This paper presents a formal unification of physics, geometry, and arithmetic through the 6Π4 Model. We propose that the physical universe is not merely governed by mathematical laws, but is the dynamical manifestation of a transcendental arithmetic computation. By mapping the projection of a 6D fixed lattice onto a 3D observable membrane, we demonstrate that the fundamental constants of nature—specifically the fine-structure constant α and the electron-muon mass ratio—are geometric eigenvalues of the prime number distribution. Central to this thesis is the identification of the Prime Number as the Geometric Quantum, where the Riemann Hypothesis acts as the universal law of structural stability, ensuring the parity equilibrium of the vacuum. We redefine the Leibniz series for π as the state function of the 3D-to-6D tunnel, showing that the slow convergence of the prime race (4n+1 vs. 4n+3) generates the geometric friction perceived as time and entropy. In this framework, the Big Bang is reinterpreted as a collapse of orthogonal efficiency. This work suggests that the granularity of the quantum world is an unavoidable consequence of the irreducible nature of prime nodes, concluding that physical reality is the iterative process of the lattice squaring the circle of its own existence.