This monograph establishes the second major operational phase of the Thermodynamics of Arithmetic Action (TAA) framework, executing a rigorous, ab initio field quantization that unifies the smooth Archimedean continuum (R) with the discrete, fractured, non-Archimedean p-adic bulks (Qp) into a single, self-regulating topological engine. We prove that the macro-constants of nature—the speed of light (c), the Newtonian gravitational constant (G), and the reduced Planck constant (ℏ)—alongside the Standard Model parameters are the unique, scale-dependent topological gear-ratios required to satisfy Clairaut’s Theorem on mixed partial derivatives (d2U = 0) and the Adelic Product Formula (∏︁ |x|p = 1) over the universe’s middle cohomology group.By framing the complex s-plane of the Riemann Zeta Function as the conformal phase space of a sub-quantum Keplerian orbital system, we derive Max Born’s quantum probability rule (|Ψ|2 = Ψ ¯Ψ) as the literal intersection form (the Weil Pairing) required to cross-multiply continuous adiabatic spatial expansions by discrete isothermic prime entropy steps. Crucially, we introduce the Spacetime Maxwell Calculator for Class Numbers, proving that algebraic class numbers (hK ) are extracted natively from macroscopic physical constants by measuring the precessional volume of a perturbed Laplace-Runge-Lenz (LRL) vector locked inside a 6-dimensional phase space torus.