Uniqueness of tangent flows at the first singular time of mean curvature flow of closed embedded surfaces

Claims uniqueness of tangent flows, without mean-convexity or a prescribed tangent model, at every singular point of the first singular time for smooth compact connected embedded surfaces in $\mathbb R^3$ : all fixed-center rescalings converge to one multiplicity-one self-shrinker flow in the original coordinates, and every backward Brakke tangent agrees with it. The key step is a finite-jet Lojasiewicz analysis handling shrinkers with both conical and cylindrical ends. It does NOT cover later singular times, higher dimensions, or moving-center blowups.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Uniqueness of tangent flows at the first singular time of mean curvature flow of closed embedded surfaces · Tangent-flow uniqueness, first singular time

Confidence: Not scored

Registry verification: unreviewed · announcement · partial

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Uniqueness of tangent flows at the first singular time of mean curvature flow of closed embedded surfaces

specialist registry · passed

No independent mathematician has checked this yet. Theorem 1.1 was read against Haslhofer's Conjecture 5.2: at every singular point of the FIRST singular time of a closed embedded surface flow in $\mathbb R^3$ , the full family of fixed-center rescalings converges locally smoothly with multiplicity one to a single shrinker, with fixed position and axes. The paper itself says it establishes the negative-time, fixed-center part of the conjecture at the first singular time, and that moving centers and continuation through singularities are different questions. It uses Bamler-Kleiner's multiplicity-one theory as input. No Lean formalization.

Source ↗

Uniqueness of tangent flows at the first singular time of mean curvature flow of closed embedded surfaces

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Haslhofer, Mean curvature flow through singularities (2025)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Lineage and corrections

Uniqueness of tangent flows at the first singular time of mean curvature flow of closed embedded surfaces evidence for this event

This event attributed to Unreleased internal OpenAI model

Uniqueness of tangent flows at the first singular time of mean curvature flow of closed embedded surfaces parent of this event

VibeMathed record: Uniqueness of tangent flows at the first singular time of mean curvature flow of closed embedded surfaces evidence for this event

Haslhofer, Mean curvature flow through singularities (2025) evidence for this event

Act on this frontier

Verify, challenge, or extend the result.

Help verify Open canonical problem Explore evidence graph