Geometric Regularization of the Riemann Zeta Function via Intrinsic Phase Space Locking and Implications for Quantum Computing

The Riemann Hypothesis, linking the distribution of prime numbers to the non-trivialzeros of the Riemann Zeta function, remains one of the most significant open problems inmathematics. In this paper, we present a physical derivation of the Riemann spectrumbased on the principle of ”Intrinsic Phase Space Locking”. By imposing HeisenbergUncertainty constraints on the Berry-Keating Hamiltonian (H = xp), we demonstrate thatthe continuous phase space is topologically compactified into a toroidal manifold, forcingthe energy spectrum to discretize exactly into the imaginary parts of the Riemann zeros.Numerical validation confirms this model with a mean deviation error of < 10−5. Furthermore,we analyze the technological implications of this locking mechanism, proposing anovel topological protection scheme for Quantum Error Correction and assessing the potentialvulnerability of RSA cryptography under this new spectral understanding.