Universal Volume Growth Bounds from Positive Intermediate Curvature

Gioacchino Antonelli

GPT-5.6 Sol proposed the Hodge-obstruction and rank-improvement strategy behind the bound Vol B_R(p)≤C(n)R^(n−2) on complete connected n-manifolds with Ric≥0 and Scal≥1.

Sources for this record

What was already known

Gromov posed the codimension-two bound. Ge posted an independent heat-kernel proof one day before Antonelli’s first preprint.

AI involvement AI-centered

Antonelli credits GPT-5.6 Sol with the central strategy for the codimension-two corollary. He claims the broader intermediate-curvature result and major proof revisions as human work.

The author explicitly identifies GPT's central induction strategy behind Corollary 1.3, while reserving the stronger intermediate-curvature theorem and major revisions for human work.

Importance Notable

Provides an alternative route to the codimension-two bound, rather than its first public resolution.

Limitations

Antonelli and colleagues developed the effective final proof and the stronger intermediate-curvature extension. No completed check of Antonelli’s exact final argument is documented; independent proofs do not check it.

Technical verification Reported

The v2 manuscript supplies a full human-written proof and records discussions that modified the original model strategy, but not a completed check of this exact final argument. Independent proofs of the same conclusion do not verify the assessed argument. Reported is the evidence default.

Human understanding Full

Antonelli explains the Hodge obstruction, rank-improvement induction and the changes making the proof effective; named colleagues contributed to those changes. The central mechanism of the assessed codimension-two route is human-explained.

Correction and publication history

2026-10-18 · publication

Provides an alternative route to the codimension-two bound, rather than its first public resolution.

Read this published revision