Prime Cycles in Quantum Spacings and Zeta Zeros: A Number-Theoretic Bridge Between Classical and Quantum Physics

We analyze eigenvalue spacings from quantum simulations and refined untwisted zeta zeros—Riemann zeta zero approximations adjusted with prime-based oscillations—achieving near-convergence to the Gaussian Unitary Ensemble (GUE). Quantum spacings yield a Kolmogorov-Smirnov (KS) statistic D = 0.1159 with p = 0.0658, surpassing the 0.05 threshold, while refined zeros achieve D = 0.0901 and a Cramer-von Mises (CvM) p = 0.9465, indicating exceptional GUE alignment. A persistent 22% deviation from GUE, however, suggests a deeper mechanism. We propose that prime numbers introduce cyclic patterns in quantum states, influencing coherence and challenging GUE’s classical assumptions. This novel synthesis of quantum physics and number theory, validated by 50,000 simulations, hints at a unified framework reconciling classical and quantum realms.