# Log-concave entropy and isotropic geometry benchmark

Family 101: The sharp simplex conjecture for isotropic constants. First review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Probability researchers can test extremizers and compare entropy calculations against the sharp stated lower bound.

## Applicability and commercial boundary

Theoretical log-concavity and isotropic normalization are strong conditions. An entropy inequality alone does not build a compression system or calibrate arbitrary learned distributions.

## Initial business decision

Research infrastructure. Commercial demand and profitability remain hypotheses.

## Next verification action

Read the equality family and construct a small exact or high-precision reference.

## Evidence scope

The catalog statement was individually reviewed. Main-paper and selected formal-scope passages were additionally inspected for families 090, 093, 094, 097, 325, 328 and 332; this record does not claim a full proof audit or independent Lean verification. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).