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

Abstract

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 \(S^{2}\!\times\!\mathbb{T}_{\mathrm{lox}}\) with fixed flux \(\int\omega_{st}=16\pi^{2}\). No existing theory employs this bipartite, distributed-charge geometry. A ledger-based unification principle: \[ A_u\,\mathrm{curl}={F_q}^{2}{\lambda_C}^{2},\]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 \(S^{2}\) 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 \(\chi_x\), 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: \[ \beta_0=\frac{1}{16\pi^{2}},\]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: \[ \frac{m_p}{m_e}=6\pi^{5},\]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 \(A_u\,\mathrm{curl}\), and \({F_q}^{2}{\lambda_C}^{2}\) forming the falsifiable closure\[ \mathcal{C}=\frac{A_u\,\mathrm{curl}}{{F_q}^{2}{\lambda_C}^{2}}-1.\] These features constitute a genuinely new unification program: geometric, topological, and metrological, with no free scales and no reliance on SI or empirical fitting.