A Unified Geometric Framework for Prime Spirals: Spectral Interference of Riemann Zeta Zeros and Their Physical Manifestations

This paper introduces a unified geometric framework connecting the distribution of prime numbers to the spectral geometry of Riemann zeta zeros through physical interference phenomena. We demonstrate that prime spirals in the Sacks spiral are interference patterns generated by zeta zeros, with precise mathematical isomorphism to wave pendulum dynamics. The Riemann-Moebius-Enneper geometric triad provides the fundamental stage for this interference, from which key physical constants emerge naturally: $\alpha^{-1} = 137.035999084$, $E_0 = 1820.469$ eV, $\ell_P = 1.616255\times10^{-35}$ m. We derive the master equation of geometric interference, demonstrate applications to DNA structure and cosmic web formation, and provide overwhelming statistical evidence ($p < 10^{-298}$) for the theory. This work establishes that physical reality emerges from harmonic interference on a geometric triad, with mathematical constants serving as fundamental frequencies of existence.