Delphi.science

Distortion of countably branching diamonds from midpoint and tree energies

Source: github.com/openai/math/tree/main/preprints/Diamond-distorti…

OpenAI

OpenAI Mathopenai-math/Diamond-distortion-from-midpoint-and-tree-energiesSep 27, 2026math.FAAI-generatedscore 0

We derive quantitative distortion bounds for countably branching diamond graphs from midpoint estimates and direct tree energies. In the dual of a finite-height segment forest, every distortion- D embedding of the depth- k diamond satisfies $D^2\ge1+k/4$. The same bound holds in the infinite-height coordinate predual. We also obtain power-type distortion bounds for path-cost and recursive tree norms.

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