Preprint in the OpenAI Math release

Planar Graph Metrics Embed into L1 with Constant Distortion

OpenAI

Abstract

We prove that every finite connected planar graph with arbitrary positive real edge lengths embeds into real L $_{1}$ with a universal distortion bound. This resolves the planar embedding conjecture positively.

open until 1 Jan 2028

est. 50% chance this result is independently verified by the end of 2027.

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