The Critical Line as Pe=1 Saturation Locus: Riemann Zeros and the Conjugacy Boundary

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Authors: Anthony W. Eckert
Cited by: 0

Abstract

Establishes that the critical line Re(s)=1/2 of the Riemann zeta function is the Pe=1 manifold of the void framework conjugacy theorem. The functional equation ζ(s)=χ(s)·ζ(1-s) is a conjugacy map; its fixed-point axis is exactly where the Pe-asymmetry cost |Pe(s)-Pe(1-s)| vanishes. Montgomery's 1973 GUE pair correlation result — zeros distribute as a maximum-entropy ensemble under symmetry constraint — is structurally identical to the Pe=1 maximum-entropy configuration. Three independent convergent lines: functional equation symmetry, zero-pair energy minimization, and GUE maximum-entropy confirmation.

Fields of Study & Subjects

Analytic Number Theory Research Advanced Mathematical Theories and Applications Smarandache Functions and Recreational Number Theory

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
3 March 2026
Language
EN
Document type
Preprint