Preprints.org 2026 Preprint
Two Boundary-Certificate Proofs of the Crouzeix Theorem: Fiberwise Fourier Recurrence and Defect-Gram Telescoping
A preprint proposing two candidate proof routes for the finite-dimensional scalar Crouzeix inequality.
01 / The question
Can boundary-based certificates establish the sharp constant in the scalar numerical-range inequality?
02 / The approach
Boundary-Certificate Proofs
The manuscript proposes a fiberwise Fourier recurrence and a defect-Gram telescoping argument, then discusses their relationship and accompanying Lean 4 developments. Version 2 consolidates the earlier manuscript, The Sharp Numerical-Range Spectral-Set Inequality; it remains a preprint without peer review.
03 / Citation
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04 / Versions & records
Publication record
- The Sharp Numerical-Range Spectral-Set Inequality
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Full paper
Earlier manuscript version — title The Sharp Numerical-Range Spectral-Set Inequality. Public version 1; not peer reviewed. The site’s current publication record describes version 2.
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