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

The ERB Model of Flavor Physics

This preprint introduces the Emergent Resonant Brane (ERB) model. It demonstrates that the complex parameters of the Standard Model (CKM matrix and CP violation) are not arbitrary constants, but geometric necessities of a resonant phase-space.

1. THE CORE PRINCIPLE: THE FLAVOR CLOCK

The model identifies a fundamental topological anchor for matter stability:

Phase Closure: gamma = 2*pi (The "Flavor Clock")

Stability is achieved only when the phase vortex closes perfectly. This 2*pi-locking removes the need for manual phase-fitting and dictates the mixing behavior of fermion generations.

2. GEOMETRIC ARCHITECTURE

• Generational Radii: Mapped to the zeros of spherical Bessel functions j0(x), representing discrete resonance nodes on the brane.

• Mass as Optics: Particle masses act as "Phase Lenses", governing the local density of the resonant field.

• CP Violation: Derived as the physical area of the generational triangle.

Formula: J = N * Area

(Where N is analytically derived from Gaussian wave-packet normalization, not from experimental fitting).

3. PERFORMANCE & PREDICTIONS

The model is NOT fine-tuned. Sensitivity scans (included in the supplementary notebook) prove that the hierarchy remains stable even under +/- 20% parameter variation.

Precision Results:

• CKM Accuracy: MAE approx. 0.000023

• PMNS Angles: Deviations < 0.4 degrees

The "Neutrino Bet" (Falsifiable Prediction):

• Target: Leptonic CP Phase (delta_CP)

• Predicted Value: 352 degrees

• Status: Testable by upcoming DUNE / Hyper-K experiments.