Dynamic Derivation of Cosmological Scaling from Closure Field Eigenmodes: From Loxodromic Geometry to Ψ-Field Transport in QMU

This work provides a dynamical derivation of cosmological expansion within the Aether Physics Model (APM) using Quantum Measurement Units (QMU). Previous results established that the Hubble parameter follows the scaling relation = Fq \, ₐ^4/5 H, Fq is the quantum frequency, ₐ is the Aether fine-structure parameter, and H is a dimensionless geometric factor. The exponent 4/5 arises from the intrinsic geometry of the Aether unit. In the present work, this scaling is derived from first principles by constructing a closure-field operator governing the propagation of closure imbalance. The closure field (x, t) represents the local degree of Aether completion and is described by a variational field theory with dimensionless QMU coordinates. Solving the closure-field eigenvalue problem along loxodromic transport paths yields a standard closed-loop spectrum\ₙ n², that the eigenvalue structure alone does not generate the fractional scaling exponent. The exponent instead emerges from a geometric closure measure defined over the Aether unit. The transport structure consists of eight orientation-resolved loxodromic channels distributed across five independent volumetric--chronovibrational constraints, producing a geometric exponent₂₋ = 85. \ This leads to a closure-density scaling\₂₋ = ₐ^8/5, determines the magnitude of cosmological expansion. The Hubble parameter follows from the root-mean-square closure imbalance, = Fq H \, ₂₋. \ Numerical evaluation yields\H 83, that² = Fq² ₐ^8/5 H. \ This expression reproduces the observed expansion rate, 2. 51 10^-18\ s^-1 (77. 5\ km\, s^-1\, Mpc^{-1}), establishes a direct correspondence between closure geometry and cosmological dynamics. The factor H acts as a geometric density parameter of Aether expansion, mirroring the 8/3 coefficient in Friedmann-type cosmology, while the source term is supplied by the dimensionless closure-density ₂₋. The result provides a unified framework in which geometry, field dynamics, and cosmological expansion arise from closure imbalance within the Aether-unit structure.