This manuscript identifies the Fine-Structure Constant (\bm{\alpha \approx 1/137.035}) as a geometric consequence of the 1.22 Universal Scaling Invariant. While the "Vacuum Catastrophe" (\bm{10^{120}}) represents the scaling of energy density across the cosmos, this work demonstrates that the electromagnetic coupling constant is the localized manifestation of the same 0.22 Connectivity Tax. By applying the Scales Invariant (\bm{\frac{10^{120}}{10^{137}} \approx 10^{-17}}), we provide a unified mathematical bridge between Quantum Electrodynamics (QED) and Cosmological Expansion (\bm{H_0}). This serves as the definitive "Micro-scale" validation of the 1.22 framework, proving that the geometric price of network connectivity is a fundamental constant of nature across all scales. Note on Access: This document is currently under restricted access to maintain priority art during the institutional verification phase. Related work and registration data are indexed under DOI 10.17605/OSF.IO/9VQ8K.