Atomic Physics in the Ω-Model: A Geometric Theory of Quantum Spectra and Curvature

The Ω-Model provides a geometric unification of gravity, electromagnetism, and quantum phenomena by encoding matter interactions as dual-frequency curvature on a horn torus topology. This paper presents a mathematically rigorous derivation of the core atomic predictions of the model, including spectral line quantization and anomalous magnetic moment corrections. Using a dual-frequency force law and a curvature-based invariant, the Ω-Model reproduces observed hydrogenic transitions with high precision and offers a predictive framework for curvature-induced quantum effects. All formulas presented are derived from geometric first principles and matched against observed atomic data.