Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 336-01. Spectral scalar curvature and uniform Urysohn width
Manuscript map · lines 8895–8904
OpenAI@2026-10-07#rem:oai-p-336-01
Authors: OpenAI. Family 336.
Title: Spectral scalar curvature and uniform Urysohn width.
Abstract: For every n ≥ 4, a complete connected smooth Riemannian n-manifold without boundary satisfying $-4{}Delta+{}mathop{{}mathrm{Scal}}{}nolimits {}ge1$ as a quadratic-form inequality admits a continuous map to a simplicial complex of dimension at most $n-2$ whose entire fibers have diameter bounded only in terms of n. The bound is measured in the original metric. This extends the uniform Urysohn width theorem from a pointwise scalar-curvature lower bound to a spectral lower bound.
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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