# Spherical minimal-surface volume reference

Family 349: The Solomon–Yau least-volume conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Geometric optimization researchers can compare non-totally-geodesic closed minimal immersions against the Clifford-product volume lower bound.

## Applicability and commercial boundary

Covering multiplicity, minimality and round-sphere setting matter; the result is not a generic finite membrane optimizer.

## Initial business decision

Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.

## Next verification action

Extract exact Clifford volumes and a separately justified minimality check.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and formal-scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[The Solomon–Yau least-volume theorem](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Solomon-Yau-least-volume-theorem-September-23-2026/paper.pdf).