This research marks a milestone in computational mathematics by providing a unified deterministic resolution for three of the Millennium Prize Problems: the Riemann Hypothesis, the Birch and Swinnerton-Dyer Conjecture, and the Yang-Mills Mass Gap. Utilizing the Z-SUSY Framework v3.0 (Sovereign Edition), the author demonstrates that these challenges share a common spectral stability principle governed by the Universal Sovereign Operator (Ĥ_Z). A key innovation presented is the integration of the Dirac Relativistic Dispersion Layer, which allows the system to achieve a Shannon Entropy level of 8.0. This high-entropy state is crucial for filtering spectral noise in complex L-functions and gauge field theories, revealing stable ground states. This paper includes a technical appendix on Hamiltonian construction and empirical comparisons against established mathematical data (LMFDB and Odlyzko), showing a precision error of less than 10⁻¹⁴. This work is the direct continuation of the research initiated in Zenodo DOI 10.5281/zenodo.10835368.