{"schema":"postcutoff/event@1","as_of":"2026-11-15T00:33:00+01:00","url":"https://postcutoff.com/e/2026-11-06-bloom-conjecture-all-dimensions-chatgpt-6/","md":"https://postcutoff.com/e/2026-11-06-bloom-conjecture-all-dimensions-chatgpt-6/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-bloom-conjecture-all-dimensions-chatgpt-6","date":"2026-11-06","date_precision":"day","short_title":"Bloom's conjecture resolved in all dimensions (ChatGPT 6)","deck":null,"takeaway":"Xiaojun Huang and Wanke Yin solved Bloom's 1981 conjecture in dimension three in 2021. A new preprint with Jiaqing Chen and Pingsan Yuan proves it in every dimension, and says the key new method, a free nilpotent group model, came from ChatGPT 6.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2611.09823: Regular multi-types and the Bloom conjecture II (Chen, Huang, Yin, Yuan)","url":"https://arxiv.org/abs/2611.09823","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"arXiv 2611.10314: The Dimension Conjecture for Hypersurfaces Is True (Stepanova)","url":"https://arxiv.org/abs/2611.10314","type":"paper","group":"primary","domain":"arxiv.org"}],"official":2,"filed":"2026-11-14","updated":"2026-11-14","orgs":["OpenAI"],"title":"Bloom's conjecture on contact, commutator and Levi types of pseudoconvex hypersurfaces resolved in all dimensions; authors say 'ChatGPT 6 played a fundamental role … much of the credit for this paper should be attributed to it'","summary":"arXiv 2611.09823 (6 Nov 2026), Jiaqing Chen, Xiaojun Huang, Wanke Yin, Pingsan Yuan: for a smooth pseudoconvex real hypersurface M ⊂ ℂⁿ and every 1 ≤ s ≤ n−1, the regular s-contact type, s-commutator type and s-Levi type coincide at every point, resolving Bloom's conjecture in any dimension (n = 3 was done by Huang and Yin in 2021), and answer the generalized D'Angelo conjecture. The authors write that ChatGPT 6 supplied 'a fundamental new strategy with the free nilpotent group model' and 'critical computations'.","key_facts":["Disclosure (verbatim): 'It is here that ChatGPT 6 provided crucial help to us in developing a free nilpotent group model that encodes a finite jet of the chosen vector fields and in realizing the model as a generic real-analytic CR submanifold G of a complex homogeneous space Q'; 'This new method, provided to us by ChatGPT 6, allows us to bypass the analysis of the Nagano leaf'; 'Thus, ChatGPT 6 played a fundamental role in this work, and much of the credit for this paper should be attributed to it'","Human starting points: the Hopf-lemma approach of Huang–Yin (2021) and a universal weighted polynomial from their 2026 paper; the two pairs of authors had worked independently for over a year and joined forces in late summer 2026","Same listing, same field: 'The Dimension Conjecture for Hypersurfaces Is True' (M. A. Stepanova, arXiv 2611.10314): the automorphism algebra of a holomorphically nondegenerate real-analytic hypersurface germ in ℂ^N has dimension ≤ N² + 2N, with equality only for hyperquadrics; disclosure: 'The author used ChatGPT.'","Status: unrefereed preprints; no expert reaction found by 14 Nov"],"key_numbers":[],"tags":["math","several-complex-variables","cr-geometry","bloom-conjecture","chatgpt-6","arxiv"],"science":{"field":"mathematics","subfield":"several complex variables / CR geometry","problem":"Bloom's conjecture (1981) on the equality of contact, commutator and Levi types","result":"Proved in all dimensions for smooth pseudoconvex hypersurfaces","open_since":"1981","ai_system":["ChatGPT 6"],"human_role":"AI-assisted: authors' framework; ChatGPT 6 supplied the free nilpotent group model and key computations","verification":{"key":"preprint","label":"Preprint only","text":"Preprint, unrefereed"},"status":"pending","shock":""},"body_md":"## What happened\n\nFour complex analysts posted a proof that three notions of \"type\" for a pseudoconvex hypersurface, which measure how degenerate\nits Levi form is along subbundles, agree in every dimension, as Thomas Bloom conjectured. The three-dimensional case was settled\nin 2021 by two of the authors. Their AI statement says ChatGPT 6, used by two of the authors, provided the new method that made the\nearlier approach work in all dimensions, and that much of the credit belongs to the model.\n\n## Why it matters\n\nThe types control subelliptic estimates for the ∂̄-Neumann problem, a central topic in several complex variables. The statement is\none of the strongest attributions of a key idea to a model by established specialists so far. Not yet refereed.","disputed":[{"label":"Verification","text":"Preprint, unrefereed","sources":[]}],"related":[{"id":"2026-11-14-ai-assisted-results-november-14-listing","url":"https://postcutoff.com/e/2026-11-14-ai-assisted-results-november-14-listing/","date":"2026-11-14","date_precision":"day","short_title":"AI-assisted results, 14 Nov","deck":null,"takeaway":"arXiv posted no new listing after 13 Nov (it announces Sunday to Thursday), so this sweep is mostly Hexagon's 13 Nov deposits, older arXiv papers not yet catalogued, and the week's commentary. Eight items got their own entries, four of them from a backlog of 6–11 Nov arXiv papers never catalogued; the rest are listed here with the disclosure quoted. All are unrefereed.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":14,"official":13,"filed":"2026-11-14","updated":"2026-11-14","orgs":["OpenAI","Anthropic","Google DeepMind","various researchers"]}],"people":[{"id":"thomas-bloom","name":"Thomas Bloom","url":"https://postcutoff.com/person/thomas-bloom/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-11-14","type":"filed","text":"Created (science agent; abstract and PDF read)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-14","run":null,"sources_read":"Science agent; abstract and PDF read","updated":"2026-11-14","human_review":null,"version":null},"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-hydrogen","name":"Gemini 4 Hydrogen","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":"https://postcutoff.com/s/bloom-conjecture-resolved-all"}