Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 331-03. Distortion of countably branching diamonds from midpoint and tree energies
Manuscript map · lines 8795–8804
OpenAI@2026-10-07#rem:oai-p-331-03
Authors: OpenAI. Family 331.
Title: Distortion of countably branching diamonds from midpoint and tree energies.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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