Energy-Flow Cosmology: Unified Analysis of BAO, SN Ia, and RSD with a Derived Effective Gravitational Coupling

We present a unified cosmological analysis testing Energy-Flow Cosmology (EFC) against combined baryon acoustic oscillation (BAO), Type Ia supernova (SN Ia), and redshift-space distortion (RSD) observations. The effective gravitational coupling μ(a) = G_eff/G is derived from the EFC field equation rather than phenomenologically fitted. We show that the entropy field S(a) governing μ(a) = 1 + β S(a) produces a late-time enhancement in structure growth while leaving background expansion identical to ΛCDM (by construction, with γ = 0). With one free amplitude parameter (β = 0.16) and transition hyperparameters fixed a priori, EFC achieves χ²_total = 51.1 compared to ΛCDM's χ² = 49.4 (Δχ² = +1.7). The RSD fit is slightly worse but remains compatible within statistical fluctuations. This constitutes a first-pass regime-consistency check, demonstrating that EFC does not introduce internal tension between geometry and growth probes.