Elastic Response of Spacetime Geometry and Effective Gravitational Phenomena at Galactic and Cosmological Scales

We present a reformulation, from first principles, of General Relativity, without introducing new entities beyond the geometry of spacetime itself, from which we derive observational consequences in galactic and cosmological regimes. In the context of General Relativity treated as a discrete quantum system (RGTQ), gravitational phenomena commonly attributed to dark matter and dark energy emerge from the elastic response of spacetime itself, governed by a single geometric constant. The resulting theory reproduces flat galactic rotation curves, the baryonic Tully--Fisher relation, and late-time cosmic acceleration, without free parameters or additional fields.