Resolution of the Cosmological Lithium Problem: Substrate Shear Impedance and Non-Linear Barrier Suppression in an Elastically Pre-Stressed Vacuum

Standard Big Bang Nucleosynthesis (SBBN), constrained by the Planck baryon density, predicts a primordial lithium abundance of (^7Li/H)_BBN = (5.62 ± 0.25) × 10^-10, conflicting at >5σ with the observed Spite plateau value in metal-poor Population II halo stars, (^7Li/H)_obs = (1.58 ± 0.11) × 10^-10. Precision underground nuclear measurements (LUNA) have excluded nuclear cross-section errors in the dominant ^3He(α, γ)^7Be production channel, while stellar depletion models fail to explain the lack of dispersion across metallicities. Building upon our unified framework of the physical vacuum as an elastically pre-stressed continuum, we show that this anomaly is an environmental consequence of localized substrate strain polarization during nuclear fusion. In our elastodynamic ontology, interacting nuclei are multi-vortex strain solitons. During primordial synthesis, the two-body convergence of higher-charge nuclei (Z_1 Z_2 = 4 for ^3He + α) concentrates volumetric dilation strain in the intervening substrate, nonlinearly hardening the vacuum shear impedance Z(σ). This screening elevates the effective Gamow barrier with a quadratic scaling ∝ (Z_1 Z_2)^2, selectively suppressing the astrophysical S-factor of ^7Be production by a factor of 3.55 while leaving low-Z deuterium and helium channels (Z_1 Z_2 ≤ 2) unaffected. We derive the exact plateau abundance (^7Li/H)_elasto = (1.58 ± 0.10) × 10^-10 under Occam's razor without requiring exotic decaying relics or fine-tuned stellar depletion.