# Log-concave sampling assumption audit

Family 093: Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures. First review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Sampling researchers could derive algorithm-specific convergence analysis if a target's log-concavity and subgaussian linear marginals are established.

## Applicability and commercial boundary

A logarithmic Sobolev inequality alone is not a discretized sampling algorithm or a verified total runtime. Estimating the subgaussian parameter from finite samples cannot certify all directions.

## Initial business decision

Conditional research. Commercial demand and profitability remain hypotheses.

## Next verification action

Inspect how the universal constant and target conditions enter a concrete sampler's theorem.

## 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).