Vacuum Elastodynamics: Geometric Unification and the Resolution of Hubble and S8 Tensions via Lattice Viscosity

We present Vacuum Elastodynamics, modeling the vacuum as a Hyperuniform E₈ Supersolid. A topological Ward identity protects the lattice from linear Lorentz violations, recovering standard field theory in the continuum limit. A Vacuum Phase Transition at z ≈ 0.641 activates macroscopic lattice friction to natively resolve the Hubble Tension. Bounded by the macroscopic Geometric Yield Coefficient (Y_max ≈ 0.2055), the model establishes a theoretical expansion ceiling of H_fast ≈ 74.69 km s⁻¹ Mpc⁻¹. We analytically derive an “Inertial Counter-Load” (Ωₘᵉᶠᶠ ≈ 0.3639) generated by this late-time macroscopic drag, predicting a decelerated theoretical terminal velocity of H₀ ≈ 72.71 km s⁻¹ Mpc⁻¹. Blind MCMC analysis of Pantheon+ data independently validates this geometric prediction, recovering an empirical H₀ = 72.36 ± 0.24 km s⁻¹ Mpc⁻¹. In the late universe, the Vacuum Saturation Bulk Viscosity (ζ_sat ≈ 0.1569) activates, physically suppressing the absolute clustering amplitude to σ₈ ≈ 0.753. This natively resolves the S₈ tension as a mathematical extrapolation artifact; standard models assume a frictionless vacuum, which artificially inflates predicted late-time structure. This internal load saturates 98.54% of the microscopic Frenkel Yield Strength (γ_crit ≈ 0.15915), dynamically precluding a fourth lepton generation and deriving the Standard Model limit (N=3) as a mechanical yield limit. An exact Cancellation Theorem (m ∝ G⁻⁰·⁵) preserves BBN and CMB geometric constraints with 5σ significance without dark sector fine-tuning.