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 13 We present Version 13 of the Emergent Resonant Brane (ERB) model. The central advance is the identification of the relativistic origin of the two fundamental ERB parameters. δ = 1/2 as brane mass ratio. The lattice tension of the two primary branes satisfies εB/εA = mB/mA at fixed oscillation frequency. Since εB/εA = 3/2, the primary branes have mass ratio mB/mA = 3/2, and δ = (mB − mA) /mA = 1/2 exactly. The Isospin Master Equation is not a quantum postulate imposed from outside — it is a material property of the vacuum medium. The asymmetry was always there, at the source. γ = 2π as common denominator. Two branes with mass ratio 3/2 can only interfere stably when their phases close on a common period. The ground state (Q = 1, single vortex) corresponds to one full 2π rotation — the smallest common phase of two oscillators with ratio 3/2. γ = 2π is necessary, not empirical. α = γ − 1 as time-dilation exponent. Each generation rotates with orbital velocity vᵢ = ω·rᵢ. In the ultrarelativistic limit the Lorentz factor γᵢ ~ rᵢ, and the rest mass scales as m₀ᵢ ~ rᵢ^ (α−1), giving mᵢ ~ rᵢ^α — exactly the ERB log-ladder formula. The candidate α = 2π − 1 ≈ 5. 28 (2. 9% from measured 5. 13) means one full Flavor Clock rotation accumulates exactly this time dilation. Analytical proof is the next open question. All previous results are retained: MAE (CKM) = 2. 32×10⁻⁵, J = −3. 08×10⁻⁵ (PDG: 3. 0×10⁻⁵), δ = 1/2 exact (0. 000% cost), Ωᵤp/Ωdn = 5/3 (zero free parameters), Mₛcale = ΛQCD·√ (2π) topologically confirmed, GL dynamics proven as overdamped limit of VERB (v12). The complete derivation chain from v4 to v13 is provided in the companion notebook ERBCompleteᵥ13. ipynb. The Standard Model flavour sector reduces to one number: mB/mA = 3/2. Everything else is emergent.