# Free entropy notion separation reference

Family 298: Two notions of free entropy differ even when both are finite. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Give noncommutative probability researchers a counterexample to equality of the two specified finite free-entropies.

## Applicability and commercial boundary

These are free entropy invariants, not Shannon entropy of an ordinary dataset or an automatic compression limit.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

## Next verification action

Extract exact variables and independently computable approximations.

## Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[A finite-entropy separation of microstates and nonmicrostates free entropy](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-finite-entropy-separation-of-microstates-and-nonmicrostates-free-entropy-September-25-2026/paper.pdf).