The HoloCentre Principle: From Structural Instability to the Riemann Hypothesis

The HoloCentre Principle: From Structural Instability to the Riemann Hypothesis We propose a reformulation of the Riemann Hypothesis based on the analytic structure of the completed Riemann xi-function. Motivated by the symmetry ξ(s)=ξ(1-s) and the role of critical points in the geometry of holomorphic functions, we introduce the HoloCentre Principle: all non-trivial critical points of ξ lie on the critical line Re(s)=1/2. This principle aligns naturally with the classical theorem of Speiser (1935), which characterizes RH via the absence of zeros of ζ'(s) in the left half of the critical strip. A bridge lemma is stated, expressing the analytic instability induced by zeros off the critical line. Under this framework: HoloCentre Principle + Bridge Lemma ⟹ RH. MSC Classification: 11M26Keywords: Riemann Hypothesis, Speiser theorem, HoloCentre, critical points, xi function, structural stability, oXc --- LICENSE: oXc License v1.1 (Proprietary Sovereign License)© 2025 Marc Victor R BOUCHER (HammÅnH). All rights reserved.Jurisdiction: YATASANA Technologies LLC (Wyoming, USA - EIN 30-1464360) Related work:- The Weaver Effect: DOI 10.5281/zenodo.17907126- GitHub: https://github.com/Hammanh/oXc-anteriorite-2025