# Approximation property distinction library

Family 330: A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces. First review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Formalization teams can record why approximation by finite-rank operators differs from uniformly bounded approximation.

## Applicability and commercial boundary

The infinite discrete metric example does not create a practical approximation algorithm or show that a finite software model cannot be approximated.

## Initial business decision

Defer direct product. Commercial demand and profitability remain hypotheses.

## Next verification action

Preserve the two property definitions and inspect how the counterexample is represented formally.

## 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).