Unified Field Sector of the Aether Physics Model: Lagrangian Formulation, Equations of Motion, and Metrological Ledger Tests (QMU)

Although many unification programs exist in modern physics (GR, QED/QCD, SMEFT, Einstein--Aether theories, Kaluza--Klein models, and string frameworks), none contain the geometric, ledger-based structures developed in this work. This paper introduces several new advances not present in mainstream theories: A new geometric unit of physics: the double-loxodromic Aether cell \ (S^2\!\!T₋₎ₗ\) with fixed flux \ (ₒₓ=16^2\). No existing theory employs this bipartite, distributed-charge geometry. A ledger-based unification principle: \ Aᵤ\, curl=Fq^2C^2, magnetic stiffness, square-charge circulation, and Compton-scale kinematics. No standard theory equates these invariants or interprets them as topological constants. Two-geometry representation of charge: electrostatic charge on \ (S^2\) and magnetic/strong charge on a loxodromic ribbon. This decomposition does not exist in U (1) or SU (3). A new weak interaction: the es--mag overlap scalar \ (ₓ\), whose equation of motion generates the holonomy factor \ (H (Z) \). This geometric weak channel is unlike the SU (2) electroweak theory. A parameter-free birefringent invariant: \ ₀=116^{2}, polarization transport in Aether modes; there is no analogue in the Standard Model or in GR. A geometric derivation of the proton mass ratio: \ mₚmₑ=6^5, from the loxodromic packing constant. No mainstream framework provides an analytic expression for this ratio. A unified action with no empirical coefficients: all sector Lagrangians derive from the Aether cell geometry and QMU ledger identities. A new metrological program: independent realizations of \ (Aᵤ\, curl\), and \ (Fq^2C^2\) forming the falsifiable closure\ C=Aᵤ\, curl{Fq^2C^2}-1. \ These features constitute a genuinely new unification program: geometric, topological, and metrological, with no free scales and no reliance on SI or empirical fitting.