Resolution of the Higgs Hierarchy Problem: Elimination of Quadratic Divergences, Substrate Volumetric Dilatation Resonances, and the Electroweak Scale in an Elastically Pre-Stressed Vacuum

In standard perturbative quantum field theory, the Higgs boson is the sole fundamental scalar excitation in the particle spectrum. Radiative loop corrections to its mass parameter diverge quadratically with the ultraviolet cutoff Λ, demanding an unnatural 34-decimal-place fine-tuning if the cutoff is at the Planck scale (Λ ~ M_Pl ~ 10^19 GeV). Decades of null results at the Large Hadron Collider searching for supersymmetry, extra dimensions, or composite Higgs dynamics have cast standard naturalness criteria into deep crisis. Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that the hierarchy problem is an artifact of treating the physical vacuum as a continuous, empty manifold. In our elastodynamic ontology, the Higgs field is not an autonomous scalar in a void, but the longitudinal volumetric breathing mode (θ = ∇ · u) of an elastic substrate possessing bulk modulus K_v, shear modulus G_v, and holding pre-stress P_0. The physical unit-cell scale ℓ_0 = (h c / P_0)^1/4 acts as a natural Brillouin-zone cutoff, eliminating quadratic loop divergences (δμ^2 ≡ 0) by discrete lattice translational invariance. Furthermore, we derive the electroweak scale v = 246.22 GeV and physical Higgs mass m_H ≈ 125.2 GeV as the fundamental acoustic dilatation resonance of the substrate (c_L = √3 c), proving that the hierarchy ratio v / M_Pl ~ 10^-17 is an exact geometric scaling ratio between the unit cell and the soliton interaction envelope without fine-tuning.