RCA Ω 2027 — Phase VIII–XII: Four Falsifiable Predictions from Non-Monotonic Horndeski Braiding, mu-Sigma Separation, and Full Boltzmann Validation

Relativistic Coupling Ansatz (RCA) — v8.2.0 (2026-06-07) The RCA posits a dark energy–dark matter interaction with a non-monotonic gate profile: Q(t) = beta * H(t) * rho_DE(t) * gate(z(t)), where gate(z) = z/(1+z) * exp(-(z/z_cut)^2) peaks at z~0.19 and vanishes at z=0 and z>>1 (CMB-safe by construction). NEW IN v8.2.0: (1) hi_class gravity_model=rca_gate: custom Horndeski gravity model implementing alpha_B(a) = c_B*gate(z(a)) analytically. Gate-matched P(k) k-spread ~6.4% at z<0.3, declining to ~0.7% at z=1. Background verified: alpha_B peak=0.055 at z=0.196, D>0, c_s^2>0. (2) EFTCAMB gate_parametrization_1D (model 20): Fortran source for independent Horndeski verification via EFTCAMB RPH framework. (3) Full 10-page theory paper (LaTeX + PDF) with 3 figures and 4 falsifiable predictions testable by DESI Y3 and Rubin LSST. (4) CAMB QS verification: growth-correction ~0.3-0.7% (scale-independent), consistent with hi_class full Horndeski ~6.4% (scale-dependent). Phase XVIII MCMC: Omega_m=0.294, H0=69.30 km/s/Mpc, delta=0.258 (95% UB<0.716), corr(beta,delta)=-0.052.