Resolution of the Muon (g− 2) Anomaly via Nonlinear Vacuum Elastodynamics: Substrate Shear Impedance Saturation and the Mechanical Back-Reaction of Lepton Solitons

High-precision measurements of the anomalous magnetic dipole moment of the muon, aµ = (gµ− 2)/2, conducted at Brookhaven National Laboratory (E821) and the Fermilab Muon g− 2 experiment (E989), continue to display an unresolved tension (> 4σ− 5σ) with the dispersive theoretical consensus of the Standard Model. Rather than postulat- ing unobserved supersymmetric partners, leptoquarks, or dark photons, we demon- strate that this anomaly arises naturally from the nonlinear constitutive mechanics of an elastically pre-stressed vacuum continuum. In our framework, leptons are not struc- tureless point charges, but topologically localized strain solitons (toroidal vortex rings) stabilized by the background hydrostatic holding pressure P0. Because the muon’s mass-energy density is (mµ/me)3 ≈ 8.84 × 106 times greater than that of the electron, its core elastic strain approaches the nonlinear shear saturation regime of the sub- strate. By expanding the vacuum’s shear modulus Gv and characteristic impedance Z(ω) to include second-order strain invariants, we derive an exact elastodynamic back- reaction torque acting upon the circulating soliton. This mechanical drag produces a positive shift ∆aelasto µ ∝ (mµ/me)2(Psoliton/PSchwinger), matching the observed empirical surplus ∆aµ ≈ (24.9 ± 4.8) × 10−10 without ad-hoc parameters or virtual particle infini- ties.