# Geodesic entropy rigidity research reference

Family 339: Katok's entropy rigidity conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Dynamics researchers can relate Liouville entropy maximality to local symmetry under strictly negative sectional curvature.

## Applicability and commercial boundary

Exact measure entropy and global smooth assumptions are not established by a finite orbit sample and do not give a numerical classifier.

## 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

Find a quantitative stability statement before a noisy geometry diagnostic.

## 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).

[Entropy equality and local symmetry in negative curvature](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Entropy-equality-and-local-symmetry-in-negative-curvature-September-23-2026/paper.pdf).