# Metric versus linear representation counterexample explorer

Family 324: Lipschitz equivalent Banach spaces need not be linearly isomorphic. First review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Representation researchers can review cases where global metric equivalence does not imply linear equivalence.

## Applicability and commercial boundary

Infinite-dimensional Banach-space examples do not establish a practical failure of a finite neural representation or a new learning algorithm.

## Initial business decision

Defer direct product. Commercial demand and profitability remain hypotheses.

## Next verification action

Inspect which finite approximations can convey the distinction without overstating the 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).