# Mean curvature first-singularity comparison reference

Family 355: Unique tangent flows at the first surface singularity. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Geometric solver researchers can organize tangent-flow uniqueness at first singularities of smooth embedded compact surfaces in R3.

## Applicability and commercial boundary

The fixed-center all-negative-time measure conclusion does not identify the tangent model, provide convergence rates or certify later singularities.

## 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

Inspect effective convergence and a known shrinker reference before a diagnostic.

## 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).

[Uniqueness of tangent flows at the first singular time of embedded surface mean-curvature flow](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Tangent-flow-uniqueness-2026-09-24/paper.pdf).