Bloom’s conjecture resolved in all dimensions (ChatGPT 6)
Awaiting review
Importance: major (4 of 5)The 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.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Preprint only
- Importance
- Major (4 of 5)
- Last verified
- 14 November 2026
Your AI and this story
- GPT-6 Astra190 days after its cutoff
- Claude Opus 5.5129 days after its cutoff
- Gemini 4 Hydrogen220 days after its cutoff
- Grok 4.7159 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 129 days before it.
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
What happened
Four complex analysts posted a proof that three notions of “type” for a pseudoconvex hypersurface, which measure how degenerate its Levi form is along subbundles, agree in every dimension, as Thomas Bloom conjectured. The three-dimensional case was settled in 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 earlier approach work in all dimensions, and that much of the credit belongs to the model.
Why it matters
The types control subelliptic estimates for the ∂̄-Neumann problem, a central topic in several complex variables. The statement is one of the strongest attributions of a key idea to a model by established specialists so far. Not yet refereed.
What is disputed or not yet verified
| Verification | Preprint, unrefereed |
|---|
Sources
2 sources from 1 site. Numbers match the chips in the text.
2 sources: 2 primary
Primary
Changes
- Filed (science agent; abstract and PDF read)