The Arithmetic Structure of Geometry, Dynamics, Information, and Topology

This monograph presents an Arithmetic Framework proposing that spacetime, quantum information, and matter, emerges from an arithmetic quantum statistical system, specifically the Bost-Connes (BC) system. Thermal time, maximal acceleration, and SU(N) symmetries arise from this framework, and the Riemann Hypothesis (RH) becomes a condition for its physical stability. This proof hinges on the argument that a stable physical vacuum requires zero geometric dissipation, which mathematically mandates the de Bruijn-Newman constant (ΛDB) to be zero, a condition equivalent to the RH. Ultimately, the work identifies the vacuum as a Shimura Variety, framing physics within the Geometric Langlands Program and connecting anomalies to arithmetic torsion.