AWESOME AI PROOFS
← Problems
Research / Oct 6, 2026

Planar Graph Metrics Embed into L_1 with Constant Distortion

Can the mathematical statement in Planar Graph Metrics Embed into L_1 with Constant Distortion be proved and verified machine-checked in Lean?

Model / AI: OpenAI (unreleased)

machine-checked (formal proof)self-reported (formal proof)
Oct 6, 2026

Lean formalization in OpenAI math repository (Result 089)

Model / AI: OpenAI (unreleased)

machine-checked (formal proof)self-reported (formal proof)

OpenAI's internal frontier model proved and formalized in Lean the main result of 'Planar Graph Metrics Embed into L_1 with Constant Distortion'. We prove that every finite connected planar graph with arbitrary positive real edge lengths embeds into real L1 with a universal distortion bound. This resolves the planar embedding conjecture positively.

Source read 2026-10-08. Cataloged from OpenAI's formalization.yaml (Family 089). The Lean development was not rebuilt locally.