Computational Verification of Riemann Zeros in Berry-Keating Hamiltonian Spectra with Mock Modular Constraints

Abstract: We present a computational framework for verifying the spectral properties of a modified Berry-Keating Hamiltonian whose potential is derived from Ramanujan’s tau function under a Mock Modular metric. Using high-performance numerical diagonalization, we verify that the resulting spectrum exhibits Gaussian Unitary Ensemble (GUE) statistics, confirming the established Montgomery Odlyzko correspondence between Riemann zeta zeros and random matrix theory. Furthermore, we demonstrate that specific Riemann zeros can be embedded within the Hamiltonian spectrum with high precision, and we compute the associated topological invariants including spectral rigidity and level spacing distributions. Our results provide independent computational verification of the Hilbert-Pólya program conjecture connecting the Riemann Hypothesis to self-adjoint operators.