# Finite Lp embedding contract audit

Family 094: Subpolynomial dimension reduction in <i>L</i><sub><i>p</i></sub>. First review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Search and representation teams can review whether a compressed finite dataset preserves the same Lp distance within a stated distortion.

## Applicability and commercial boundary

The manuscript explicitly states an existential theorem without an efficient embedding algorithm. Nonlinear and dataset-specific maps need not support future-query placement.

## Initial business decision

Prototype diagnostic. Commercial demand and profitability remain hypotheses.

## Next verification action

Build an all-pairs empirical distortion audit, preserving its floating-point and finite-dataset limitations.

## 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).