The Analytic Resolution of the CKM Hierarchy and the Geometrization of Mass

The Resonant Brane (ERB) model v17 achieves a landmark unification of the fermionic sectors, proving that the radical contrast between quark mixing and neutrino mixing is a direct consequence of a singular Duality Principle. By applying a common mechanical seed—a three-to-two brane-mass ratio—to both localized and evanescent resonance modes, this framework derives the entire flavor landscape from first principles. We demonstrate that Quarks and Leptons are not distinct species governed by separate laws, but simply different vibrational states of the same vacuum resonance. ERB v17 provides a definitive, testable prediction for leptonic CP violation at approximately 352 degrees, offering a precise target for next-generation experiments. From subatomic oscillations to the macroscopic force ratio of the Dark Sector, the universe is revealed as a mathematically closed, mechanical symphony of the vacuum.