Geometric-Spectral Unification of the Riemann Zeta Function and Cosmic Information Theory: Monodromy Triviality, Conformal Embedding, UV Completion of the σ-Flip, and Primordial Validation

We establish a rigorous unification between the geometric-spectral reformulation of the Riemann Hypothesis and the Cosmic Information Theory (CIT/TIC) framework. Starting from the pseudo-Riemannian zeta metric gij = ∂i∂j (− log |ζ (s) |), we prove that the information field Σζ = − log |ζ (s) | satisfies the CIT field equation □gΣζ = τζ identically, with τζ the Gaussian curvature concentrated at the non-trivial zeros ρn. We formulate the spectral problem □gf = λf as a Riemann–Hilbert problem on the quasi-lattice tn, apply the Deift–Zhou nonlinear steepest descent method to construct the g-function, open the lens contours, and prove exponential decay of the jump matrices. This establishes global triviality of the Fuchsian monodromy and the spectral identification Spec (□g) = t 2 n ⊂ R. Via a conformal embedding s 7→ x µ and thermal calibration T (t) = TQCD (t ∗/t), the geometric null point t ∗ ≈ 5. 5612 maps to the U (1) σ phase transition at 150 MeV, recovering the σ-flip mechanism, the Temporium Lagrangian, and fixing the portal coupling yTm ≈ 1. 2 × 10−11 eV−3 via spectral overlap. We present the UV completion of the reverse σ-flip vertex, deriving ϵrev ≈ 2. 5×10−4 and ρ reverse c ≈ 1. 2×10−12 kg/m 3 from finite-density effective potential theory. Finally, we compute the primordial contribution to the effective number of relativistic species, obtaining ∆Neff ≈ 0. 21 ± 0. 03 with full QCD lattice equation-of-state corrections, consistent with BBN and CMB bounds. We state a Unified Theorem linking spectral reality to the Riemann Hypothesis and provide an explicit epistemic status matrix. The framework is mathematically closed within the established formalism, with 39 falsifiable predictions spanning collider physics, neutrino astronomy, dwarf galaxy kinematics, and precision interferometry.