Information-Causality Field and the Unified Field Theory Based on 11-Dimensional T^3 Torus Fractal Geometry -- Paper III: Unified Dark Sector Field Theory: Dark Energy as Global Topological Stress and Dark Matter as Vacuum Elastic Restoring Strain in

We present a unified geometric field theory of the dark sector without invoking hypothetical dark matter particles (WIMPs, Axions) or ad-hoc scalar field dark energy components. Within an 11-dimensional T^3 x Z_900 topological framework, dark energy and dark matter are derived as dual thermodynamic phases of a single geometric stress-energy tensor Θ_μν(x). In cosmic voids (δ_m → -1), the T^3 lattice relaxes into a uniform negative expansion stress (Θ_μν^DE) representing the vapor phase (dark energy, w_0 = -0.945, β = -0.0116). Conversely, where baryonic matter indentations occur (δ_m ≫ δ_c), the lattice responds with a localized elastic restoring force (ρ_halo), condensing into the ice phase (dark matter halo). This vacuum elastic strain manifests as an extra gravitational pulling force. We implement a 3D FFT potential solver over 50,000 galaxies from the SDSS DR17 catalog (128^3 grid, 1000 Mpc/h box). Under the strict condition of zero particle dark matter density (ρ_DM ≡ 0), core-softened rotation curves (r_core = 150 kpc) reproduce the flat velocity plateau v(r) ≈ 220 km/s out to 3000 kpc with an exceptional fit (χ^2/N = 0.7031, χ^2 = 4.2188).