{"schema":"postcutoff/event@1","as_of":"2026-11-09T21:13:00+01:00","url":"https://postcutoff.com/e/2026-11-04-amplituhedron-magic-number-conjecture-counterexample-chatgpt/","md":"https://postcutoff.com/e/2026-11-04-amplituhedron-magic-number-conjecture-counterexample-chatgpt/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":"2026-11-04-amplituhedron-magic-number-conjecture-counterexample-chatgpt","date":"2026-11-04","date_precision":"day","short_title":"Amplituhedron magic number conjecture: counterexample found by ChatGPT","deck":null,"takeaway":"Evgeniya Akhmedova, Thomas Lam and Calvin Yost-Wolff (arXiv 2611.05216) give a tiling of the m = 4 amplituhedron A(11,3,4) with 489 tiles, one fewer than the magic number 490, refuting the strong form of the magic number conjecture ([GL, Conjecture 3.9]).","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2611.05216: Two examples in amplituhedron tilings","url":"https://arxiv.org/abs/2611.05216","type":"paper","group":"primary","domain":"arxiv.org"}],"official":1,"filed":"2026-11-04","updated":"2026-11-04","orgs":["OpenAI","University of Michigan"],"title":"Amplituhedron tiling with fewer tiles than the 'magic number': Akhmedova, Lam and Yost-Wolff report counterexamples 'first discovered by ChatGPT'","summary":"Evgeniya Akhmedova, Thomas Lam and Calvin Yost-Wolff (arXiv 2611.05216) give a tiling of the m = 4 amplituhedron A(11,3,4) with 489 tiles, one fewer than the magic number 490, refuting the strong form of the magic number conjecture ([GL, Conjecture 3.9]). The tiling uses an injective cell of degree two. 'Counterexamples to [GL, Conjecture 3.9] were first discovered by ChatGPT.' They conjecture that the degree-weighted count is always the magic number.","key_facts":["Tiling T3 of A(11,3,4) has 489 tiles vs magic number 490, obtained from a BCFW tiling by three bistellar flips","First known tiling using a cell of degree higher than one; all BCFW cells have degree 1","New Conjecture 1.6: for even m, the sum of degrees of the cells of any tiling equals the magic number M(k, ℓ, m/2)","Disclosure: 'Counterexamples to [GL, Conjecture 3.9] were first discovered by ChatGPT. We further directed ChatGPT to search for the specific counterexamples that are reported here … the data in the appendix was written by ChatGPT under our supervision.'","Verification: preprint (computational, human-written main text)"],"key_numbers":[],"tags":["math","physics","combinatorics","amplituhedron","chatgpt","openai","arxiv"],"science":{"field":"mathematics","subfield":"positive geometry / algebraic combinatorics","problem":"Magic number conjecture for amplituhedron tilings (strong form, [GL] Conjecture 3.9)","result":"Counterexample: a 489-tile tiling of A(11,3,4) (magic number 490)","open_since":"","ai_system":["ChatGPT"],"human_role":"ChatGPT found the first counterexamples and wrote appendix data; authors directed the search and wrote the paper","verification":{"key":"preprint","label":"Preprint only","text":"Unrefereed preprint"},"status":"pending","shock":""},"body_md":"## What happened\n\nThe amplituhedron (Arkani-Hamed and Trnka) encodes scattering amplitudes in N=4 super Yang–Mills. It was conjectured that every tiling of the even-m amplituhedron has the same number of tiles, the \"magic number\". The new paper reports a tiling of A(11,3,4) with 489 tiles instead of 490, and says ChatGPT found the first counterexamples. The authors propose that a weighted count (by cell degree) is still invariant.\n\n## Why it matters\n\nA senior algebraic combinatorialist (Lam) reports an AI-found counterexample to a conjecture in a field linked to physics. The weaker, degree-weighted form stays open.","disputed":[{"label":"Verification","text":"Unrefereed preprint","sources":[]}],"related":[{"id":"2026-11-04-ai-assisted-results-november-4-listing","url":"https://postcutoff.com/e/2026-11-04-ai-assisted-results-november-4-listing/","date":"2026-11-04","date_precision":"day","short_title":"AI-assisted results, 4 Nov: arXiv of 4 Nov and Hexagon of 2–3 Nov","deck":null,"takeaway":"The 4 Nov sweep listed 374 arXiv papers that mention AI (193 new), 104 conjecture papers and 33 uncited Hexagon works. Three got own entries: Chandran–Gajjala's NP-completeness of Huffman coding with unequal letter costs (Codex), Yang's (1+1/e)Δ colouring mixing claim (GPT-6 Astra Pro) and Akhmedova–Lam–Yost-Wolff's ChatGPT-found counterexample to the amplituhedron magic number conjecture.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":60,"official":60,"filed":"2026-11-04","updated":"2026-11-04","orgs":["OpenAI","Anthropic","various researchers"]}],"people":[{"id":"thomas-lam","name":"Thomas Lam","url":"https://postcutoff.com/person/thomas-lam/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-11-04","type":"filed","text":"Created from the arXiv PDF"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-04","run":null,"sources_read":"The arXiv PDF","updated":"2026-11-04","human_review":null,"version":{"date":"2026-11-04"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":188,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":127,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":218,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":157,"in_training_data":false}],"short_url":null}