Density-Weighted Closure Eigenmodes: A Measure-Theoretic Derivation of Cosmological Scaling in QMU

This work develops a density-gradient operator derivation of cosmological scaling within the Aether Physics Model (APM) using Quantum Measurement Units (QMU). The paper constructs a density-weighted closure operator for the closure field \(\Psi(x,t)\), with the local Aether density \(\rho_A(x)\) acting as the weighting function for the closure medium. Linearization about a stable closure state gives a self-adjoint density-weighted core operator, while loxodromic transport introduces directed closure dynamics. Reducing the operator locally along closed loxodromic paths yields a periodic eigenvalue spectrum,\[\lambda_n \sim n^2.\]The result shows that the eigenvalue spacing determines the allowed closure modes, but does not itself produce the cosmological exponent. The fractional exponent arises instead from the density-weighted closure measure. The Aether unit contains eight directed loxodromic transport arcs constrained by five independent volumetric--chronovibrational closure conditions, giving\[D_{\mathrm{cl}}=\frac{8}{5}.\] The closure imbalance therefore scales as\[\Omega_{\mathrm{cl}}=\alpha_a^{8/5},\]where \(\alpha_a\) is the Aether fine-structure parameter. The paper derives \(\alpha_a\) from QMU charge relations,\[\alpha_a=\frac{e^2}{8\pi {e_a}^2},\]with \(e_a^2\) determined by the maximum Aether magnetic charge. Numerically,\[\alpha_a \approx 2.0345684859\times 10^{-48}.\] Combining the closure-measure exponent with the isotropic volumetric closure factor\[\Gamma_{\mathrm{iso}}=\frac{8\pi}{3}\]gives the fully determined cosmological scaling relation\[H=F_q\alpha_a^{4/5}\sqrt{\frac{8\pi}{3}}.\] Using\[F_q \approx 1.235589965\times 10^{20}\ \mathrm{s^{-1}},\]the predicted expansion rate is\[H\approx 2.5131\times 10^{-18}\ \mathrm{s^{-1}},\]or\[H\approx 77.55\ \mathrm{km\,s^{-1}\,Mpc^{-1}}.\] This result connects Aether density gradients, closure-field eigenmodes, QMU charge structure, and cosmological expansion in a single measure-theoretic framework.