Problem detail · source-aware
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The BCHM theorem makes the log canonical ring of a projective klt pair finitely generated. Generalized pairs, introduced by Birkar and Zhang, add an auxiliary nef part and have become a central tool in birational geometry, so it is natural to ask whether finite generation survives. It does not: Liu and Wang construct a smooth projective klt generalized pair whose generalized log canonical ring is not a finitely generated algebra.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
Stated in the abstract, which is unusual: "The main result of this paper is obtained by generative AI, particularly GPT-5.6-sol-ultra, Fable 5, and the Danus system." Remark 1.5 adds that Danus is a specialised agent built on the Rethlas system, and that human verification and polishing were done afterwards.
Provider: OpenAI, Anthropic, Rethlas · Prompt public: unknown · Independence: unknown
A preprint days old, with no independent review. The claim is an explicit construction rather than an existence argument, so it is checkable by anyone who works in the area.
Correctness: unknown · statement fidelity: unaudited · peer review: none
The paper records how stuck this was: the first author had discussed the question with Caucher Birkar, Osamu Fujino, Christopher D. Hacon, Junpeng Jiao, Vladimir Lazic and Lingyao Xie, and writes that despite a general feeling that a negative answer was likely, no precise counterexample could be found. The authors also note that, given the limitations of generative AI, they may have missed related literature and welcome corrections.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.