Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 336-02. Spectral scalar curvature and Urysohn width in dimension three
Manuscript map · lines 8905–8914
OpenAI@2026-10-07#rem:oai-p-336-02
Authors: OpenAI. Family 336.
Title: Spectral scalar curvature and Urysohn width in dimension three.
Abstract: Every connected complete smooth Riemannian three-manifold without boundary satisfying $-4{}Delta+{}mathop{{}mathrm{Scal}}{}nolimits {}ge{}lambda{}gt 0$ as a quadratic-form inequality admits a continuous map to a graph whose entire fibers have diameter at most $500/{}sqrt{}lambda$ in the original metric. No orientability, spin, compactness, or bounded-geometry assumption is required.
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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