Universal volume growth bounds from positive intermediate curvature

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Corrects Universal volume growth bounds from positive intermediate curvature →

Supersedes Universal volume growth bounds from positive intermediate curvature →

Brendle, Hirsch, Johne - A generalization of Geroch's conjecture, where intermediate curvature is introduced evidence for this event

Kong and Zhu, Positive Scalar Curvature and Volume Growth (arXiv, 14 Aug 2026) evidence for this event

Ge, Heat kernel geometry and Gromov's volume growth conjecture (arXiv, 13 Aug 2026) evidence for this event

VibeMathed record: Universal volume growth bounds from positive intermediate curvature evidence for this event

Universal volume growth bounds from positive intermediate curvature evidence for this event

This event attributed to GPT-5.6 Sol

Universal volume growth bounds from positive intermediate curvature parent of this event

Gromov's 1986 question drew three independent proofs within about 24 hours, two with AI in the loop. Ge's non-AI proof (heat-kernel Fisher metric, Nash entropy) came first, 13 August. Antonelli's proof here (14 August, GPT-5.6 Sol) takes a different route, Hodge obstruction and rank improvement, and its headline addition is the general family: for every $0\le m\le n-2$, nonnegative Ricci plus positive $(m{+}1)$-intermediate curvature forces at most $m$-dimensional growth - linear growth under biRicci curvature at $m=1$, plus a noncollapsed Urysohn-width bound; the author states this extension is his own, not the model's. Kong and Zhu's proof (also 14 August; GPT-5.6 Sol Ultra and Codex, "essential ideas were generated by AI") proves the same case plus a related codimension-one conjecture via a heat-transport deficit, close to Ge's method by its own account, produced before Ge's went public and not derived from it. Headline axes stay Antonelli's, for the broader scope. parent of this event

This event attributed to Gioacchino Antonelli