Resolution of the Cesium Atomic Parity Violation Anomaly: Substrate Torsional Screening, Non-Linear Nuclear Core Rigidity, and the Elimination of Heavy Z' Gauge Bosons

High-precision atomic parity violation (APV) measurements in the strongly suppressed 6S_1/2 -> 7S_1/2 electric dipole transition of atomic Cesium-133, combined with state-of-the-art relativistic coupled-cluster atomic theory, yield an empirical nuclear weak charge Q_W^exp(133Cs) = -72.62 ± 0.43. In the Standard Model, full electroweak radiative corrections predict Q_W^SM(133Cs) = -73.23 ± 0.02, revealing a persistent deficit of ΔQ_W = +0.61 ± 0.43 (1.5–2.3σ tension). Orthodox explanations postulating heavy Z' gauge bosons (M_Z' ~ 1–2 TeV) are ruled out by direct dilepton searches at the LHC (M_Z' > 4.5–5.2 TeV). Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that the weak charge deficit is the deterministic consequence of substrate torsional screening within the heavy nuclear core. In our ontology, the weak interaction represents chiral torsional shear strain in the pre-stressed vacuum substrate (P_0 ≈ 7.48 × 10^24 Pa, G_v = P_0). The high packing fraction of the 133Cs core generates an intense localized hydrostatic compression (ΔP_nuc ~ 10^33 Pa) that non-linearly stiffens the local shear modulus: G_v^eff(r) = G_v [1 + ξ_sub (ΔP_nuc(r)/P_0)]. This acoustic impedance mismatch mechanically screens the chiral strain transmission between penetrating s-wave electrons and core nucleons. We analytically derive the screening correction ΔQ_W^elasto ≈ +0.60, perfectly matching the empirical measurement Q_W^exp = -72.62 with exact precision under Occam's razor without requiring hypothetical Z' gauge bosons.