Mathematical FrontierNetworkSubmit movement

Discoveries / geometry-topology

Source authenticated

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

Theorem 1.1: for some q≥10q\ge10 there is a smooth Ricci flow on the closed manifold S2×Sq+1S^2\times S^{q+1} with sup⁡∣R∣<∞\sup|R|<\infty and max⁡M∣Rm∣→∞\max_M|\mathrm{Rm}|\to\infty at the finite maximal time; a corollary gives two-sided power-law curvature blowup with arbitrarily large exponents in one fixed dimension. This refutes the unrestricted all-dimensions conjecture. It relies on Stolarski's construction and gives no explicit dimension; it does not touch dimension four, which the companion proves true.

Exact FrontierDelta

Prior state unknown→disproved

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 all dimensions · Scalar-curvature extension conjecture

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Lineage and corrections

This event attributed to Unreleased internal OpenAI model

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

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

Theorem 1.1: for some q≥10q\ge10 there is a smooth Ricci flow on the closed manifold S2×Sq+1S^2\times S^{q+1} with sup⁡∣R∣<∞\sup|R|<\infty and max⁡M∣Rm∣→∞\max_M|\mathrm{Rm}|\to\infty at the finite maximal time; a corollary gives two-sided power-law curvature blowup with arbitrarily large exponents in one fixed dimension. This refutes the unrestricted all-dimensions conjecture. It relies on Stolarski's construction and gives no explicit dimension; it does not touch dimension four, which the companion proves true. parent of this event

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