Complete Geometric Unification of Hydrogen Spectrum: From Fine Structure to Hyperfine Splitting in eH and μH

Precision atomic spectroscopy has historically tested fundamental physics, yet current models rely on a patchwork of theories—Dirac equation for Fine Structure and QED for the Lamb Shift—requiring empirical constants and probabilistic methods. We introduce \textbf{Discrete Continuity Theory of Super-Asymmetry (DCTSA)}, a unified framework in which all spectral corrections emerge deterministically from \textbf{spacetime geometry and topology}. The theory models the proton using two geometric parameters: the \textbf{Wobble Ratio ($\delta$)} and the \textbf{Relativistic Factor ($\gamma$)}, which are shown sufficient to derive the Fine-Structure Constant ($\alpha$), the Proton g-Factor ($g_p$), and all higher-order energy corrections of Hydrogen. Electrons are described as topological oscillations sustained by the underlying continuity field, producing the precise \textbf{volume perturbations} required for the Lamb Shift. This work demonstrates \textbf{complete geometric closure} of the Hydrogen spectrum, providing non-empirical, closed-form expressions for fundamental constants and energy levels, while reducing reliance on probabilistic field interactions. The framework lays the foundation for extending deterministic derivations to hyperfine structures and anomalous magnetic moments in future work. The theory deterministically derives the proton Zemach radius $(R_Z \approx 1.02 fm)$ and provides a simple geometric expression that reproduces the net effect of complex QED structure corrections to muonic hydrogen hyperfine splitting. The theory's geometric structural factor $\mathcal{C}{\text{Struct}}^{\text{DCTSA}} = 1 - \delta{\text{core}}\Gamma_{\text{damping}}/5$ precisely matches the net effect of complex QED proton structure corrections, suggesting that deterministic geometry may underlie the mathematical complexity of quantum field theory.