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 \(Ψ(x,t)\), with the local Aether density \(ρ_A(x)\) 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,\[λ_n ~ n^2.\]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\[Dcl=8/5.\] The closure imbalance therefore scales as\[Ωcl=α_a8/5,\]where \(α_a\) is the Aether fine-structure parameter. The paper derives \(α_a\) from QMU charge relations,\[α_a={e^2}{8π {e_a}^2},\]with \(e_a^2\) determined by the maximum Aether magnetic charge. Numerically,\[α_a ≈ 2.0345684859× 10⁻⁴⁸.\] Combining the closure-measure exponent with the isotropic volumetric closure factor\[Γᵢₛₒ=8π/3\]gives the fully determined cosmological scaling relation\[H=F_qα_a4/5√8π/3.\] Using\[F_q ≈ 1.235589965× 10²⁰\ {s⁻¹},\]the predicted expansion rate is\[H≈ 2.5131× 10⁻¹⁸\ {s⁻¹},\]or\[H≈ 77.55\ {km\,s⁻¹\,Mpc⁻¹}.\] This result connects Aether density gradients, closure-field eigenmodes, QMU charge structure, and cosmological expansion in a single measure-theoretic framework.