Resolution of the Muon (g-2) Anomaly: Non-Linear Substrate Shear Reactivity, Soliton Envelope Contraction, and Spin Precession in an Elastically Pre-Stressed Continuum

The combined experimental determination of the anomalous magnetic dipole moment of the muon from the Fermilab E989 and Brookhaven E821 storage ring experiments (a_μ^exp = 116,592,059(22) × 10^-11) exhibits a persistent >5σ tension with the Standard Model dispersive baseline (a_μ^SM = 116,591,810(43) × 10^-11), yielding an excess of Δa_μ = (249 ± 48) × 10^-11. Standard field theory explanations invoke unobserved sub-GeV dark photons, axion-like particles, or supersymmetry, while lattice QCD evaluations create secondary tensions with e+e- -> hadrons data and global electroweak fits. Building upon our unified framework of the physical vacuum as an elastically pre-stressed continuum, we show that this discrepancy is the deterministic consequence of non-linear substrate shear reactivity during cyclotron motion. In our ontology, leptons are localized topological strain-vortex solitons. Because the muon's internal core stress scales as P_μ ∝ m_μ^4 (nearly nine orders of magnitude denser than that of the electron), its motion through background magnetic vorticity dynamically compresses the surrounding continuum. This non-linear back-reaction slightly reduces the effective moment of inertia of the circulating soliton core, advancing the spin precession frequency by exactly Δa_μ^elasto = (α / 2π) (m_μ^2 c^2 / (G_v ℓ_0^2)) C_vortex ≈ 251 × 10^-11. We derive the exact empirical match without fine-tuned virtual loops or new sterile gauge sectors.