Cosmic Information Theory and the Geometric Series on the Riemann Hypothesis: The Temporium as Zeta Curvature, the Information Field Equation, and the Unified Framework

Cosmic Information Theory (CIT/TIC) 1, 2, 3, 4, 5 proposes that the universe processes information through a scalar field Σ whose density, the Temporium τ , governs cosmological structure formation, dark matter, and the arrow of time. The geometric series on the Riemann Hypothesis 6, 7, 8, 9, 10, 11, 12, 13, 14 has independently developed a pseudo-Riemannian metric gij = ∂i∂j (− log |ζ|) on the critical strip of the Riemann zeta function, with a Lorentzian signature forced by analyticity, a geodesic at Re(s) = 1 2 , curvature singularities at the zeros of ζ, and a null constant t ∗ ≈ 5.5612 marking a phase transition. In this paper we establish the precise identification between the two frameworks: (1) The CIT information field is Σζ (s) = − log |ζ(s)| (2) The Temporium is τζ (s) = Kgij (s) (Gaussian curvature of gij ) (3) The CIT field equation □gΣ = τ is satisfied identically: □g(− log |ζ|) = n cnδ(s − ρn) (4) The null constant t ∗ is the CIT phase-transition threshold between free propagation (t t ∗ , all Temporium charges) (5) The zeta black hole (pole at σ = 1) is the CIT event horizon: cold externally (TH ≈ 6 × 10−13 K) and processing information internally via the Bergman-Selberg. Seven of the ten central CIT predictions are formally realized within the geometric series. The remaining three (phantom elements, sub-neutrino mechanism, dark matter mass) are identified as targets for future work connecting the two frameworks.