OpenAI reports uniqueness of first-time surface mean-curvature tangents

At every singular point of the first singular time for the mean-curvature flow of a smooth compact connected embedded surface in R³, the full fixed-center rescaling family converges locally smoothly on compact negative-time intervals to one multiplicity-one homothetic self-shrinker in the original ambient coordinates.

Sources for this record

What was already known

Uniqueness was established for compact, round-cylinder and asymptotically conical multiplicity-one tangent models. The general first-time embedded-surface case without mean convexity or a prescribed tangent model remained open.

AI involvement AI-led

OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.

OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.

Importance Major

Gives fixed-center tangent-flow uniqueness for all such first singularities.

Limitations

The statement concerns the first singular time and negative-time rescalings; it does not assert a corresponding forward-time model.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.

Correction and publication history

2026-10-18 · publication

Primary manuscript, attribution, and prior-work review for non-notifying local inclusion; technical verification remains Reported.

Read this published revision