OpenAI · 352-01 · 2026-09-24 · Differential geometry
A finite-time singularity of Calabi flow on projective space
preprints/A-finite-time-singularity-of-Calabi-flow-on-projective-space-September-24-2026
Family 352. Finite-time singularity of Calabi flow.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Disproves Chen's smooth long-time existence conjecture for Calabi flow by constructing a smooth -invariant Kähler metric on whose flow develops a finite-time singularity. The metric lies in the Fubini–Study class, so the failure occurs even in a class containing a constant-scalar-curvature metric.
We construct a smooth Kähler metric in the Fubini–Study class of whose Calabi flow develops unbounded scalar curvature in finite time. This disproves Chen's smooth long-time existence conjecture, even in a class containing a constant-scalar-curvature metric.
Preprint source and Lean scope
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