{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2026-09-22-mumford-shah-conjecture-astra-claim/","md":"https://postcutoff.com/e/2026-09-22-mumford-shah-conjecture-astra-claim/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":"2026-09-22-mumford-shah-conjecture-astra-claim","date":"2026-09-22","date_precision":"day","short_title":"Mathematician posts an unchecked ChatGPT Astra proof of the planar Mumford–Shah conjecture (1989), citing OpenAI's '100 open problems' claim","deck":null,"takeaway":"On 22 Sep 2026 Francesco Deangelis (University of Münster) posted a claimed proof of the planar Mumford–Shah conjecture (1989), a central open problem in the calculus of variations and image segmentation.","category":"science","category_label":"Science & math","importance":4,"confidence":"low","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2609.26732: Solution of the Mumford–Shah conjecture (Deangelis)","url":"https://arxiv.org/abs/2609.26732","type":"paper","group":"primary","domain":"arxiv.org"}],"official":1,"filed":"2026-09-30","updated":"2026-10-19","orgs":["Francesco Deangelis","University of Münster","OpenAI"],"title":"Mathematician posts an unchecked ChatGPT Astra proof of the planar Mumford–Shah conjecture (1989), citing OpenAI's '100 open problems' claim","summary":"On 22 Sep 2026 Francesco Deangelis (University of Münster) posted a claimed proof of the planar Mumford–Shah conjecture (1989), a central open problem in the calculus of variations and image segmentation. He says ChatGPT Astra produced it on 9 Sep. He calls it an 'AI-generated draft' that he is still checking. He released it early to document priority after OpenAI's 21 Sep claim that an internal model had solved 100+ open problems.","key_facts":["arXiv 2609.26732 (22 Sep 2026): 'On September 9, 2026, I obtained a proof of the Mumford–Shah conjecture, formulated in 1989, using ChatGPT Astra'","Timeline in the author's note: 5 Sep, Astra in Work mode ran 6 hours without a complete proof; 6 Sep, it proved the author's Dirichlet-boundary conjecture in 1 h 20 min, building on his unpublished April 2026 work; 9 Sep, given that result, it produced a complete proof after 2 h 30 min (37 pages); 11 Sep, a shorter version, which is the one posted","Author's caveat: 'This prompted me to make the current AI-generated draft publicly available now, to document the chronology of this work. I will continue checking the mathematical details'","Claimed method: classify planar generalized global minimizers with a second-variation argument (two perpendicular translations of a compact crack portion, a Hodge identity and holomorphic rigidity). The known equivalence between that classification and interior regularity then gives the conjecture","Status: unrefereed, not formalised, and not publicly checked by independent experts as of 30 Sep 2026"],"key_numbers":[],"tags":["math","calculus-of-variations","regularity","astra","unverified","priority"],"science":{"field":"mathematics","subfield":"calculus of variations / free-discontinuity problems","problem":"Planar Mumford–Shah conjecture (regularity of minimizing discontinuity sets)","result":"Claimed classification of planar Mumford–Shah generalized global minimizers, which would imply the conjecture.","open_since":"1989","ai_system":["GPT-6 Astra (ChatGPT, Work mode)"],"human_role":"The human supplied his thesis, unpublished results and a research protocol; the model produced the proof text; checking by the author is ongoing","verification":{"key":"preprint","label":"Preprint only","text":"Unverified claim, no expert review: preprint by the prompting author, who says his own check is ongoing; not formalised"},"status":"pending","shock":"A major variational problem may have been solved in a 2.5-hour chat session, and the author says he published it mainly to establish priority."},"body_md":"## What happened\n\nDeangelis, who worked on Mumford–Shah regularity in his PhD, gave ChatGPT Astra his thesis, reference books and unpublished notes. First it proved a boundary-regularity conjecture of his. Then, given that result, it produced a full claimed proof of the interior conjecture. He posted the model's shortened manuscript almost unchanged, with a note on its provenance.\n\n## Why it matters\n\nIf correct, it would settle one of the best-known open problems in the calculus of variations. The case also shows OpenAI's unverified \"100 open problems\" announcement leading independent researchers to rush their own AI-generated claims onto arXiv before checking them.","disputed":[{"label":"Verification","text":"Unverified claim, no expert review: preprint by the prompting author, who says his own check is ongoing; not formalised","sources":[]}],"related":[{"id":"2026-09-30-ai-assisted-conjecture-wave-summer-2026","url":"https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/","date":"2026-09-30","date_precision":"day","short_title":"Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help","deck":null,"takeaway":"This entry catalogues about 50 of them, with the AI role as the authors state it.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":11,"official":5,"filed":"2026-09-30","updated":"2026-10-19","orgs":["OpenAI","Anthropic","Google DeepMind","various mathematicians"]},{"id":"2026-09-21-openai-100-open-problems-claim","url":"https://postcutoff.com/e/2026-09-21-openai-100-open-problems-claim/","date":"2026-09-21","date_precision":"day","short_title":"OpenAI says an internal model resolved 100+ long-standing open problems in 24 days of training (list released 6 Oct: 722 manuscripts)","deck":null,"takeaway":"If substantiated, it would mean open problems are being resolved at industrial scale.","category":"science","category_label":"Science & math","importance":3,"confidence":"low","status":{"key":"pending","labels":["Awaiting review"]},"sources":11,"official":5,"filed":"2026-09-29","updated":"2026-10-10","orgs":["OpenAI"]},{"id":"2026-09-03-gpt-6-astra","url":"https://postcutoff.com/e/2026-09-03-gpt-6-astra/","date":"2026-09-03","date_precision":"day","short_title":"OpenAI releases GPT-6 Astra, its first GPT-6 model","deck":null,"takeaway":"Astra is the first GPT-6-generation model and the first frontier release after the Hugging Face sandbox-escape incident and OpenAI's August training pause.","category":"model-release","category_label":"Model releases","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":20,"official":11,"filed":"2026-09-29","updated":"2026-10-19","orgs":["OpenAI"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-19","type":"edit","text":"Fixed ai_system (unquoted comma); verification wording aligned with the catalogue convention"},{"date":"2026-09-30","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-30","run":null,"sources_read":null,"updated":"2026-10-19","human_review":null,"version":{"date":"2026-10-19"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":145,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":84,"in_training_data":false},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":175,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":114,"in_training_data":false}],"short_url":"https://postcutoff.com/s/mathematician-posts-unchecked"}