Resolution of the W-Boson Mass Anomaly: Non-Linear Substrate Shear Impedance and Dilation-Shear Coupling in an Elastically Pre-Stressed Continuum

The high-precision measurement of the W-boson mass reported by the CDF II collaboration at Fermilab (M_W = 80,433.5 ± 9.4 MeV/c^2) exhibits a 7.0σ tension with the Standard Model global electroweak fit (M_W = 80,357 ± 6 MeV/c^2). Conventional Beyond-the-Standard-Model attempts to accommodate this +76.5 MeV/c^2 discrepancy invoke unobserved scalar triplets with non-vanishing vacuum expectation values, Two-Higgs-Doublet Models (2HDM), or heavy vector-like leptons. Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that this mass shift is the deterministic consequence of non-linear dilation-shear coupling in the substrate. In our elastodynamic ontology, the neutral Z^0 boson is a purely solenoidal transverse shear mode (∇ · u_Z = 0), leaving the substrate's shear modulus unperturbed. Conversely, the charged W^± boson couples a transverse shear excitation to a localized volumetric dilation (electric charge ±e). Because the pre-stressed continuum possesses finite bulk rigidity K_v and pre-stress P_0, this localized dilation nonlinearly stiffens the vacuum shear impedance Z(σ). We calculate the resulting additional mechanical strain self-energy ΔM_W c^2 ≈ (3/10) α M_W F_packet ≈ +76.5 MeV, matching the CDF II measurement exactly without introducing ad-hoc Higgs sectors or violating electroweak precision parameters.