The Riemann Hypothesis as a Theorem of Cosmic Information Theory: Thermodynamic Stability, Spectral Confinement, and Informational Conservation

We establish the Riemann Hypothesis (RH) as a theorem within the Cosmic Information Theory (TIC/CIT) framework, under four axioms: information substrate (A1), metric non-degeneracy (A2), informational second law (A3), and unitarity (A4). The positivity of the spectral gap ∆ = t1 − t ∗ > 0 is a proved theorem (Corollary 3.8), not an axiom. The essential self-adjointness of □g ξ is established conditionally: it holds if and only if all non-trivial zeros lie on the critical line, making the proof by contradiction non-circular. The sign change of g ζ tt(1/2, ·) at the explicit point t0 = 6 is established via polygamma bounds (Proposition 3.7), giving a rigorous analytic foundation for the Intermediate Value Theorem argument. The entropy of boundary conditions S∂ > 0 is stated as a Working Hypothesis with a derivation sketch. The framework extends to the Generalised Riemann Hypothesis for the Selberg class S.