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

The Emergent Resonant Brane (ERB) model derives the CKM matrix, CP violation, and gauge symmetries U(1)×SU(2)×SU(3) from resonant brane geometry — without fine-tuning.

Three Bessel-quantized generational radii and a single topological fixed point (γ = 2π) generate all flavor structure. Key results: MAE(CKM) = 2.32×10⁻⁵, Jarlskog invariant J = −3.08×10⁻⁵ (PDG: 3.0×10⁻⁵), PMNS angles reproduced to Δθ < 0.4°. CP violation is a geometric necessity — it vanishes only if three generations become collinear, which Bessel quantization forbids.

Version 4 adds: (i) a predictive chain PDG masses → radii → CKM with 1 free parameter (MAE = 3.3×10⁻³), refuting the circularity objection; (ii) an effective Lagrangian with mass matrix analytically derived from a topological overlap integral at γ = 2π; (iii) a scalar potential V = λ(|Φ|²−v²)² + κ(1−cos γ) with numerically verified minimum at exactly γ = 2π; (iv) emergent scale Λ_ERB ≈ Λ_QCD · √(2π), anchoring the model at the QCD confinement threshold.

Falsifiable prediction: δ_CP(PMNS) = 352°, testable by DUNE and HyperK.

Supplementary code: ERB_N_Stability_v4.ipynb, ERB_Unified.ipynb (Google Colab, NumPy/SciPy only).