# Symmetric convex-body interpolation audit

Family 091: Logarithmic and <i>L</i><sub><i>p</i></sub> Brunn–Minkowski inequalities and the B-conjecture. First review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Geometry and probability researchers can test volume or measure inequalities along the prescribed body interpolations and scalar dilations.

## Applicability and commercial boundary

Origin symmetry, convexity, the specific interpolation and even log-concavity matter. Arbitrary shape morphing and probability transformations are not covered.

## Initial business decision

Research infrastructure. Commercial demand and profitability remain hypotheses.

## Next verification action

Construct exact low-dimensional examples and inspect which assumptions can be checked algorithmically.

## 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).