# Mean-dimension comparison evidence

Family 302: Radius of comparison equals half the mean dimension. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Track radius of comparison for crossed products of minimal homeomorphisms and the zero-dimensional companions.

## Applicability and commercial boundary

Mean dimension is an infinite dynamical invariant, not the dimension of a machine-learning feature vector.

## 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

Read computable dynamical examples and distinguish all equivalent zero conditions.

## 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).

[Filtered products and boundary-preserving compression in complex cobordism](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Filtered-products-and-boundary-preserving-compression-in-complex-cobordism-September-25-2026/paper.pdf).