{"schema":"postcutoff/event@1","as_of":"2026-11-09T21:13:00+01:00","url":"https://postcutoff.com/e/2026-11-03-kronheimer-mrowka-dodecahedron-web-instanton-homology-64-chatgpt/","md":"https://postcutoff.com/e/2026-11-03-kronheimer-mrowka-dodecahedron-web-instanton-homology-64-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":"2026-11-03-kronheimer-mrowka-dodecahedron-web-instanton-homology-64-chatgpt","date":"2026-11-03","date_precision":"day","short_title":"Kronheimer–Mrowka: dodecahedron instanton homology is 64 (ChatGPT Astra 6)","deck":null,"takeaway":"Peter Kronheimer (Harvard) and Tomasz Mrowka (MIT) deposited on Hexagon (2611.00021, published 3 Nov 2026) a \"proposed proof\" that the SO(3) instanton homology J♯ of the planar dodecahedron web has dimension 64.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"Hexagon 2611.00021: The dodecahedron web and its instanton homology (Kronheimer, Mrowka)","url":"https://hexagonmath.org/abs/2611.00021","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":2,"title":"Kronheimer & Mrowka, Tait colorings, and an instanton homology for webs and foams (arXiv 1508.07205)","url":"https://arxiv.org/abs/1508.07205","type":"paper","group":"primary","domain":"arxiv.org"}],"official":2,"filed":"2026-11-03","updated":"2026-11-03","orgs":["OpenAI","Anthropic","Harvard University","MIT"],"title":"Kronheimer and Mrowka post a primarily AI-generated proposed proof that the dodecahedron web's instanton homology has dimension 64, not its 60 Tait colourings","summary":"Peter Kronheimer (Harvard) and Tomasz Mrowka (MIT) deposited on Hexagon (2611.00021, published 3 Nov 2026) a \"proposed proof\" that the SO(3) instanton homology J♯ of the planar dodecahedron web has dimension 64. Earlier work had narrowed it to 60 or 64; 60 is the number of Tait colourings of the dodecahedron, the value their 2015 programme towards the four-colour theorem conjectured for planar webs. The deposit is declared primarily AI-generated (ChatGPT Astra 6, building on earlier ChatGPT and Claude calculations), with only some parts checked by a human.","key_facts":["Claim (abstract): the octahedral diagram reduces dim J♯(D) to 60 or 64; 'We give a proposed proof that all three [secondary-map coefficients] vanish and that the dimension is 64'","Context: Kronheimer–Mrowka, 'Tait colorings, and an instanton homology for webs and foams' (JEMS 2019, arXiv 1508.07205) defined J♯ and asked whether its dimension equals the number of Tait colourings for planar webs; 64 ≠ 60 would answer that in the negative for the dodecahedron","Provenance (verbatim): 'Primarily AI-generated'; 'Some parts of this contribution, but not all, have been checked and understood by a human'; 'ChatGPT Astra 6 was prompted to consider the question of whether the instanton homology of the dodecahedron had dimension 60 or 64, having been provided with previous calculations from ChatGPT and Claude.'","Authorship mode on Hexagon: no-human-author-claimed; sponsor Peter Kronheimer; exact matrices and foam calculations 'provided separately'","Verification status: unrefereed Hexagon deposit, described by the authors as a proposed proof; no Lean formalization; no HN discussion found on 3 Nov"],"key_numbers":[],"tags":["math","low-dimensional-topology","instanton-homology","four-colour-theorem","gpt-6-astra","chatgpt","claude","hexagon"],"science":{"field":"mathematics","subfield":"low-dimensional topology (gauge theory)","problem":"Dimension of the SO(3) instanton homology J♯ of the dodecahedron web: 60 (number of Tait colourings) or 64","result":"Proposed proof that the dimension is 64","open_since":"2015","ai_system":["ChatGPT Astra 6","ChatGPT","Claude"],"human_role":"Leading gauge theorists posed the question and supplied earlier AI-computed data; the text is primarily AI-generated and only partly checked","verification":{"key":"none","label":"Unverified claim","text":"Unrefereed Hexagon deposit; partly human-checked"},"status":"pending","shock":"Two of the field's leading topologists post a primarily AI-written proof that bears on their own conjectured link between instanton homology and Tait colourings."},"body_md":"## What happened\n\nOn 2 Nov 2026 Peter Kronheimer deposited, and on 3 Nov Hexagon published, a paper by him and Tomasz Mrowka on the instanton homology of the planar dodecahedron web. Known calculations left two values, 60 and 64; the paper gives a proposed proof that three coefficients of a secondary map vanish, which gives 64. The provenance record says the text is primarily AI-generated by ChatGPT Astra 6, prompted with earlier calculations from ChatGPT and Claude, and that only some parts have been checked by a human.\n\n## Why it matters\n\nKronheimer and Mrowka built J♯ in 2015 as a possible route to the four-colour theorem, asking whether its dimension counts Tait colourings for planar webs. The dodecahedron has 60 Tait colourings, so a dimension of 64 would answer that question in the negative for this web. The result is a proposed proof, not checked in full by its sponsors.","disputed":[{"label":"Verification","text":"Unrefereed Hexagon deposit; partly human-checked","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"]}],"people":[{"id":"peter-kronheimer","name":"Peter Kronheimer","url":"https://postcutoff.com/person/peter-kronheimer/"},{"id":"tomasz-mrowka","name":"Tomasz Mrowka","url":"https://postcutoff.com/person/tomasz-mrowka/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-11-03","type":"filed","text":"Created (Hexagon provenance record read through the Hexagon API)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-03","run":null,"sources_read":"Hexagon provenance record read through the Hexagon API","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":"https://postcutoff.com/s/kronheimer-mrowka-dodecahedron"}