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

This paper presents version 10 of the Emergent Resonant Brane (ERB) model, which defines elementary particles as resonant oscillation nodes within an elastic vacuum brane (tension $\epsilon_0 \approx 0.1099$). The central element of this framework is the identification of a fundamental 7.02% geometric asymmetry ("gap") between the up- and down-quark sectors, acting as the mechanical driver for global phase synchronization.

We mathematically derive that the system enforces a topological phase-lock at $\gamma = 2\pi$, enabling the definition of a stable 4-pi fermion state. We demonstrate the existence of an algebraic coupling between the dispersion exponent $\beta$ of the whip-core and the mass-scaling exponent $\alpha$ in the form of $\alpha \cdot \beta = \gamma = 2\pi$. This relation allows for the direct calculation of the fine-structure constant $\alpha_{em}$ as a mechanical amplitude ratio with 99.9% accuracy relative to experimental values.

Furthermore, the observed hierarchy of the six quark masses—including the extreme scaling factor of $8 \cdot 10^4$ between the up and top quarks—is attributed to an exponential $r^{2\pi}$ dependence. While the topological structure is strictly dictated by $2\pi$, we identify a remaining numerical divergence as the effect of a transducer operator $T$. This operator mediates between the "naked" Bessel geometry and the effective inertia of the brane. The consistency of the model is validated through a simultaneous fit of both isospin sectors, where the "honest limit" of the theory is discussed as a necessary consequence of vacuum warping effects.