# Ricci flow singularity evidence audit

Family 351: Scalar curvature and finite-time Ricci-flow singularities. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Geometric flow researchers can distinguish scalar-curvature monitoring sufficient for extension in dimension four from failure in higher dimensions.

## Applicability and commercial boundary

Dimension and smooth closed-domain assumptions matter. A sampled bounded scalar field is not a uniform all-time bound or a numerical continuation certificate.

## Initial business decision

Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.

## Next verification action

Extract the higher-dimensional example and specify which diagnostics a finite solver can legitimately observe.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and formal-scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[A closed Ricci flow with bounded scalar curvature and finite-time curvature blowup](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026/paper.pdf).