Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 325-01. A direct proof of the complete Crouzeix inequality
Manuscript map · lines 8705–8714
OpenAI@2026-10-07#rem:oai-p-325-01
Authors: OpenAI. Family 325.
Title: A direct proof of the complete Crouzeix inequality.
Abstract: We give a direct proof of the sharp constant-two numerical-range inequality for matrix-valued polynomials in all finite base and coefficient dimensions. This resolves the complete Crouzeix conjecture in its matrix formulation, including matrices whose numerical ranges are points or line segments.
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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