# Nuclear C-star regularity equivalence adapter

Family 291: Cuntz comparison, nuclear dimension, and equivariant Jiang–Su stability. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Record equivalences among comparison, nuclear dimension and Jiang–Su stability, including restricted equivariant companions.

## Applicability and commercial boundary

Unitality, nuclearity, simplicity and finiteness or action conditions differ. Equivalence does not compute a decomposition cheaply.

## 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

Map regimes separately and inspect effective constructions.

## 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).

[Equivariant Jiang–Su Stability for Amenable Actions in the Unital Stably Finite Case](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equivariant-Jiang-Su-Stability-for-Amenable-Actions-in-the-Unital-Stably-Finite-Case-October-5-2026/paper.pdf).