Causal–Geometric Resolution of the Riemann Hypothesis: Metageometric Foundations and Critical-Line Equilibrium

This work develops a causal–geometric framework that yields a structural resolution of the Riemann Hypothesis. The approach is based on metageometric projection, where analytic objects such as the Riemann zeta function are embedded within a causal space whose equilibrium constraints determine the location of their non-trivial zeros. Within this framework, the zeta function admits a decomposition into amplitude and phase components governed by causal opposition.The resulting equilibrium condition singles out the critical line ℜ(s)=1/2, providing a constructive route to the Riemann Hypothesis through the interplay of structural ascension, independence, and causal symmetry. The model is supported by three independent external consistencies: (1) the predicted threshold for cosmic structure emergence, confirmed by JWST observations at z∼16; (2) compatibility with high-precision hydrogen fine-structure measurements; and (3) the successful causal interpretation of the 20 GeV Fermi–LAT excess in the Milky Way halo. By linking logical structure, analytic continuation, and causal geometry, this work proposes a unified mechanism through which critical-line behaviour emerges naturally from geometric equilibrium.It forms the foundational entry in a broader metageometric program exploring deep connections between mathematical structure and physical law. - - - - - - - Keywords : Riemann Hypothesis • zeta function • analytic number theory • non-trivial zeros • critical line • causal geometry • metageometric projection • structural ascension • proof theory • mathematical logic • ordinal analysis • Peano Arithmetic • independence results • mathematical physics • prime distribution • Open Science.