Resolution of the Cabibbo Angle Anomaly and First-Row CKM Unitarity Deficit: Substrate Hydrostatic Stress Stiffening of Nuclear Fermi Coupling in an Elastically Pre-Stressed Vacuum

Recent precision evaluations of universal electroweak radiative corrections (Δ_R^V) to superallowed 0+ -> 0+ nuclear β-decays, combined with determinations of |V_us| from kaon decays and neutron lifetime measurements, have revealed an apparent deficit in the first-row unitarity relation of the CKM matrix: |V_ud|^2 + |V_us|^2 + |V_ub|^2 = 0.9985 ± 0.0005 (a 3.5σ–4.0σ tension known as the Cabibbo Angle Anomaly). Standard Model extensions invoke a fourth chiral quark generation, vector-like quarks, or heavy W' bosons. Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that CKM unitarity is strictly conserved in nature (|V_ud|^2 + |V_us|^2 + |V_ub|^2 ≡ 1) and that the observed deficit is an environmental artifact of vacuum substrate elastodynamics. In our ontology, the Fermi constant is the transmission compliance of the weak shear-mode vector propagator. While muon decay calibrates G_F^(μ) in unperturbed vacuum, nuclear β-decay takes place inside the dense, localized hydrostatic stress field of the nuclear soliton bag (ΔP_nuc ~ 10^33 Pa). This localized compressive stress hardens the substrate shear impedance Z(σ), attenuating the effective nuclear weak coupling by δ_elasto ≈ 0.075%. Consequently, the extracted matrix element is systematically suppressed by |V_ud|_extracted = |V_ud|_true (1 - δ_elasto), producing the spurious deficit Δ_CKM ≈ 2 δ_elasto ≈ +0.0015. We derive this analytical shift without fine-tuning, preserving electroweak gauge unitarity under Occam's razor.