Geometric-Spectral Unification of the Riemann Zeta Function and Cosmic Information Theory: Deift–Zhou Monodromy, Conformal Embedding, and the σ-Flip Mechanism

We present 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, and 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 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 state a Unified Theorem linking spectral reality to the Riemann Hypothesis and provide an explicit epistemic status matrix. The framework is mathematically complete within the established formalism, with 39 falsifiable predictions spanning collider physics, neutrino astronomy, and precision interferometry.