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

Emergence of Flavor Mixing, CP Violation, and Mass Hierarchy from a Resonant Brane Model — ERB Model Version 12

We present Version 12 of the Emergent Resonant Brane (ERB) model, a geometric framework in which the CKM matrix, CP violation, and the quark mass hierarchy emerge from resonant brane dynamics without fine-tuning.

The model rests on two primary results. First, the Whip phase Φ(Δr) = φ₀·Δr + w·(1+αw·sgn(Δr))·|Δr|^γ generates CP violation exclusively through its sgn(Δr) term: without it, the interference matrix H is effectively real and J = 0 exactly — verified in four progressive cases. Second, the Isospin Transducer gives the mass hierarchy m_i ~ r_i^Ω(I₃) with Ω(I₃) = 2π·(1+δ·I₃), where α·β = γ = 2π is an exact algebraic identity and Ω_up/Ω_dn = 5/3 follows with zero free parameters.

Version 12 closes the key open question from v11: the Ginzburg-Landau stabilisation used to derive M_scale is proven to be the overdamped limit of V_ERB Klein-Gordon dynamics. The generalised NLS equation (i+γ_damp)·∂_t ψ = −Δψ + ∂V_ERB/∂ψ* reduces to GL exactly as γ_damp → ∞, with α = μ/γ and β = λ/γ determined by V_ERB alone. No new physics is added. The ERB vortex ψ = tanh(r)·exp(iθ) stabilises to a topological energy invariant varying by only 0.3% over a 10× range of core radii, giving M_scale = Λ_QCD·√(2π) = 0.526 GeV (fit: 0.517 GeV, 1.8%).

All results are numerically confirmed: MAE(CKM) = 2.32×10⁻⁵, J = −3.08×10⁻⁵ (PDG: 3.0×10⁻⁵), δ = 1/2 exact (0.000% optimisation cost), δ_CP = 352° (prediction, DUNE/HyperK 2030). All code is provided in the companion notebook ERB_Complete_v12.ipynb.