: Steps Towards Autonomous AI Discovery on the Busy Beaver Frontier (Google DeepMind)","url":"https://arxiv.org/abs/2610.22603","type":"paper","group":"primary","domain":"arxiv.org"},{"n":7,"title":"arXiv 2610.22660: Spectral stability for strong ideal-gas shock layers (Humpherys)","url":"https://arxiv.org/abs/2610.22660","type":"paper","group":"primary","domain":"arxiv.org"},{"n":8,"title":"arXiv 2610.23792: Revisiting separators in string graphs (Davies, Rzążewski, Spalding-Jamieson, Walczak)","url":"https://arxiv.org/abs/2610.23792","type":"paper","group":"primary","domain":"arxiv.org"},{"n":9,"title":"arXiv 2610.23785: Hornich–Hlawka inequality, constructions and reductions (Lee)","url":"https://arxiv.org/abs/2610.23785","type":"paper","group":"primary","domain":"arxiv.org"},{"n":10,"title":"arXiv 2610.23817: Extremal problems related to the Krzyż conjecture","url":"https://arxiv.org/abs/2610.23817","type":"paper","group":"primary","domain":"arxiv.org"},{"n":11,"title":"arXiv 2610.22612: Proof Perplexity (Das, Banerjee)","url":"https://arxiv.org/abs/2610.22612","type":"paper","group":"primary","domain":"arxiv.org"},{"n":12,"title":"arXiv 2610.22447: Energy-critical NLS, higher-kinetic-energy regime","url":"https://arxiv.org/abs/2610.22447","type":"paper","group":"primary","domain":"arxiv.org"},{"n":13,"title":"arXiv 2610.22663: Rational decomposition of polyhedra and a conjecture of Brlek and Reutenauer","url":"https://arxiv.org/abs/2610.22663","type":"paper","group":"primary","domain":"arxiv.org"},{"n":14,"title":"arXiv 2610.22387: QMBL, the Quantum Many-Body Leaderboard","url":"https://arxiv.org/abs/2610.22387","type":"paper","group":"primary","domain":"arxiv.org"}],"official":14,"filed":"2026-10-19","updated":"2026-10-19","orgs":["OpenAI","Anthropic","Google DeepMind","Harmonic","various mathematicians"],"title":"AI-assisted results in the 19 Oct 2026 arXiv listing: experts rework OpenAI's release papers (Deligne–Drinfeld, Hénon–Lane–Emden, Navier–Stokes), Wright's harmonic-analysis problems disproved with Codex, an Aaronson–Ambainis lower bound, and DeepMind's Busy Beaver agent","summary":"Catalogue of the 19 Oct 2026 arXiv announcement (papers submitted 15–16 Oct). Four results have their own entries: Brennan's conjecture (Smirnov's group checks OpenAI's proof and shortens it), Smith–Toda V(4) for p ≥ 11 (Angeltveit after OpenAI), the lonely runner bound (1+c)/2n with ChatGPT 6 Pro, and the asymptotic maximum number of Hamiltonian cycles in tournaments (proofs found by GPT-5.6). This page lists the rest. Hirose gives an alternative proof of the Deligne–Drinfeld conjecture, \"for which a proof was previously presented in the OpenAI Math Release\". Li–Lu–Zhang extend OpenAI's Hénon–Lane–Emden argument to fractional orders. Cen–Hong–Wu disprove Wright's Problems 14 and 15 with ChatGPT and Codex. Weikang Li proves an Ω(√(N log N)) lower bound for 2D quantum spatial search, answering Aaronson and Ambainis, with GPT-6 Astra and Opus 5.5. Google DeepMind's Gemini agent finds Lean-verified accelerations for eleven BB(6) machines. Humpherys proves strong shock-layer stability with ChatGPT and Claude (Lean). Davies et al. repair the string-graph separator theorem, with Lean proofs written by Aristotle.","key_facts":["Own entries: Brennan (2610.23853), Smith–Toda V(4) (2610.23215), lonely runner (2610.23790), tournaments (2610.23755)","Deligne–Drinfeld, second human proof: Minoru Hirose, 'Confluence relations, Hoffman basis over Z_(2), and the Deligne–Drinfeld conjecture' (2610.23719): every multiple zeta value is a Z_(2)-combination of the Hoffman basis (Hirose–Sato conjecture); with Brown and Furusho this 'gives an alternative proof of the Deligne–Drinfeld conjecture, for which a proof was previously presented in the OpenAI Math Release' (family 008). AI: 'The author used ChatGPT (GPT-6 Astra Pro) for mathematical discussions and assistance with the exposition'","Fractional Hénon–Lane–Emden (Kui Li, Haoyang Lu, Zhitao Zhang, 2610.22802; not in the sweep's AI list, found by our full-text scan): subcritical nonexistence for orders 0 < s < 1; 'The localized kernel identity and the comparison of level-set intervals in OpenAI [26] and Mei-Wei [27] provide the starting point'; acknowledgement: 'We used AI assistance in parts of the proof of the subcritical fractional Hénon-Lane-Emden conjecture.' OpenAI family 370","Navier–Stokes follow-up in physics: Antti Niemi (Nordita), 'Magnetic flux ring splitting near a Navier–Stokes singularity' (2610.22510), simulates resistive MHD driven by a flow reproducing 'the geometry and scaling of the collapsing core' of OpenAI's forced singular flow; code and analysis 'written with the assistance of large language models (both Anthropic Claude and OpenAI models)'","Wright's Problems 14 and 15 disproved (Xi Cen, Guixiang Hong, Xinfeng Wu, 2610.23563): a compactly supported singular measure with Fourier decay of every order < 1/2 whose dyadic maximal operator has infinite weak-L¹ and H¹→weak-L¹ norms, refuting the proposed endpoint bounds from James Wright's 2017 harmonic-analysis problem list; 'the authors used ChatGPT and Codex to discuss possible proof strategies, assist in drafting and checking parts of the mathematical arguments'","Quantum spatial search (Weikang Li, Tsinghua IIIS, 2610.23560): a local quantum walk needs Ω(√(N log N)) steps to find a marked vertex on an L×L lattice, 'resolving the long-standing open question posed by Aaronson and Ambainis in 2003', so Tulsi's algorithm is optimal; proof via an electrostatics correspondence; 'We acknowledge the use of GPT-6 Astra and Opus-5.5 to assist with theoretical calculations'; code github.com/LWKJJONAK/QuSearch","Busy Beaver agent (Google DeepMind: Dos Santos, Veeriah, Havrilla, Bolt, Zuzic, Singh, Zahavy; 2610.22603): a Gemini-based pipeline (pattern detection, LLM conjecturing, informal proof, Lean 4 proof) 'autonomously discovered and formally verified novel Collatz-like accelerations for eleven machines in BB(6)', provisionally classified as Cryptids; follows DeepMind's cryptids repo of 9 Oct","Strong shock layers (Jeffrey Humpherys, 2610.22660): analytic proof of 1D spectral stability of sufficiently strong ideal-gas Navier–Stokes shock layers on a region including air and monatomic gases, verified in Lean; 'ChatGPT (OpenAI) and Claude (Anthropic) contributed substantially to this work, ChatGPT to the development of the energy estimates and the exposition, and Claude to the Lean formalization'","String-graph separators repaired (James Davies, Paweł Rzążewski, Jack Spalding-Jamieson, Bartosz Walczak; 2610.23792): O(√m) balanced separators for string graphs, region intersection graphs over minor-closed families and induced-minor-free graphs, after a 2024 flaw broke Lee's proof and the works built on it; main results 'obtained entirely by the human authors'; Lean formalization 'almost entirely constructed using the proprietary LLM-based tool Aristotle', the improved bound formalized and first obtained with GPT 5.6 Sol","Hornich–Hlawka (Seokbin Lee, 2610.23785): answers three of five Marinescu–Niculescu problems; 'An initial version of the proof of Theorem 4.3 was generated by ChatGPT-5.6 Sol'; parts of Theorem 1.4 and Lemma 6.7 'discovered by ChatGPT-6 Astra'","Krzyż-type extremal problems (Instanes, Llinares, Vukotić; 2610.23817): ChatGPT 5.6 Sol simplified Lemma 19 and suggested Example 10; ChatGPT 6 Astra supplied Lemma 20, removing an extra assumption from Theorem 2(a); Claude Opus 5.5 proofread and suggested Remark 14","Smaller roles: energy-critical NLS upper cone (Ma, Miao, Yang, Zhang, Zheng; 2610.22447; ChatGPT 5.6 Sol 'used to assist in the proof of Lemma 4.1'); Brlek–Reutenauer conjecture proved (D'Alessandro, Papi; 2610.22663; AI only for literature checks); online geometric matching (2610.23130; ChatGPT used for Section 4 results); Erdős–Pósa for induced even cycles (2610.22967; language editing only)","Methods and tools: 'Proof Perplexity' (Das, Banerjee, Cambridge; 2610.22612) scores Claude's Riemann-zeta zeros proof against Mathlib; QMBL quantum many-body leaderboard, 1,434 energies, aggregation 'made cheap by AI agents' (2610.22387); Lean rate–distortion library (2610.22404); LLM-assisted CHC solving (2610.23771)","Scanned in full text with no AI statement (19 Oct): Kosniowski's conjecture for four fixed points (2610.23855), Beauville–Voisin for Debarre–Voisin fourfolds (2610.23376), Mbekhta's conjecture (2610.23229), matroid-tangle counterexamples (2610.23059), Niu's tandem-queue conjecture (2610.22837), metric Poissonian pair correlation (2610.22836, 2610.22833), local antimagic leaf counterexamples (2610.22783), Lovász number of random circulants (2610.22971), and Reid's square achievement game (2610.22410; Lean-formalized, answers Erickson's question, no AI statement)"],"key_numbers":[],"tags":["math","physics","computer-science","arxiv","catalogue","chatgpt","gpt-6-astra","codex","claude","gemini","aristotle","lean","openai-math-release","busy-beaver"],"science":{"field":"mathematics","subfield":"multiple (algebraic topology, number theory, harmonic analysis, PDE, combinatorics, quantum computing, computability)","problem":"Deligne–Drinfeld conjecture; Wright's Problems 14–15; Aaronson–Ambainis 2D spatial search; BB(6) holdouts; strong shock stability; Fox–Pach-type separators; see list","result":"Catalogue of AI-assisted results in the 19 Oct 2026 arXiv announcement, led by human follow-ups to OpenAI's release","open_since":"","ai_system":["ChatGPT","GPT-6 Astra","GPT-5.6 Sol","Codex","Claude Opus 5.5","Gemini","Aristotle"],"human_role":"Mostly human-led with AI for proof steps, checks and Lean; DeepMind's Busy Beaver pipeline is autonomous","verification":{"key":"lean","label":"Lean-verified","text":"Unrefereed arXiv preprints; Lean for Busy Beaver accelerations, shock layers and separators"},"status":"pending","shock":"","verified_by":["preprint","lean"],"kind":"batch"},"body_md":"## What happened\n\nMonday's arXiv announcement (19 Oct, submissions of 15–16 Oct) was the first big batch since Thursday. Its main theme is that\nmathematicians are now publishing papers that check, simplify and extend results from OpenAI's 6 Oct release. Two of them\n(Brennan, Smith–Toda) have their own entries. Three more follow up OpenAI release papers:\n\n- **Deligne–Drinfeld.** After Thomas Willwacher's simplified version of OpenAI's proof (arXiv 2610.15592), Minoru Hirose gives an\n  independent route through his Z_(2)-integrality of the Hoffman basis. He discussed the mathematics with GPT-6 Astra Pro.\n- **Hénon–Lane–Emden.** Li, Lu and Zhang start from OpenAI's localized kernel identity (family 370) and extend nonexistence to\n  fractional orders. Their one-line AI acknowledgement sits at the end of the paper, which is why the sweep's abstract filter missed it.\n- **Navier–Stokes.** Niemi tests the physical meaning of OpenAI's forced singular flow with magnetic reconnection simulations.\n\nTwo other strong results are human-led with substantial AI help. Cen, Hong and Wu disprove two endpoint bounds proposed in\nJames Wright's problem list, with ChatGPT and Codex. Weikang Li's lower bound for quantum walk search on the 2D grid answers a 2003\nquestion of Aaronson and Ambainis, with GPT-6 Astra and Opus 5.5 assisting with calculations. Google DeepMind's Busy Beaver paper\nis the most autonomous item: a Gemini agent finds and Lean-proves compact descriptions of eleven unresolved BB(6) machines.\n\nNo Hacker News thread or high-reach X post on any of these papers was found on the morning of 19 Oct (HN Algolia search; X not\nsearchable through fxtwitter without post ids).\n\n## Why it matters\n\nTwo weeks after the release, verification of OpenAI's release papers has moved from blog posts and forum threads to arXiv papers by\nspecialists. So far the pattern is the same each time: no errors found, the arguments are longer than they need to be, and the\nexperts quickly strengthen the results.","disputed":[{"label":"Verification","text":"Unrefereed arXiv preprints; Lean for Busy Beaver accelerations, shock layers and separators","sources":[]}],"related":[{"id":"2026-10-19-ai-assisted-results-zenodo-october-17-19","url":"https://postcutoff.com/e/2026-10-19-ai-assisted-results-zenodo-october-17-19/","date":"2026-10-19","date_precision":"day","short_title":"AI-assisted maths on Zenodo, 17–19 Oct 2026","deck":"A claimed proof of the 1985 Arad–Herzog conjecture, Messerschmidt's conjecture confirmed with Codex, and a Claude-run study on AI-written science","takeaway":"Zenodo, not arXiv, carried the weekend's AI-assisted results: an unknown author claims the 40-year-old Arad–Herzog conjecture on products of conjugacy classes with agentic OpenAI and Anthropic tools and a literature-relative Lean check, and a Bologna mathematician confirms Messerschmidt's 2018 conjecture with Codex. None is refereed.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":13,"official":13,"filed":"2026-10-19","updated":"2026-10-19","orgs":["OpenAI","Anthropic","various mathematicians"]},{"id":"2026-10-18-ai-assisted-results-october-17-listing","url":"https://postcutoff.com/e/2026-10-18-ai-assisted-results-october-17-listing/","date":"2026-10-17","date_precision":"day","short_title":"AI-assisted results, 16–17 Oct 2026 (Zenodo and arXiv leftovers)","deck":"Ramanujan's prime-counting inequality settled unconditionally with Claude, a Claude Code paper mill on the Hodge conjecture, and LLM agents in materials science","takeaway":"With no new arXiv announcement over the weekend, the notable AI-assisted items came from Zenodo, led by Padhi's Claude-assisted proof that Ramanujan's inequality holds unconditionally for all x ≥ 38,358,837,683.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":14,"official":14,"filed":"2026-10-18","updated":"2026-10-18","orgs":["Anthropic","various mathematicians"]},{"id":"2026-10-16-brennan-conjecture-openai-proof-binder-ivrii-prause-smirnov","url":"https://postcutoff.com/e/2026-10-16-brennan-conjecture-openai-proof-binder-ivrii-prause-smirnov/","date":"2026-10-16","date_precision":"day","short_title":"Brennan's conjecture: experts confirm and shorten OpenAI's proof","deck":null,"takeaway":"The first famous result from OpenAI's October maths release to be checked by leading experts in its field: four complex analysts, including Fields medallist Stanislav Smirnov, found no gap. They say the AI combined known techniques in a way 'missed by the human experts'.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":5,"official":4,"filed":"2026-10-19","updated":"2026-10-19","orgs":["OpenAI","University of Toronto","Tel Aviv University","Åbo Akademi University","University of Geneva"]},{"id":"2026-10-16-smith-toda-v4-angeltveit-improves-openai","url":"https://postcutoff.com/e/2026-10-16-smith-toda-v4-angeltveit-improves-openai/","date":"2026-10-16","date_precision":"day","short_title":"Smith–Toda V(4) for p ≥ 11, after OpenAI's p = 1009","deck":null,"takeaway":"A homotopy theorist checked two Smith–Toda papers from OpenAI's maths release, found no errors but 'strange choices' (a suspiciously high prime, needless ultrafilters), and widened the result from one prime to all primes p ≥ 11.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-19","updated":"2026-10-19","orgs":["OpenAI","Australian National University"]},{"id":"2026-10-16-lonely-runner-constant-gap-hu-jing-chatgpt","url":"https://postcutoff.com/e/2026-10-16-lonely-runner-constant-gap-hu-jing-chatgpt/","date":"2026-10-16","date_precision":"day","short_title":"Lonely runner: (1+c)/2n bound with ChatGPT 6","deck":null,"takeaway":"A human-led result on the 1967 lonely runner problem in which ChatGPT 6 Pro proposed the GCD-sum route, pointed to Green–Walker and fixed gaps, but 'the models were unable to improve the lonely runner bound on their own'.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":2,"filed":"2026-10-19","updated":"2026-10-19","orgs":["OpenAI","University of Chinese Academy of Sciences","Ohio State University"]},{"id":"2026-10-16-max-hamiltonian-cycles-tournaments-gpt-5-6-wormald","url":"https://postcutoff.com/e/2026-10-16-max-hamiltonian-cycles-tournaments-gpt-5-6-wormald/","date":"2026-10-16","date_precision":"day","short_title":"Tournament Hamiltonian cycles: GPT-5.6 settles Alon's question","deck":null,"takeaway":"Princeton's Divoux and Wang asked GPT-5.6 for a lower bound; a second instance turned the method into the matching upper bound, closing a line of work that runs from Szele's 1943 paper through Alon (1990) and Friedgut–Kahn.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-19","updated":"2026-10-19","orgs":["OpenAI","Princeton University"]},{"id":"2026-10-09-deepmind-cryptids-smaller-turing-machines-goldbach-riemann-zf","url":"https://postcutoff.com/e/2026-10-09-deepmind-cryptids-smaller-turing-machines-goldbach-riemann-zf/","date":"2026-10-09","date_precision":"day","short_title":"Gemini Argon shrinks Goldbach, Riemann and ZF Turing machines","deck":null,"takeaway":"Smaller machines tighten the known bounds on where the Busy Beaver function stops being computable from standard mathematics.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":3,"official":2,"filed":"2026-10-16","updated":"2026-10-16","orgs":["Google DeepMind"]},{"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":84,"official":13,"filed":"2026-10-07","updated":"2026-10-19","orgs":["OpenAI"]},{"id":"2026-09-08-openai-navier-stokes-blowup","url":"https://postcutoff.com/e/2026-09-08-openai-navier-stokes-blowup/","date":"2026-09-08","date_precision":"day","short_title":"OpenAI claims a Millennium Prize problem","deck":"10,000 AI agents prove forced Navier–Stokes blow-up; priority dispute erupts","takeaway":"It is the first credible AI claim on a Clay Millennium Prize problem, even if only a technically permitted variant.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"disputed","labels":["Disputed"]},"sources":39,"official":4,"filed":"2026-09-29","updated":"2026-10-19","orgs":["OpenAI"]}],"people":[{"id":"scott-aaronson","name":"Scott Aaronson","url":"https://postcutoff.com/person/scott-aaronson/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-19","type":"filed","text":"Created (24 disclosure PDFs and 14 no-disclosure PDFs read in full text)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-10-19","run":null,"sources_read":"24 disclosure PDFs and 14 no-disclosure PDFs read in full text","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":172,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":111,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":202,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":141,"in_training_data":false}],"short_url":null}