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 (mB/mA = 3/2). The core advancement of v14 is the analytical derivation of the topological constant = 2 from the Euler-Lagrange equations of the coupled brane system. While 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 S₈₍ₓ = (1 - (A - 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 10^-5 and a Jarlskog invariant of J = -3. 08 10^-5 (PDG: 3. 0 10^-5). Furthermore, the model predicts an exact rational ratio of mass exponents ₔ₏/₃₍ = 5/3 via the "Isospin Transducer" (= 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 (2. 5) for the Whip asymmetry 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.