Resolution of the Core-Cusp and Too-Big-To-Fail Anomalies in Dwarf Galaxies: Substrate Finite Bulk Compliance, Cauchy Stress Saturation, and the Non-Singular Elastodynamic Halo Profile

High-resolution N-body simulations of collisionless Cold Dark Matter (ΛCDM) establish a universal Navarro-Frenk-White (NFW) halo density profile characterized by a steep central cusp (ρ(r) ∝ r^-1 as r -> 0) and predict numerous dense subhalos orbiting Milky Way-sized galaxies with peak circular velocities V_max ~ 30–50 km/s that are "too big to fail" (TBTF) at forming stars. However, stellar kinematic measurements in dwarf spheroidal galaxies (dSphs) and high-resolution H I rotation curves of low-surface-brightness dwarf galaxies reveal flat, constant-density cores (ρ(r) ≈ const as r -> 0, yielding v_c(r) ∝ r) and an absence of dense central subhalos. Attempted solutions via supernova-driven baryonic feedback fail in ultra-faint dwarf galaxies (UFDs) due to insufficient stellar energy, while Self-Interacting Dark Matter (SIDM) models conflict with galaxy cluster merger bounds. Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that both the Core-Cusp and Too-Big-To-Fail anomalies are artifacts of treating gravitation as a singular point-particle potential rather than an elastic stress gradient in a finite-rigidity medium. In our ontology, gravitation is the convergent hydrostatic stress gradient (g = ρ_0^-1 ∇·σ) of a pre-stressed substrate characterized by bulk modulus K_v = (5/3) P_0, shear modulus G_v = P_0, and holding pressure P_0 ≈ 7.48 × 10^24 Pa. Spherical regularity of the radial displacement field in the Navier-Cauchy equilibrium equation prohibits divergent central strain gradients, saturating the inner acceleration to g_r(r) ∝ r. We derive the analytical non-singular elastodynamic halo profile ρ_elasto(r) = ρ_c [1 + (r / r_core)^2]^-1 with core radius r_core = √(G M_b / a_0^sub) ≈ 0.5–1.0 kpc, reproducing observed rotation curves and bounding satellite circular velocities to v_c(r_1/2) ≈ 10–20 km/s under Occam's razor without dark matter particles or ad-hoc baryonic feedback.