We introduce the Thermodynamics of Arithmetic Action (TAA), an architectural framework thatunifies arithmetic geometry, informational code theory, and general relativity into a single, cohesive paradigm. This monograph maps the macroscopic universe—including space, time, and the fields of the Standard Model—as the continuous Archimedean completions of a global adélic variety governed by a singular Grothendieck Motive. By demonstrating that the absolute stability of the spacetime metric is structurally bound to the unitarity of the global intertwining operator over GL(2, AQ), weshow that any violation of the Riemann Hypothesis (RH) induces a non-vanishing covariant divergence in the macroscale stress-energy tensor. This mathematical rupture violates the foundational Bianchi identities and triggers an immediate, catastrophic metric collapse. Consequently, the Riemann Hypothesis emerges not as an isolated problem in pure number theory, but as the fundamentalphysical boundary condition that preserves the structural sanity of the spacetime vacuum against self-dissolution.