Resolution of the Galactic Cusp-Core Problem: Substrate Bulk Rigidity, Non-Singular Pressure Saturation, and the Elimination of Cold Dark Matter Halos

Cosmological N-body simulations of collisionless Cold Dark Matter (CDM) halos systematically predict steep, divergent central density cusps (ρ_CDM(r) ∝ r^-γ with γ ≈ 1–1.5, e.g., the Navarro-Frenk-White profile). In sharp contrast, high-resolution H I and Hα kinematic observations of dwarf spheroidal and low-surface-brightness (LSB) galaxies (THINGS, LITTLE THINGS) reveal flat, constant-density cores (ρ ≈ const) and solid-body rotation curves (v(r) ∝ r). The conventional resolution invokes stochastic supernova-driven baryonic feedback to cyclically flatten the potential well; however, dwarf galaxies possess insufficient cumulative stellar energy to unseat NFW cusps, and cored profiles persist even in star-formation-quenched systems. Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that the cusp-core discrepancy is an artifact of treating space as an empty geometric manifold. In an elastic substrate, galactic rotation is governed by macroscopic strain vorticity. As matter converges toward the rotational core, the vacuum’s intrinsic bulk modulus K_v and background pre-stress P_0 generate an opposing acoustic-elastic restore potential (∇P_eff = K_v ∇δ_v). This regularizes the inner density field into a non-singular core of finite radius r_c ≈ √(K_v / (4π G ρ_0^2)). Inside r_c, solid-body shear enforces linear velocity profiles, smoothly transitioning into flat outer rotation via angular momentum conservation without non-baryonic halos or fine-tuned feedback.