Energy-Flow Cosmology: An Effective Phenomenological Law for Gravitational Response in Structure-Dominated Regimes

Energy-Flow Cosmology (EFC) v4.1 presents an effective phenomenological law describing gravitational response in structure-dominated regimes (galaxies and galaxy-scale lensing). The model introduces a fixed response function [ g_{\text{obs}} = g_{\text{bar}} , R(g_{\text{bar}}/a_0) ] with a frozen acceleration scale (a_0 = 1.2 \times 10^{-10},\mathrm{m,s^{-2}}) and no tunable parameters per system. The formulation is explicitly regime-limited to late-time, non-linear structure (L2/L3) and does not modify local microphysics, general relativity in the Solar System, or early-universe cosmology.The framework is defined as an effective theory with pre-specified fail conditions, preventing post hoc adjustment. Validation against the SPARC rotation curve sample yields a reduced (\chi^2_\nu \approx 0.76) with minimal systematic bias, while galaxy-scale strong-lensing Einstein-radius ratios are consistent within observational uncertainties. Cluster-scale systems remain an open problem and define the primary domain for potential falsification or extension.This work establishes a regime-decoupled, empirically testable gravitational phenomenology independent of assumptions about dark matter particle content or modifications to fundamental constants