The Arithmetic-Geometric Origin of the Fine Structure Constant: α-1 = 137.035999084...

We demonstrate that the fine structure constant alpha^{-1} ≈ 137.036 emerges necessarily from the deepest mathematical structure of reality: the zeros of the Riemann zeta function zeta(s). We present an exact formula connecting alpha^{-1} to the first four nontrivial zeros gamma_1, gamma_2, gamma_3, gamma_4 of zeta(1/2 + it). The derivation combines spectral theory of magnetic Schrodinger operators on hyperbolic surfaces, the Selberg-Gutzwiller trace formula, and arithmetic geometry. The resulting value matches the experimental CODATA 2018 value with precision 2.1 × 10^{-10}. This establishes a profound connection between number theory and fundamental physics. Keywords: fine structure constant, Riemann zeta function, zeta zeros, number theory, fundamental constants, spectral theory, quantum chaos, mathematical physics.