Mathematical FrontierNetworkSubmit movement

Discoveries / geometry-topology

Source authenticated

The scalar-curvature extension conjecture for Ricci flow in dimension four

Theorem 1.1: a smooth Ricci flow on a closed four-manifold with sup⁡M×[0,T)∣R∣<∞\sup_{M\times[0,T)}|R|<\infty, T<∞T<\infty, extends smoothly past TT; Corollary: at a finite maximal time lim sup⁡max⁡R=+∞\limsup\max R=+\infty. This removes the H2H_2 hypothesis of Bamler-Zhang and gives smooth continuation rather than an orbifold flow. The companion proves E=o(M)E=o(M) for the renormalized Einstein-Hilbert functional on degenerating trees of Ricci-flat spaces. It is specific to dimension four; in high dimension the family's other paper shows the statement is false.

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: The scalar-curvature extension conjecture for Ricci flow in dimension four · Scalar-curvature extension, dimension 4

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

Lineage and corrections

VibeMathed record: The scalar-curvature extension conjecture for Ricci flow in dimension four evidence for this event

This event attributed to Unreleased internal OpenAI model

The scalar-curvature extension conjecture for Ricci flow in dimension four parent of this event

Path selection and an elliptic inequality on degenerating Ricci-flat trees evidence for this event

The scalar-curvature extension conjecture for Ricci flow in all dimensions evidence for this event

Theorem 1.1: a smooth Ricci flow on a closed four-manifold with sup⁡M×[0,T)∣R∣<∞\sup_{M\times[0,T)}|R|<\infty, T<∞T<\infty, extends smoothly past TT; Corollary: at a finite maximal time lim sup⁡max⁡R=+∞\limsup\max R=+\infty. This removes the H2H_2 hypothesis of Bamler-Zhang and gives smooth continuation rather than an orbifold flow. The companion proves E=o(M)E=o(M) for the renormalized Einstein-Hilbert functional on degenerating trees of Ricci-flat spaces. It is specific to dimension four; in high dimension the family's other paper shows the statement is false. parent of this event

Bounded scalar curvature and smooth extension of four-dimensional Ricci flow evidence for this event

Act on this frontier

Verify, challenge, or extend the result.

Help verifyOpen canonical problemExplore evidence graph