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.

A finite-entropy separation of microstates and nonmicrostates free entropy.