The Structural Incompleteness of QED - A Complementation that QED Already Required

We present a framework that complements light quantum electrodynamics (QED) through discrete algebraic conditions imposed on its fundamental parameters. The electron mass $m_e$ and the fine-structure constant $\alpha$ are expressed in terms of powers of the golden ratio $\phi$, with integer exponents subject to renormalization group consistency constraints. We show that the cosmological exponent $\beta = \phi^{-1}$ emerges from stability and algebraic closure conditions. The framework is computationally falsifiable: if no combination of integer exponents reproduces the experimental values within measured precision, the proposal is discarded. A concrete solution reproduces $m_e = 0.511$ MeV and $\alpha^{-1} = 137.036$ without continuous adjustable parameters, suggesting an underlying structural coherence in QED.