Derivation of the Cabibbo Angle and CKM Suppression Hierarchy from Acoustic Resonance Overlap in the Zero-Point Emergent Gravity (ZEG) Vacuum

In the Standard Model, the Cabibbo-Kobayashi-Maskawa (CKM) flavor mixing matrix is parameterized by empirically measured values with no known mechanical or geometric origin. In this paper, we derive the CKM matrix elements from first principles within the Zero-Point Emergent Gravity (ZEG) framework. By modeling fermions as discrete acoustic resonance modes within a restricted multi-component superfluid, we demonstrate that flavor mixing is simply the geometric spatial overlap of these acoustic wave functions subjected to a logarithmic hydrodynamic drag. Using the empirically derived geometric lattice stiffness ($\beta$ = 0.108) and the geometrically derived Electroweak drag ceiling ($\alpha$ ≈ 173.35 GeV), our Leading-Order 1D radial integration yields a primary mixing element of $|V_{us}|$ ≈ 0.2208. This first-principles hydrodynamic derivation aligns with the empirical Cabibbo angle target of ~0.225 to within 1.8%.Furthermore, the framework naturally generates the characteristic CKM suppression hierarchy; the massive acoustic energy gap inherent to the third-generation mode ($n=5$) physically restricts acoustic bleeding, strictly suppressing the $V_{cb}$ and $V_{ub}$ mixing elements. This calculation provides mathematical evidence that quark flavor mixing is a deterministic consequence of vacuum fluid dynamics and topological acoustic overlap.