Unified Curvature Dynamics from Atomic to Galactic Scales: A Comprehensive Framework Based on the Ω-Model

This thesis presents the Ω-Model, a unified geometric framework integrating gravitational, electromagnetic, and inertial phenomena using dual-frequency spacetime curvature and toroidal geometry. We derive the generalized Ω-invariant and demonstrate predictions for planetary precession, lunar nutation, flat galactic rotation curves, relativistic binaries, and a dimensional constant linking curvature-induced acceleration to Newtonian gravity, entirely from first principles.