Resolution of the Missing Satellites and Too-Big-to-Fail Problems: Substrate Shear-Elastic Cutoffs, Suppression of Sub-kpc Halo Clustering, and the Natural Satellites of the Milky Way

Cosmological N-body simulations based on collisionless cold dark matter (Aquarius, Via Lactea) systematically predict hundreds to thousands of dense, bound subhalos orbiting Milky Way-mass hosts. In sharp contrast, astronomical surveys identify only ~60 dwarf satellite galaxies, establishing the Missing Satellites Problem. Furthermore, kinematic measurements of classical dwarf spheroidals reveal the Too-Big-to-Fail (TBTF) paradox: observed dwarfs have central stellar velocity dispersions (σ_* ≈ 6–12 km/s) and dynamical masses far lower than the predicted central densities of the most massive simulated subhalos (V_max ≳ 30 km/s). These massive subhalos should easily ignite star formation, yet are completely absent in nature. Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that both dilemmas are artifacts of modeling dark matter as collisionless particles. In our continuum elastodynamics, galactic halos are macroscopic shear-strain deformation profiles in a pre-stressed substrate possessing finite shear modulus G_v and pre-stress P_0. Because the medium obeys Cauchy stress equilibrium, localized matter perturbations are stabilized by shear stress resistance below an intrinsic elastodynamic Jeans length λ_cut = 2π √(G_v / (ρ_0 ω_shear^2)) ≈ 1.2 kpc. Matter concentrations below this threshold cannot induce bound potential wells. We derive the low-mass halo cutoff M_min ≈ (π/6) ρ_vir λ_cut^3 ~ 10^8–10^9 M_sun, proving that sub-kpc subhalos are mechanically smoothed by the substrate's shear elasticity, naturally resolving the missing satellites and TBTF anomalies without fine-tuned supernova feedback or warm dark matter particles.