ONE AXIOM : The Critical Ridge : Phase Coherence as a Structural Invariant of ζ(s)

7B — The Critical Ridge: Phase Coherence as a Structural Invariant of (s) Description: Overview This paper presents a formal structural establishment of the Geometric Riemann Hypothesis (G-RH) within the ONE AXIOM framework. Moving beyond traditional analytic number theory, document 7B identifies the distribution of Riemann zeros as a structural necessity of holographic decompression. By employing a Dual-Track Methodology, the work bridges Lens 2 (Geometric/Classical) and Lens 4 (Ontological), revealing RH as a compatibility condition between the VOID (₄) and the relational layer (₆). Key Contributions The Bridge Theorem: The central result of the paper, establishing that G-RH implies the Classical Riemann Hypothesis. The theorem demonstrates that phase pinning at \0, \ and the exclusion of off-axis quadruplets are mandatory for ontological coherence. Possibility Selection Principle (PSP): Application of the 51: 13 structural filter derived from Fano-K7 duality. The paper demonstrates that 13 out of 64 phase sectors are "FORBIDDEN, " preventing any off-axis zero formation. Statistical Validation: A rigorous analysis of the first 400 Riemann zeros shows an overwhelming fit for the ONE AXIOM model (² = 713. 22) with a Bayes Factor (BF > 10^154), ruling out the null hypothesis of random distribution. Independent Experimental Validation: Integration of recent findings by Wei et al. (arXiv: 2511. 11199), providing external empirical support for the structural predictions of the model. Quantum Gap Analysis: The analysis reveals a 90-point quantum gap: 100% of on-critical zeros occupy ALLOWED sectors, versus only 10. 2% of off-critical points. This disparity confirms the "Critical Ridge" as a preferred state of ontological stability. Methodology & Formalism The work introduces an "Epistemological Switch, " shifting from numerical verification to structural recognition. It contains 8 formal theorems (Section 8) that define the Ontological Coherence Field (OCF) and the mechanism of phase-locking. The paper formalizes the condition = 1/2 \0, \ on the critical line, linking Hardy’s Z-function to the q^ = 3/2* Tsallis critical exponent at Layer ₅. ₅. Target Audience Researchers in complex analysis, quantum chaos, and theoretical physics interested in non-extensive statistics, holographic principles, and the structural foundations of mathematics.