— Structure Dynamics, Elimination of the 𝑆 8 S 8 Tension, and Environmental Halo-Dark Interaction

As Chapter III of the Environmental Transition Cosmology (ETC) monograph, continuing from Chapter II (Zenodo DOI: 10.5281/zenodo.24089622), this paper investigates structure growth dynamics, linear perturbation equations, and the suppression mechanisms of the growth factor amplitude (fσ8f\sigma_8fσ8). By formulating the modified density growth equation and analyzing halo-dark coupling across galactic and cosmological scales, ETC provides an analytical framework to address the S8S_8S8 tension between weak lensing surveys and CMB observations. Maintaining strict separation between derived formulations and parametric approximations, we evaluate flat-core halo consistency with SPARC data and its observational implications.