We report a universal geometric identity for charged particles: the product of the classical electron radius r_e and the Schwarzschild radius r_s is fixed by the Planck length and the fine-structure constant: r_e r_s = 2 alpha l_P^2. The mass m completely cancels, indicating that this constraint is independent of the specific particle mass and represents a universal relation between charged matter and spacetime geometry. Two independent paths provide cross-validation: (1) an algebraic path—direct multiplication of the classical definitions; and (2) a dynamical path—Dekker (2014) derived the characteristic radius r_c = l_P sqrt(alpha) from exact solutions of the Einstein—Maxwell equations, which is algebraically equivalent to the identity above. From this identity, a natural length scale r_res = l_P / sqrt(2 alpha) is defined, corresponding to the Compton energy E_res = sqrt(2 alpha) E_P approx 1.47 x 10^18 GeV, which contains no free parameters and lies within a potentially testable window of ultra-high-energy cosmic-ray physics. We also propose an S^3 x R^3 fiber-bundle geometry as a heuristic framework providing a geometric picture for the resonance scale.