Derivation of Cosmological Expansion from Closure Asymmetry: Linking $\alpha_a$ to $H_0$ in QMU

This paper derives a direct scaling relation between the Aether fine-structure parameter and the Hubble expansion rate within the Aether Physics Model and Quantum Measurement Units. Previous work established that primary constants arise as invariants of first stable bifurcation, and that the electromagnetic fine-structure constant represents a boundary-sector projection of closure asymmetry. This paper extends that framework by expressing the cosmological expansion rate directly in terms of the underlying Aether closure-asymmetry parameter. The central result is \[H = F_q \alpha_a^{4/5}\sqrt{\frac{8\pi}{3}} .\] Here \(F_q=c/\lambda_C\) is the fundamental QMU chronovibrational frequency, \(\alpha_a\) is the Aether fine-structure parameter, and \(8\pi/3\) is derived as the isotropic double-loxodromic closure-field projection factor. The suppression exponent is derived from the geometry of the Aether unit. Eight directed loxodromic closure arcs are distributed across five independent volumetric--chronovibrational closure constraints, giving \[N=\frac{8}{5}.\] Since the Hubble rate depends on the root-mean-square residual closure amplitude, the final scaling contains the exponent \(4/5\): \[\frac{H}{F_q}=\alpha_a^{4/5}\sqrt{\frac{8\pi}{3}} .\] An SI bridge calculation gives \[H_0 = 77.55\ \mathrm{km\,s^{-1}\,Mpc^{-1}},\] using \(c\), the electron Compton wavelength, and the Aether fine-structure parameter. The result links cosmological expansion to the same closure-asymmetry structure that governs subatomic closure, charge differentiation, and Aether-unit stability.