This work presents the Flux–Shadow Gravity Model, a relativistic framework that removes the need for particle dark matter while preserving dark energy as the driver of cosmic expansion. The model is built from two general-relativistic, geometrically grounded components:(1) a cosmic expansion–flux term derived from the FLRW background expansion rate H(t), and(2) a baryon-linked shadow term generated by geometry-dependent obstruction of that expansion flow.Gravitational acceleration arises as a drift response to anisotropic flux availability rather than from unseen particle mass. The formulation satisfies all major theoretical consistency conditions—including the Poisson equation, Friedmann and Raychaudhuri equations, Maxwell-type constraints, Jeans stability, and energy–momentum conservation. It recovers exact Newtonian gravity for spherical systems, reproduces flat galactic rotation curves, explains lensing enhancements, and yields a logarithmic effective mass profile without invoking non-baryonic matter. The model includes covariant shadow dynamics, a variational principle, and a constraint-sector nonlocal kernel whose behavior follows directly from FLRW expansion obstruction. It provides late-time and linear-regime behavior consistent with CMB acoustic-peak formation, as verified numerically using a Boltzmann code, and offers a geometric interpretation of relativistic effects such as time dilation and length contraction. The framework embeds smoothly into standard cosmology while offering a geometry-driven mechanism for halo formation and gravitational amplification tied directly to baryonic anisotropy. Numerical tests demonstrate Solar-System consistency at the 10⁻⁹ level, reproduction of the baryonic Tully–Fisher relation, and multi-galaxy rotation-curve fits using SPARC data, yielding realistic flat outer rotation profiles without invoking any dark-matter halos. Individual galaxy analyses, including representative cases such as NGC 2403, illustrate the mechanism in detail. This deposition invites the scientific community to explore independent numerical and cosmological tests—such as transfer-function evaluation, perturbation growth, weak-lensing predictions, and extended Boltzmann-code simulations—to further assess the model’s viability.