Electron EDM in QMU: CP-odd Square-Charge Dipole from Aether-Unit Holonomy

Electron EDM in QMU: CP-odd Square-Charge Dipole from Aether-Unit Holonomy This paper reformulates the electron "EDM" observable in the Aether Physics Model (APM) using Quantum Measurement Units (QMU), where the primitive charge dimension is square-charge and electrostatic potential is reciprocal capacitance. In this framework, the natural EDM-like observable is not a linear-charge dipole \(d_e\), but a CP-odd square-charge first moment of a distributed square-charge density. QMU potential and driver. Electrostatic potential is defined as reciprocal capacitance,\[Φ_Q := 1/C,\]and the electrostatic driver is its gradient,\[G := ∇ Φ_Q.\] Square-charge EDM observable and ledger-closed coupling. Let \(ρe^2( r)\) be the signed distributed square-charge density (magnetic basis). The square-charge dipole vector is the first moment\[De^2 := ∫ ρe^2( r)\, r\,d^3r.\]The ledger-closed interaction energy with external electrostatic structure is\[Δ U = -\,De^2·∇Φ_Q,\]which replaces the legacy coupling \(- d· E\) by changing the driver to \(∇Φ_Q\) and the dipole to a square-charge moment. Holonomy origin and CP-odd invariant. The Aether-unit two-sphere chronovibration supports a 5D closed action whose 4D forward-time projection can exhibit holonomy. A CP-odd defect one-form \(δωCP\) is defined from the 5D-to-4D connection mismatch, and the dimensionless CP-holonomy invariant is\[ΔCP := 1/2π∮γ_+δωCP,\]where \(γ_+\) is the forward-time leg of the chronovibrational cycle. The square-charge dipole is parameterized by\[De^2 = {e_emax}²\,λ_C\,ΔCP\, ŝ,\]with \({e_emax}²\) the distributed square-charge unit in the magnetic basis, \(λ_C\) the electron Compton length, and \( ŝ\) the spin direction. Domain taxonomy, seams, and obstruction index. A minimal octant-domain cover of the electron sheet is introduced, with antipodal pairing and a loxodromic seam-crossing loop. Under a local-exactness hypothesis on each octant, the CP-odd holonomy reduces to a seam-sum cocycle. Quantized seam jumps are written as multiples of the octant increment \(π/4\), producing an integer obstruction index \(τCP∈ Z\) and a discrete spectrum\[ΔCP = αᵖ\,{τCP}{8},\]where \(α\) is the fine structure constant and \(p≥ 1\) is the leading order at which the CP-odd defect survives seam pairing. Metrology and experimental bridge. An action scale is defined in QMU as\[h_e := m_e\,{λ_C}²\,F_q,\]so the measurable frequency shift is \(Δ f=Δ U/h_e\). In EDM platforms, the relevant driver is the internal reciprocal-capacitance gradient component\[Geff := n̂·∇Φ_Q,\]leading to a spin-reversal splitting proportional to \(|ΔCP|\,|Geff|\). State-of-the-art null bounds from electron-EDM experiments (e.g. ACME) are interpreted here as constraints on admissible microstate classes and packing-weighted populations rather than on an intrinsic point-parameter. Next-step program and parameter-free prediction target. With canonical octant labeling and the loxodromic seam loop fixed, Milestone M1 is to compute the leading CP-odd chirality connection \(ω⁽¹⁾χ\) and the associated seam integers \(mᵢⱼ\), and to determine whether \(p=1\) (non-canceling order-\(α\) seam cocycle) or \(p≥ 2\) (order-\(α\) cancellation). If the explicit summation yields \(p=1\) and the minimal obstruction \(τCP=1\), then the framework makes a parameter-free magnitude prediction in native QMU units:\[|De^2| = {e_emax}²\,λ_C\,α/8.\]For appendix-only SI-bridge purposes, the charge-basis relation\[e² = 8πα\,{e_emax}²\]connects the square-charge unit to the elementary-charge-squared scale used in legacy reporting.