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.