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

This paper presents Version 8 of the Emergent Resonant Brane (ERB) model, a novel framework that derives particle masses and mixing hierarchies from the geometric resonance of a pulsating membrane. The central advancement is the introduction of the Isospin Master Equation, which governs the symmetry breaking between up-type and down-type quarks. We demonstrate that the isospin load parameter $\delta$ reaches its absolute error minimum at exactly 1/2, identifying it as a fundamental geometric eigenvalue of the lattice rather than a free fit parameter.

The model establishes an Emergent Parameter Hierarchy where the complex CKM matrix and quark mass scales arise from a reduced set of anchored constants. Key findings include a high-precision correlation between the model’s base tension and the strong coupling constant, as well as a predictive link between the ERB energy scale and the non-perturbative QCD threshold.

While the primary isospin symmetry is proven to be structurally stable (0.000% loss penalty), a critical audit reveals a high sensitivity in the secondary coupling ratios to minimal variations in base tension. We identify this "instability cliff" and the existence of bimodal energy minima as evidence of a dynamic "Whip Effect"—a kinetic correction caused by vortex rotation within the brane. These results suggest that while the core geometry is fixed, the observed flavor hierarchy is a dynamic steady-state, offering a new pathway toward a self-consistent, zero-infinity theory of particle physics.