{"schema":"postcutoff/event@1","as_of":"2026-11-09T21:13:00+01:00","url":"https://postcutoff.com/e/2026-11-06-ai-assisted-results-november-6-listing/","md":"https://postcutoff.com/e/2026-11-06-ai-assisted-results-november-6-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":"2026-11-06-ai-assisted-results-november-6-listing","date":"2026-11-06","date_precision":"day","short_title":"AI-assisted results, 6 Nov: arXiv of 6 Nov and Hexagon of 5 Nov","deck":null,"takeaway":"The 6 Nov sweep listed 183 new arXiv papers mentioning AI and 26 uncited Hexagon works. Own entries: Tusnády's problem (two preprints), Singmaster's bound by Claude Opus 5.5 and the Hopfield capacity bracket.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"Hexagon 2611.00127","url":"https://hexagonmath.org/abs/2611.00127","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":2,"title":"Hexagon 2611.00126","url":"https://hexagonmath.org/abs/2611.00126","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":3,"title":"Hexagon 2611.00125","url":"https://hexagonmath.org/abs/2611.00125","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":4,"title":"Hexagon 2611.00124","url":"https://hexagonmath.org/abs/2611.00124","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":5,"title":"Hexagon 2611.00123","url":"https://hexagonmath.org/abs/2611.00123","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":6,"title":"Hexagon 2611.00122","url":"https://hexagonmath.org/abs/2611.00122","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":7,"title":"Hexagon 2611.00121","url":"https://hexagonmath.org/abs/2611.00121","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":8,"title":"Hexagon 2611.00120","url":"https://hexagonmath.org/abs/2611.00120","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":9,"title":"Hexagon 2611.00119","url":"https://hexagonmath.org/abs/2611.00119","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":10,"title":"Hexagon 2611.00118","url":"https://hexagonmath.org/abs/2611.00118","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":11,"title":"Hexagon 2611.00117","url":"https://hexagonmath.org/abs/2611.00117","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":12,"title":"Hexagon 2611.00116","url":"https://hexagonmath.org/abs/2611.00116","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":13,"title":"Hexagon 2611.00115","url":"https://hexagonmath.org/abs/2611.00115","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":14,"title":"Hexagon 2611.00114","url":"https://hexagonmath.org/abs/2611.00114","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":15,"title":"Hexagon 2611.00112","url":"https://hexagonmath.org/abs/2611.00112","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":16,"title":"Hexagon 2611.00109","url":"https://hexagonmath.org/abs/2611.00109","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":17,"title":"Hexagon 2611.00108","url":"https://hexagonmath.org/abs/2611.00108","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":18,"title":"Hexagon 2611.00107","url":"https://hexagonmath.org/abs/2611.00107","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":19,"title":"Hexagon 2611.00102","url":"https://hexagonmath.org/abs/2611.00102","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":20,"title":"Hexagon 2611.00101","url":"https://hexagonmath.org/abs/2611.00101","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":21,"title":"Hexagon 2610.00681","url":"https://hexagonmath.org/abs/2610.00681","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":22,"title":"Hexagon 2611.00093","url":"https://hexagonmath.org/abs/2611.00093","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":23,"title":"Hexagon 2611.00085","url":"https://hexagonmath.org/abs/2611.00085","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":24,"title":"Hexagon 2611.00059","url":"https://hexagonmath.org/abs/2611.00059","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":25,"title":"arXiv 2611.06985","url":"https://arxiv.org/abs/2611.06985","type":"paper","group":"primary","domain":"arxiv.org"},{"n":26,"title":"arXiv 2611.08030","url":"https://arxiv.org/abs/2611.08030","type":"paper","group":"primary","domain":"arxiv.org"},{"n":27,"title":"arXiv 2611.08198","url":"https://arxiv.org/abs/2611.08198","type":"paper","group":"primary","domain":"arxiv.org"},{"n":28,"title":"arXiv 2611.07607","url":"https://arxiv.org/abs/2611.07607","type":"paper","group":"primary","domain":"arxiv.org"},{"n":29,"title":"arXiv 2611.08230","url":"https://arxiv.org/abs/2611.08230","type":"paper","group":"primary","domain":"arxiv.org"},{"n":30,"title":"arXiv 2611.07117","url":"https://arxiv.org/abs/2611.07117","type":"paper","group":"primary","domain":"arxiv.org"},{"n":31,"title":"arXiv 2611.07280","url":"https://arxiv.org/abs/2611.07280","type":"paper","group":"primary","domain":"arxiv.org"},{"n":32,"title":"arXiv 2611.06937","url":"https://arxiv.org/abs/2611.06937","type":"paper","group":"primary","domain":"arxiv.org"},{"n":33,"title":"arXiv 2611.07259","url":"https://arxiv.org/abs/2611.07259","type":"paper","group":"primary","domain":"arxiv.org"},{"n":34,"title":"arXiv 2611.08176","url":"https://arxiv.org/abs/2611.08176","type":"paper","group":"primary","domain":"arxiv.org"},{"n":35,"title":"arXiv 2611.07196","url":"https://arxiv.org/abs/2611.07196","type":"paper","group":"primary","domain":"arxiv.org"},{"n":36,"title":"arXiv 2611.07310","url":"https://arxiv.org/abs/2611.07310","type":"paper","group":"primary","domain":"arxiv.org"},{"n":37,"title":"arXiv 2611.07626","url":"https://arxiv.org/abs/2611.07626","type":"paper","group":"primary","domain":"arxiv.org"},{"n":38,"title":"arXiv 2611.07915","url":"https://arxiv.org/abs/2611.07915","type":"paper","group":"primary","domain":"arxiv.org"},{"n":39,"title":"arXiv 2611.06986","url":"https://arxiv.org/abs/2611.06986","type":"paper","group":"primary","domain":"arxiv.org"},{"n":40,"title":"arXiv 2611.07455","url":"https://arxiv.org/abs/2611.07455","type":"paper","group":"primary","domain":"arxiv.org"},{"n":41,"title":"arXiv 2611.08455","url":"https://arxiv.org/abs/2611.08455","type":"paper","group":"primary","domain":"arxiv.org"},{"n":42,"title":"arXiv 2611.06998","url":"https://arxiv.org/abs/2611.06998","type":"paper","group":"primary","domain":"arxiv.org"},{"n":43,"title":"Hexagon 2610.00520","url":"https://hexagonmath.org/abs/2610.00520","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":44,"title":"Hexagon 2610.00505","url":"https://hexagonmath.org/abs/2610.00505","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":45,"title":"Hexagon 2610.00508","url":"https://hexagonmath.org/abs/2610.00508","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":46,"title":"Hexagon 2610.00515","url":"https://hexagonmath.org/abs/2610.00515","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":47,"title":"Hexagon 2610.00514","url":"https://hexagonmath.org/abs/2610.00514","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":48,"title":"Hexagon 2610.00521","url":"https://hexagonmath.org/abs/2610.00521","type":"paper","group":"primary","domain":"hexagonmath.org"}],"official":48,"filed":"2026-11-06","updated":"2026-11-06","orgs":["OpenAI","Anthropic","various researchers"],"title":"AI-assisted results in the 6 Nov 2026 sweep: generalized Lax conjecture for mixed determinants, L'vov–Kaplansky in degree four, unrecognizability of #²(S²×S²) by ChatGPT's agent, second Hamilton cycles from r ≥ 17, plus 26 Hexagon works","summary":"Catalogue of AI-disclosing papers from the arXiv announcement of 6 Nov 2026 and the Hexagon works of 5 Nov beyond the items with own entries. AI statements are quoted from PDFs or Hexagon provenance records (Hexagon does not judge correctness); none is refereed.","key_facts":["Own entries: 2026-11-06-tusnady-problem-settled-two-ai-assisted-preprints (2611.06998, 2611.08455), 2026-11-05-singmaster-bound-claude-opus-5-5-whitmore (Hexagon 2611.00106), 2026-11-05-hopfield-critical-capacity-claude-opus-5-5 (Hexagon 2611.00105); Najman's degrees 9–22 (Hexagon 2611.00120) added to 2026-11-04-elliptic-curve-torsion-degrees-6-9-gpt-6-1-sol-najman","Real algebraic geometry: Suvrit Sra proves the generalized Lax conjecture for the Borcea–Brändén mixed determinant (spectrahedral hyperbolicity cone) and answers four Borcea–Brändén problems negatively (Hexagon 2611.00117, mixed, understanding 'some'): 'GPT Astra (Pro) found the construction of Theorem 1.1' after a failed counterexample search; also a new proof of van der Waerden's permanent inequality by monotone averaging, 'GPT-6 Astra Pro … carried out the derivations' (2611.00118)","Algebra and topology: L'vov–Kaplansky conjecture for multilinear polynomials of degree four, 'developed through two research conversations with GPT-6-Pro … seven hours' (Qiyue Tang, 2611.00119); Qiuyu Ren, a 2-generator 3-relator universal group and #ⁿ(S²×S²) unrecognizable for every n ≥ 2, 'The main theorems were produced by ChatGPT's agent \"dot.\" … less than half a day' (2611.00112); terminal symplectic singularities for parabolic base affine spaces, Tom Gannon, 'this pdf is entirely AI generated' with ChatGPT Astra (2611.00107)","Number theory and complexity (Hexagon): Vaibhav Tulsyan with Claude Code, parity of π(x) in time x^o(1) and class numbers / quadratic non-residues in 2^O(n/√log n), both conditional on Anthropic's #SAT algorithms of 27 Oct and Lean-checked on that development (2611.00116, 2611.00115); Hadamard difference sets in C₂×C₂ᵤ² and 2-automatic Baum–Sweet Hankel determinants, Claude, 'No professional mathematician has reviewed the note yet' (2611.00102, 2611.00101); Fuchs' extremal problem for 0 < λ ≤ 3 (2611.00126)","Other Hexagon 5 Nov: Grothendieck Montpellier notes, seventy-five folders of restated statements proved in Lean with Claude Opus/Sonnet 5.5, readings not verified against the facsimile (2611.00125); twistor correspondence for analytic Einstein germs (2611.00123); sup-norm ∂̄ estimates on convex domains in C², 'primarily AI-generated', fully human-checked (2611.00121); Hurwitz interval family without degree-5 WSPR numerator, Lean (2611.00127); transcendence of the 3x+1 conjugacy map on Sturmian words (2611.00108); Voblint, Isabelle/HOL soundness (2611.00109); human-written or editing-only: 2611.00124, 00122, 00114, 00093 (Claude found Example 2.7), 00085, 2610.00681, 00059","Graph theory and combinatorics (arXiv 6 Nov): Liu–Liu–Ning, every Hamiltonian r-regular graph with r ≥ 17 has a second Hamilton cycle (was r ≥ 23, Haxell–Seamone–Verstraëte), 'The proofs in this paper were developed with substantial contributions from ChatGPT (5.5 and 6 Astra)' (2611.06985); perfect q-hash codes beat the probabilistic bound for every q ≥ 3, settling part of a Xing–Yuan conjecture, 'Claude (Anthropic) suggested the directions that led to Theorems 1.5 and 1.7' (2611.08230); maximal partial Room squares, construction 'produced by ChatGPT Plus' (2611.07117); double-factorial consecutive-pattern packings, Lean (2611.06937); simpler proof for a noncommutative harmonic oscillator determinant offered unprompted by Claude Opus 5.5 (2611.07626)","Geometry, analysis, TCS: Arman–Bondarenko–Prymak–Radchenko, a diameter-one set in R⁵ not covered by six diameter-one balls, 'The example presented in this paper was found using generative AI tools' (2611.08198); Medwed proves the Chang–Lyons–Ni length conjecture for path signatures, 'central arguments … generated with the assistance of AI (ChatGPT 5.6 Sol)' (2611.08030); Alrabiah–Goyal–Guruswami refute a conjecture on list-decoding Reed–Solomon codes, 'Initial versions of our key statements were established by GPT-6 Astra Pro' (2611.07607); Riis, linear degree lower bounds for Nullstellensatz and Polynomial Calculus with 'Astra and Claude for sustained proof search' (2611.07280)","Smaller AI-credited steps: CM counterexamples found with ChatGPT 5.6 Pro (Kim–Yu, 2611.07259); Fermat quotients with CM Jacobians, GPT-6 Astra Pro extended the proof (2611.08176); void percolation, tree-embedding idea by GPT 5.6 (2611.07196); stochastic heat equation weak uniqueness via GPT-6.1 (2611.07310); free Tₙ-Heyting algebras, implication 'found by Claude Sonnet 4.6' (2611.07915); 2×4 LEGO counts with Claude (2611.06986); worldsheet skein sequence 'found by GPT-5.6 Sol' (2611.07455)","Repos: google-deepmind/formal-conjectures added statements of Green's Open Problems 68, 70, 75, 87, 93, 97 and Erdős 651, 1164, 1166 (statements, no solutions); 3f44904 (Erdős 354(i)) was covered on 5 Nov; 2befc3a links a Turing-machine formalization (docs)","Hexagon backlog (6 lines): Basok, perfect t-embeddings exist, answering Chelkak–Laslier–Russkikh (2021), 'The proof and the main part of the writing were produced by GPT-6 Astra' (2610.00520); Enomoto, Astra re-proves the Bautista–Gabriel–Roiter–Salmerón multiplicative-basis theorem (2610.00505); Riesen, VOA realizations of untwisted Haagerup–Izumi centers, AI 'assisted in developing proof arguments' (2610.00508); Pinho, reverse Brunn–Minkowski constant C_70 ≥ exp(1/(2e)) and a degree-3 local-weight cap, AI agents, 'reviewed the results at summary level' (2610.00515, 2610.00514); Lin, de Bruijn–Newman coefficients, human-written (2610.00521)"],"key_numbers":[],"tags":["math","arxiv","hexagon","catalogue","chatgpt","gpt-6-astra","gpt-6-1-sol","codex","claude","claude-opus-5-5","lean"],"science":{"field":"mathematics","subfield":"multiple","problem":"See list","result":"Catalogue of AI-disclosing papers of 5–6 Nov beyond those with their own entries","open_since":"","ai_system":["ChatGPT","GPT-6 Astra","GPT-6.1 Sol","Codex","Claude Opus 5.5","dot"],"human_role":"From human proofs with AI help to fully AI-generated deposits with limited human checking","verification":{"key":"lean","label":"Lean-verified","text":"Unrefereed preprints and Hexagon deposits"},"status":"pending","shock":"","verified_by":["preprint","lean"],"kind":"batch"},"body_md":"## What happened\n\nThe 6 Nov sweep listed 183 arXiv papers from that day's announcement with an AI mention (most only for editing or literature search) and 26 Hexagon works of 5 Nov. The items above are those where the authors credit AI with mathematical content. Quotes come from PDFs or Hexagon provenance statements; Hexagon does not judge correctness and none of these is refereed.","disputed":[{"label":"Verification","text":"Unrefereed preprints and Hexagon deposits","sources":[]}],"related":[{"id":"2026-11-06-tusnady-problem-settled-two-ai-assisted-preprints","url":"https://postcutoff.com/e/2026-11-06-tusnady-problem-settled-two-ai-assisted-preprints/","date":"2026-11-06","date_precision":"day","short_title":"Tusnády's problem claimed settled twice, with AI help","deck":null,"takeaway":"Tusnády's problem is a standard open problem of geometric discrepancy theory, and the gap in dimensions d ≥ 3 had been open for decades.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":2,"filed":"2026-11-06","updated":"2026-11-06","orgs":["Anthropic","OpenAI"]},{"id":"2026-11-05-singmaster-bound-claude-opus-5-5-whitmore","url":"https://postcutoff.com/e/2026-11-05-singmaster-bound-claude-opus-5-5-whitmore/","date":"2026-11-05","date_precision":"day","short_title":"Singmaster's problem: new bound by Claude Opus 5.5","deck":null,"takeaway":"Singmaster's problem is a well-known open problem in elementary number theory, and the claimed exponent 1/2 improves even on what was previously known under Cramér's conjecture.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":1,"official":1,"filed":"2026-11-06","updated":"2026-11-06","orgs":["Anthropic"]},{"id":"2026-11-05-hopfield-critical-capacity-claude-opus-5-5","url":"https://postcutoff.com/e/2026-11-05-hopfield-critical-capacity-claude-opus-5-5/","date":"2026-11-05","date_precision":"day","short_title":"Hopfield critical capacity bracketed, by Claude Opus 5.5","deck":null,"takeaway":"Turning the replica prediction for the Hopfield model into a theorem has been a long-standing goal in the mathematics of spin glasses.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":2,"filed":"2026-11-06","updated":"2026-11-06","orgs":["Anthropic","OpenAI"]},{"id":"2026-11-05-ai-assisted-results-november-5-listing","url":"https://postcutoff.com/e/2026-11-05-ai-assisted-results-november-5-listing/","date":"2026-11-05","date_precision":"day","short_title":"AI-assisted results, 5 Nov: arXiv of 5 Nov and Hexagon of 4 Nov","deck":null,"takeaway":"The 5 Nov sweep listed 424 arXiv papers mentioning AI (about 240 new) and 44 uncited Hexagon works. Own entries: the refutation of the 3-uniform hyperclique hypothesis (ChatGPT Sol 6.1), Najman's elliptic-curve torsion in degrees 6–9 (GPT-6.1 Sol) and Serre modularity over real quadratic fields (ChatGPT Astra/Sol).","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":67,"official":67,"filed":"2026-11-05","updated":"2026-11-05","orgs":["OpenAI","Anthropic","various researchers"]},{"id":"2026-10-27-anthropic-claude-eth-refutation-3sat-subexponential","url":"https://postcutoff.com/e/2026-10-27-anthropic-claude-eth-refutation-3sat-subexponential/","date":"2026-10-27","date_precision":"day","short_title":"Anthropic's Claude also refutes ETH","deck":null,"takeaway":"Hours after OpenAI's ETH announcement, Anthropic posted 'A 2^o(n) Time Algorithm for 3-SAT', credited to Claude. It is a deterministic #k-SAT algorithm built on tensor-network contraction, with a different approach from OpenAI's paper, a near-identical bound and a Lean 4 proof that uses only the standard axioms. The paper says the core algorithm was found on 16 Oct with 14M output tokens and no human input. OpenAI reports its model found its disproof that same day. Neither proof has had expert review.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":10,"official":8,"filed":"2026-10-27","updated":"2026-11-06","orgs":["Anthropic"]},{"id":"2026-10-06-generalized-lax-conjecture-openai-counterexample-kummer-netzer-generic-case","url":"https://postcutoff.com/e/2026-10-06-generalized-lax-conjecture-openai-counterexample-kummer-netzer-generic-case/","date":"2026-10-06","date_precision":"day","short_title":"Generalized Lax conjecture: OpenAI counterexample claim; AI-found generic case (Kummer–Netzer)","deck":null,"takeaway":"The generalized Lax conjecture says every hyperbolicity cone is spectrahedral, a slice of a positive semidefinite cone. On 21 Sept 2026 Mario Kummer and Tim Netzer posted 'a proof found by an artificial intelligence system' for the generic case, strictly hyperbolic polynomials (arXiv 2609.24542). Family 095 of OpenAI's 6 Oct maths release (manuscripts of 24 Sept and 5 Oct) claims the general conjecture is false. It gives hyperbolicity cones that are not even spectrahedral shadows, which also disproves the projected Lax conjecture, and the main statement is in Lean. Kevin Shu's exposition on the Quasicoherent blog accepts the counterexample. Neither result is refereed. We found both only on 31 Oct, through a citation.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":6,"official":5,"filed":"2026-10-31","updated":"2026-10-31","orgs":["OpenAI"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-11-06","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-06","run":null,"sources_read":null,"updated":"2026-11-06","human_review":null,"version":{"date":"2026-11-06"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":190,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":129,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":220,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":159,"in_training_data":false}],"short_url":null}