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
Awaiting review
The 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.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Lean-verified
- Importance
- 3 of 5
- Last verified
- 19 October 2026
Your AI and this story
- GPT-6 Astra172 days after its cutoff
- Claude Opus 5.5111 days after its cutoff
- Gemini 4 Argon202 days after its cutoff
- Grok 4.7141 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 111 days before it.
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’
Show 6 more
- 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)
What happened
Monday’s arXiv announcement (19 Oct, submissions of 15–16 Oct) was the first big batch since Thursday. Its main theme is that mathematicians are now publishing papers that check, simplify and extend results from OpenAI’s 6 Oct release. Two of them (Brennan, Smith–Toda) have their own entries. Three more follow up OpenAI release papers:
- Deligne–Drinfeld. After Thomas Willwacher’s simplified version of OpenAI’s proof (arXiv 2610.15592), Minoru Hirose gives an independent route through his Z_(2)-integrality of the Hoffman basis. He discussed the mathematics with GPT-6 Astra Pro.
- Hénon–Lane–Emden. Li, Lu and Zhang start from OpenAI’s localized kernel identity (family 370) and extend nonexistence to fractional orders. Their one-line AI acknowledgement sits at the end of the paper, which is why the sweep’s abstract filter missed it.
- Navier–Stokes. Niemi tests the physical meaning of OpenAI’s forced singular flow with magnetic reconnection simulations.
Two other strong results are human-led with substantial AI help. Cen, Hong and Wu disprove two endpoint bounds proposed in James Wright’s problem list, with ChatGPT and Codex. Weikang Li’s lower bound for quantum walk search on the 2D grid answers a 2003 question of Aaronson and Ambainis, with GPT-6 Astra and Opus 5.5 assisting with calculations. Google DeepMind’s Busy Beaver paper is the most autonomous item: a Gemini agent finds and Lean-proves compact descriptions of eleven unresolved BB(6) machines.
No 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 searchable through fxtwitter without post ids).
Why it matters
Two weeks after the release, verification of OpenAI’s release papers has moved from blog posts and forum threads to arXiv papers by specialists. So far the pattern is the same each time: no errors found, the arguments are longer than they need to be, and the experts quickly strengthen the results.
What is disputed or not yet verified
| Verification | Unrefereed arXiv preprints; Lean for Busy Beaver accelerations, shock layers and separators |
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Sources
14 sources from 1 site. Numbers match the chips in the text.
14 sources: 14 primary
Primary
- arXiv 2610.23719: Confluence relations, Hoffman basis over Z(2), and the Deligne–Drinfeld conjecture (Hirose)arxiv.org, paper
- arXiv 2610.22802: The fractional Hénon–Lane–Emden conjecture (Li, Lu, Zhang)arxiv.org, paper
- arXiv 2610.22510: Magnetic flux ring splitting near a Navier–Stokes singularity (Niemi)arxiv.org, paper
- arXiv 2610.23563: Disproof of Wright’s Problems 14 and 15 on lacunary maximal functionsarxiv.org, paper
- arXiv 2610.23560: Electrostatic Limits on Quantum Spatial Search (Weikang Li)arxiv.org, paper
- arXiv 2610.22603: Steps Towards Autonomous AI Discovery on the Busy Beaver Frontier (Google DeepMind)arxiv.org, paper
- arXiv 2610.22660: Spectral stability for strong ideal-gas shock layers (Humpherys)arxiv.org, paper
- arXiv 2610.23792: Revisiting separators in string graphs (Davies, Rzążewski, Spalding-Jamieson, Walczak)arxiv.org, paper
- arXiv 2610.23785: Hornich–Hlawka inequality, constructions and reductions (Lee)arxiv.org, paper
- arXiv 2610.23817: Extremal problems related to the Krzyż conjecturearxiv.org, paper
- arXiv 2610.22612: Proof Perplexity (Das, Banerjee)arxiv.org, paper
- arXiv 2610.22447: Energy-critical NLS, higher-kinetic-energy regimearxiv.org, paper
Show all 14 sources
Changes
- Filed (24 disclosure PDFs and 14 no-disclosure PDFs read in full text)