The HoloCentre Principle: From Structural Instability to the Riemann Hypothesis

The HoloCentre Principle: From Structural Instability to the Riemann Hypothesis VERSION 1.2.0 — January 7, 2026 UPDATES IN THIS VERSION:- Bridge Lemma now PROVED (via Rouché's theorem)- Article reviewed and validated for arXiv submission- Numerical evidence section added (Levinson, Conrey references) ABSTRACT:We present a symmetry-driven formulation related to the Riemann Hypothesis, based on the distribution of critical points of the completed Riemann xi-function. Motivated by the symmetry ξ(s)=ξ(1-s), we introduce the HoloCentre Principle: all non-trivial critical points of ξ lie on the critical line Re(s)=1/2. This principle aligns 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 PROVED under local hypotheses (via Rouché's theorem), showing that a zero of ξ off the critical line forces a nearby critical point. CONCLUSION: Assuming the HoloCentre Principle, the Riemann Hypothesis follows. MSC Classification: 11M26Keywords: Riemann Hypothesis, Speiser theorem, HoloCentre, critical points, xi function, structural stability, oXc FILES:- HOLOCENTRE-ARXIV-FINAL-SAFE.tex — LaTeX article (arXiv-ready, 6-7 pages)- HOLOCENTRE-ARGUMENTAIRE-COMPLET-v2.md — Full argumentation- BRIDGE-LEMMA-PROOF.md — Proof of the Bridge Lemma (Rouché)- LICENSE-OXC-v1.1-EN.pdf — oXc License v1.1 Related work:- The Weaver Effect v2.2: DOI 10.5281/zenodo.17907126- GitHub: https://github.com/Hammanh/oXc-anteriorite-2025 LICENSE: oXc License v1.1 (Proprietary Sovereign License)© 2025-2026 Marc Victor R BOUCHER (HammÅnH). All rights reserved.