Geometric Origins of Atomic Spectra and the Fine-Structure Constant in the Ω-Model

The Ω-Model presents a unified framework in which gravity, electromagnetism, and quantum behavior emerge from dual-frequency geometric curvature on a horn torustopology. In this work, we develop a refined formulation of the model to predict atomic spectral lines with high precision, introducing a geometrically defined effectivenuclear charge Zgeo that accounts for internal torsional shielding. A generalized scaling law for the torsional frequency enables the accurate reproduction of atomic transition energies across a wide range of elements. By expressing the fine-structure constant α as the curvature-induced ratio γ/f1, the model naturally explains both the observed constancy of α and its potential variation in high-curvature regimes, including muonic atoms and black hole environments. These findings establish the Ω-Model as a predictive geometric framework that bridges atomic physics and general relativistic curvature, offering insight into the possible running of physical constants in torsion-dense spacetime.