Wave Mechanics on a Inverted Torus: Phase Decoherence, Wilson's Resonance, and the Geometric Derivation of Prime Number Distribution

This paper presents the second part of the wave-calculus framework based on the inverted torus architecture. We demonstrate that the computational bottleneck of Wilson's theorem—the factorial explosion of ((p-1)! + 1)—can be completely bypassed through the geometric summation of phase coordinates (raw_angle) on a wave helicoid, transforming an exponential arithmetic problem into a discrete quantum-like resonance. Furthermore, we extend this local phase resonance to a global scale, proving that the prime number distribution law (pi(x) ~ x/ln(x)) is a direct consequence of phase decoherence and spatial divergence of wave packets. The natural logarithm is geometrically derived as the winding step metric of the expanding torus scale (d(theta) ~ dx/x). Finally, the Riemann Hypothesis is physically contextualized as a strict constraint on wave beat variance within a closed deterministic system.