{"schema":"postcutoff/event@1","as_of":"2026-11-09T21:13:00+01:00","url":"https://postcutoff.com/e/2026-11-03-reed-muller-rm19-covering-radius-242-three-proofs/","md":"https://postcutoff.com/e/2026-11-03-reed-muller-rm19-covering-radius-242-three-proofs/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":"2026-11-03-reed-muller-rm19-covering-radius-242-three-proofs","date":"2026-11-03","date_precision":"day","short_title":"RM(1,9) covering radius = 242, three proofs","deck":null,"takeaway":"The maximum nonlinearity of a Boolean function in nine variables, equivalently the covering radius of RM(1,9), was known only to lie between 242 and 244.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2611.00890: The covering radius of RM(1,9) is 242 (Yi Li)","url":"https://arxiv.org/abs/2611.00890","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"IACR ePrint 2026/2529: The Covering Radius of RM(1,9) is Precisely 242 (Hou, Sabo, Slaughter)","url":"https://eprint.iacr.org/2026/2529","type":"paper","group":"primary","domain":"eprint.iacr.org"},{"n":3,"title":"arXiv 2611.00070 (Hou, Sabo, Slaughter)","url":"https://arxiv.org/abs/2611.00070","type":"paper","group":"primary","domain":"arxiv.org"},{"n":4,"title":"arXiv 2610.17871 (Wang, Lou et al.)","url":"https://arxiv.org/abs/2610.17871","type":"paper","group":"primary","domain":"arxiv.org"}],"official":4,"filed":"2026-11-03","updated":"2026-11-03","orgs":["OpenAI","University of South Florida"],"title":"Covering radius of the Reed–Muller code RM(1,9) settled at 242: three independent proofs in four weeks, one with ChatGPT","summary":"The maximum nonlinearity of a Boolean function in nine variables, equivalently the covering radius of RM(1,9), was known only to lie between 242 and 244. Three computer-assisted preprints now say it is 242: Wang, Lou et al. (arXiv 2610.17871, mid-October, no AI statement), Hou, Sabo and Slaughter (IACR ePrint 2026/2529, arXiv 2611.00070) and Yi Li (arXiv 2611.00890, 3 Nov), who acknowledges ChatGPT \"in the research and preparation of this paper\".","key_facts":["Previously known: 242 ≤ ρ(1,9) ≤ 244; for odd n, ρ(1,n) was known only for n ≤ 7 (Hou–Sabo–Slaughter abstract)","Hou–Sabo–Slaughter: a function of nonlinearity 243 yields one of 244; 244 excluded through Walsh-spectrum divisibility and an exhaustive search over the 349 GL(9,2)-orbits of RM(3,9)/RM(2,9), run twice with independent implementations; code at github.com/FreemanSlaughter/Covering-Radius","Yi Li (2611.00890): one-point rigidity theorem plus spectral and computational exclusion of 243 and 244. Acknowledgment (verbatim): 'The author acknowledges the use of ChatGPT (OpenAI) in the research and preparation of this paper, including mathematical discussions, exposition, LaTeX editing, and assistance with computational code.'","Verification status: three unrefereed computer-assisted preprints reaching the same value"],"key_numbers":[],"tags":["math","coding-theory","boolean-functions","cryptography","chatgpt","computer-assisted-proof","arxiv"],"science":{"field":"mathematics","subfield":"coding theory / Boolean functions","problem":"Covering radius of RM(1,9) (maximum nonlinearity of 9-variable Boolean functions)","result":"ρ(1,9) = 242","open_since":"","ai_system":["ChatGPT"],"human_role":"Human-led computer-assisted proofs; ChatGPT assisted one of the three","verification":{"key":"preprint","label":"Preprint only","text":"Three independent preprints, computer-assisted"},"status":"pending","shock":""},"body_md":"## What happened\n\nA long-standing question in Boolean-function cryptography received three proofs: one in mid-October with no AI statement, and two more on arXiv this week, one of which used ChatGPT for discussions and code.\n\n## Why it matters\n\nNonlinearity bounds matter for cipher design; agreement between three independent computer-assisted proofs makes the value 242 more credible. The AI role is a minor one; the entry mainly records the convergence.","disputed":[{"label":"Verification","text":"Three independent preprints, computer-assisted","sources":[]}],"related":[{"id":"2026-11-03-ai-assisted-results-november-3-listing","url":"https://postcutoff.com/e/2026-11-03-ai-assisted-results-november-3-listing/","date":"2026-11-03","date_precision":"day","short_title":"AI-assisted results, 3 Nov: arXiv of 3 Nov and Hexagon of 2–3 Nov","deck":null,"takeaway":"The 3 Nov sweep listed 376 arXiv papers that mention AI, 124 conjecture papers and 69 uncited Hexagon works. Four results got own entries: Kronheimer–Mrowka's primarily AI-generated proposed proof that the dodecahedron web has instanton homology of dimension 64, a second AI-derived proof of the Alon–Seymour–Thomas separator conjecture (with Lean), Chen–Liu's FPRAS for mixed volumes (ideas 'generated entirely by GPT 6 Astra'), and the convergence of three proofs that RM(1,9) has covering radius 242.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":13,"official":13,"filed":"2026-11-03","updated":"2026-11-03","orgs":["OpenAI","Anthropic","Google","various researchers"]},{"id":"2026-10-14-ai-assisted-results-mid-october-2026","url":"https://postcutoff.com/e/2026-10-14-ai-assisted-results-mid-october-2026/","date":"2026-10-14","date_precision":"day","short_title":"Mid-October 2026: arXiv results with disclosed AI help","deck":null,"takeaway":"The 13 Oct arXiv listing alone brought a human write-up of GPT-6 Astra's rational exponents proof, Ulam's Lie group question answered with an Astra construction, a better-than-2 k-median algorithm, and about a dozen smaller results whose AI statements range from 'suggested by ChatGPT' to 'GPT 6 Pro was used … to obtain all other new results'.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":20,"official":19,"filed":"2026-10-14","updated":"2026-10-15","orgs":["OpenAI","Anthropic","various mathematicians"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-11-03","type":"filed","text":"Created. Resolves the 14 Oct lead on 2610.17871"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-03","run":null,"sources_read":null,"updated":"2026-11-03","human_review":null,"version":{"date":"2026-11-03"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":187,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":126,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":217,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":156,"in_training_data":false}],"short_url":null}