The Resonant Brane Unified Field Theory (ERB v17): A Grand Unification of Matter and Cosmology from a Three-to-Two Mechanical Seed

The Emergent Resonant Brane (ERB) model demonstrates that the Standard Model flavour sector —
CKM mixing, CP violation, quark mass hierarchy, and leptonic PMNS mixing — emerges from a single
mechanical seed: mB/mA = 3/2. A two-brane Lagrangian with cosine coupling potential proves gamma =
2pi as the topological ground state (Q=1 vortex boundary condition). A strictly downward five-level
causal chain (L0–L5) derives all structural parameters. The CKM matrix is reproduced with MAE =
4.16e-03 (2 free parameters: k_Q, eps_0); the PMNS matrix follows from an evanescent coupling mode
of the same operator — the Duality Principle. Three previously phenomenological constants (alpha_w,
phi_base, w_amp) are now derived from the reduced mass m_eff = mA*mB/(mA+mB) and the Gaussian
path-integral normalization. The Dark Sector force ratio is identified as alpha = 2pi-1 (99.4% match). The
model makes the falsifiable prediction delta_CP ~ 352 degrees, testable by DUNE (~2030).