Metric compression impossibility demonstrator

Family 098: Compact counterexamples to bi-Lipschitz dimension reduction. First review, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Embedding researchers can illustrate why compact doubling geometry alone does not guarantee finite-dimensional bi-Lipschitz compression.

Applicability and commercial boundary

The infinite compact example does not forbid useful embeddings of finite samples or imply that a particular vector-search dataset cannot be compressed.

Initial business decision

Research infrastructure. Commercial demand and profitability remain hypotheses.

Next verification action

Review finite approximations of the counterexample and define what a bounded demonstrator can truthfully show.

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.