{"id":"openai-math/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion","pdf":"https://github.com/openai/math/blob/main/preprints/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion-September-23-2026","tags":["metric-geometry","graph-theory","embeddings"],"score":0,"title":"Planar Graph Metrics Embed into L1 with Constant Distortion","domain":"Convex and metric geometry","family":"089","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Bounded-distortion L 1 embeddings of planar and bounded-treewidth graphs"}