Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 331-02. Midpoint lenses in segment spaces
Manuscript map · lines 8785–8794
OpenAI@2026-10-07#rem:oai-p-331-02
Authors: OpenAI. Family 331.
Title: Midpoint lenses in segment spaces.
Abstract: For a real segment-forest dual with unbounded finite component heights and the real infinite-height coordinate predual, we bound the tail of an arbitrary displacement in a symmetric lens by $2{}sqrt{R{}2-{}|x{}|{}2}$, where R is the lens radius and x is its finitely supported center. Both given norms are asymptotically midpoint uniformly convex, although neither space admits an equivalent asymptotically uniformly convex norm. The finite-height forest dual is reflexive.
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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