Emergence of Flavor Mixing, CKM Hierarchy, and CP Violation from a Resonant Brane Model (ERB) – Preprint & Stability Proof

Emergence of Flavor Mixing, CKM Hierarchy, CP Violation and Mass Hierarchy from a Resonant Brane Model (ERB v14)

Abstract

We present Version 14 of the Emergent Resonant Brane (ERB) model—the first iteration featuring a complete theoretical Lagrangian. The model derives the entire Standard Model flavor sector from a single physical asymmetry: the mass ratio of two primary branes ($m_B/m_A = 3/2$).

The core advancement of v14 is the analytical derivation of the topological constant $\gamma = 2\pi$ from the Euler-Lagrange equations of the coupled brane system. While $\gamma$ was empirically determined in previous versions, v14 demonstrates that phase closure ($Q=1$ vortex) is a mathematical necessity for the existence of stable, localized particles. The interaction action $S_{int} = \kappa \cdot (1 - \cos(\varphi_A - \varphi_B))$ dictates stable equilibria that enforce this topological constraint.

Through the Taylor expansion of the interaction potential, the "Whip phase" emerges as the parity-breaking mechanism. Numerical validation yields high-precision agreement with PDG data: a Mean Absolute Error (MAE) for the CKM matrix of $2.32 \times 10^{-5}$ and a Jarlskog invariant of $J = -3.08 \times 10^{-5}$ (PDG: $3.0 \times 10^{-5}$). Furthermore, the model predicts an exact rational ratio of mass exponents $\Omega_{up}/\Omega_{dn} = 5/3$ via the "Isospin Transducer" ($\delta = 1/2$), eliminating the need for empirical mass fitting.

The remaining 32% deviation in mass exponents is identified as a structural gap to be addressed in v15, specifically by deriving the spatial dispersion factor ($\sim 2.5$) for the Whip asymmetry $\alpha_w$ from the underlying Bessel grid geometry. These results suggest that the hierarchical structures of quark mixing and masses are not fundamental constants, but emergent geometric consequences of resonant brane dynamics.