# Planar metric embedding and flow-cut review

Family 089: Bounded-distortion <i>L</i><sub>1</sub> embeddings of planar and bounded-treewidth graphs. First review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Routing researchers can evaluate L1 metric abstractions for planar or bounded-treewidth graph models.

## Applicability and commercial boundary

A bounded distortion theorem does not automatically provide a useful constructible embedding or preserve arbitrary operational constraints. Planarity, weights and treewidth must be verified.

## Initial business decision

Conditional research. Commercial demand and profitability remain hypotheses.

## Next verification action

Review whether the paper gives an effective construction and extract constants and preprocessing requirements.

## 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).