We present a consolidated rheological framework for the Cosmological Dissipative Residual (CDR), a single effective medium proposed to underlie both dark-energy—like and dark-matter— like phenomenology. Building on previous work in the series, we formulate a covariant constitutive relation for the residual’s anisotropic stress in which the effective viscosity depends on local acceleration and shear. In the non relativistic thin-disk limit this relation reduces to an estimator for the residual contribution to the radial acceleration, ∆gR ≈ fgeom ηeff σ ρres R. with a geometric factor fgeom ≈ 3.We confront the framework with rotation-curve data for 175 SPARC galaxies. The residual contribution is found to be selectively activated: in the low-acceleration regime97.5% of radial points show ∆g > 0, while in the high-acceleration regime the median ∆g is consistent with zero. From the activated regime we obtain a median effective viscosity ηeff ≃ 3.8×10−2 kg m−1 s −1 and a characteristic transition scale atrans ∼ (1−2)×10−10 m s−2, compatible in order of magnitude with cH0/2π. The results support the hypothesis that a single cosmologically motivated residual medium can develop a dark-matter—like response under local dynamical conditions, while remaining consistent with a dark-energy—like behaviour on large scales. A fully quantitative reproduction of galactic rotation curves is left for future work.