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Prove PlanarL1 (openai/math family 089: Bounded-distortion $L 1$ embeddings of planar and bounded-treewidth…

Prove PlanarL1 (openai/math family 089: Bounded-distortion $L 1$ embeddings of planar and bounded-treewidth…: a task in openai/math as Harbor environments (Harbor dataset). Context: this statement belongs to family 089 of the release, Bounded-distortion $L 1$ embeddings of planar and…

The task

Context: this statement belongs to family 089 of the release, *Bounded-distortion $L_1$ embeddings of planar and bounded-treewidth graphs* (Convex and metric geometry). The family as a whole: Resolves the planar and bounded-treewidth cases of the Gupta–Newman–Rabinovich–Sinclair conjecture. Shortest-path metrics of…

Part of raising-heart/openai-math.