Differential geometry·OpenAI Math·Result 352
A finite-time singularity of Calabi flow
One of the 372 results in OpenAI's public mathematics catalogue, filed under differential geometry: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and embeds the animation.
In one line: OpenAI reports a result titled ‘A finite-time singularity of Calabi flow’ (differential geometry) in a preprint dated 24 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More, is on YouTube.
Chapter 44 of 84 in Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · starts at 15:01 · watch from there on YouTube →
What OpenAI claims
Disproves Chen's smooth long-time existence conjecture for Calabi flow by constructing a smooth U(10)-invariant Kähler metric on ℂℙ10 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.
Paper
A finite-time singularity of Calabi flow on projective space
OpenAI's abstract We construct a smooth Kähler metric in the Fubini–Study class of ℂℙ10 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.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 24 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- Disproves Chen's smooth long-time existence conjecture for Calabi flow by constructing a smooth U(10)-invariant Kähler metric on ℂℙ10 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.
- Where is the proof?
- In the paper, A finite-time singularity of Calabi flow on projective space (PDF).
- Is there a video?
- Yes, on YouTube (29:20, chapter 44).
Also in
- Chapter 4 of 9 in Calabi Flow, Affine Bernstein Problem and 7 More in Differential Geometry · starts at 1:03 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · Compilation · 29:20 · chapter 44 from 15:01 · description, sources and chapters →
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