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 \(S²\!×\!Tₗₒₓ\) with fixed flux \(∫ωₛₜ=16π²\). No existing theory employs this bipartite, distributed-charge geometry. A ledger-based unification principle: \[ A_u\,curl={F_q}²{λ_C}²,\]linking 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 \(S²\) 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 \(χ_x\), 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: \[ β_0={1}{16π²},\]controlling polarization transport in Aether modes; there is no analogue in the Standard Model or in GR. A geometric derivation of the proton mass ratio: \[ m_p/m_e=6π⁵,\]arising 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 \(A_u\,curl\), and \({F_q}²{λ_C}²\) forming the falsifiable closure\[ C={A_u\,curl}{{F_q}²{λ_C}²}-1.\] These features constitute a genuinely new unification program: geometric, topological, and metrological, with no free scales and no reliance on SI or empirical fitting.