Geometric Origin of the Hydrogen Lamb Shift from Riemann Zeta Zeros

We present a first-principles derivation of the hydrogen \( 2S_{1/2}-2P_{1/2} \) Lamb shift correction from the spectral geometry of Riemann zeta zeros. The framework reveals an exact scaling factor 366 connecting pure mathematical expressions to physical observables. Starting from the first four non-trivial zeros \( \gamma_1, \gamma_2, \gamma_3, \gamma_4 \) of \( \zeta(1/2 + i\gamma_n) = 0 \), we derive: (1) the Lamb shift correction \( \Delta\nu_{\text{Lamb}} = 7.314 \) kHz, (2) the exact scaling factor \( 366 = 8\pi^2(\gamma_4/\gamma_1)^2 \), and (3) demonstrate that this factor emerges necessarily from the Enneper-Möbius geometric framework underlying fundamental constants. The derivation is mathematically self-contained, numerically exact to computational precision, and provides a unified geometric origin for \( \alpha^{-1} = 137.035999084 \), \( \ell_P = 1.616255\times10^{-35} \) m, and quantum electrodynamic corrections.