Unified Field Formulation Using Compactified Temporal Curvature: The Ω-Model

We present a unified and reformulated version of the Ω-Model, grounded entirely in geometric first principles. The model integrates a compactified temporal curvature dimension, enabling atomic and macroscopic systems to be described via dual-frequency geometry without empirical assumptions. The imaginary component of the torsional frequency f2 is reinterpreted as arising from compactified poloidal time t2, yielding natural derivations for the hydrogenic 13.6 eV energy, fine-structure, relativistic corrections, spin-orbit coupling, Lamb shift, and the anomalous magnetic moment—all from curvature recursion. This formulation allows full cross-scale unification of atomic, planetary, and galactic structure through the same torsional invariant.