Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 374-01. Sharp One-Third Stability of Brenier Maps
Manuscript map · lines 9515–9524
OpenAI@2026-10-07#rem:oai-p-374-01
Authors: OpenAI. Family 374.
Title: Sharp One-Third Stability of Brenier Maps.
Abstract: For the uniform probability measure ρ on a compact convex body in ℝd, d ≥ 2, quadratic optimal transport maps are one-third Hölder continuous in $L{}2({}rho)$ with respect to the target's 2-Wasserstein distance. The constant is uniform over all targets supported in a fixed compact set, and the exponent is optimal. A three-atom family on a fixed cube disproves Letrouit's conjectured uniform square-root estimate.
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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