A Compact-Fiber Structural Prediction of the Low-Energy Electromagnetic Coupling develops a compact-fiber structural prediction for the low-energy electromagnetic bridge coupling. The paper derives an inverse bridge capacity from the compact-fiber carrier, radiative/vibrational bridge-placement readout, cover-mediated feedback, self-consistent transport sharing, and the first closed return of the admitted feedback. The resulting quartic equation has positive root x_fiber = 137.0359991771859..., so that alpha_F = 1/x_fiber. The measured fine-structure constant is not used as an algebraic input, and no continuously adjusted coefficient appears in the bridge equation. The identification of alpha_F with the low-energy electromagnetic coupling is made by physical role: leading atomic binding reads the material/radiative bridge through two vertices and therefore carries an alpha_F^2 dependence, matching the role of alpha^2 in the Hartree/Rydberg scale. The numerical comparison with the empirical fine-structure constant is presented as a consistency check, not as an error-budget closure. Route-specific metrological extraction, QED vertex expansion, electrical-standard readout, and broader second-observable closure remain downstream work.