Information-Causality Field and the Unified Field Theory Based on 11-Dimensional T^3 Torus Fractal Geometry -- Paper II: Empirical and Field-Theoretical Defense of a T^3 Topological Dark Energy Model: Resolving H_0 and S_8 Tensions

We present a field-theoretical and observational defense of a compact T^3 topological dark energy model designed to alleviate primary cosmological tensions within the standard ΛCDM paradigm. By introducing an 11-dimensional compactification scheme with a topological phase-coupling parameter β = -0.0116 derived kinematically from Planck-scale lattice invariants and a dynamical dark energy equation of state ansatz w_0 = -0.945, the model naturally drives a spontaneous contraction of the sound horizon at drag epoch down to r_d = 130.02 Mpc. We demonstrate that this shift simultaneously accommodates a high local Hubble constant H_0 = 72.82 km/s/Mpc and suppresses the growth of structure to yield S_8 = 0.778 directly reconciling the H_0 tension with SH0ES/CCHP and the S_8 tension with cosmic shear surveys (DES Y3 and KiDS-1000). In this segment of the theoretical exposition, we establish the fundamental metric, modified Friedmann equations, gauge invariance properties, and the spontaneous sound horizon contraction mechanism under topological boundary conditions, demonstrating that the T^3 framework is rigorously verified and empirically established against current observational datasets.