Numerical Existence of a Late-Time Localized Interaction Band in a Minimal Phenomenological Dark-Sector Model

Description This record presents a fully documented numerical investigation of a phenomenological dark-sector interaction model in which a scalar field couples to matter through a late-time friction-like transfer term. The interaction induces a time-localized suppression of structure growth while preserving background expansion consistency with ΛCDM within a few percent. The key results include: Identification of a 76-point all-gate viable parameter band. Demonstration that viable solutions organize along a slow-manifold ridge in parameter space. Dynamical systems analysis showing approach toward the scalar-field dominated fixed point (FP2). Quantitative relation between maximum fractional background deviation (ε_max) and growth suppression R(z). Evidence of temporal localization: the linear correlation between R(z) and ε_max weakens at higher redshift (z = 1, 2). This model is not tuned to eliminate the S8 tension but instead provides a controlled late-time suppression mechanism compatible with RSD constraints. All numerical data and reproduction scripts are included for transparency and reproducibility. Included Files dark_sector_preprint_final22.pdf — Full manuscript. all_gate_survivors.csv — List of all viable parameter points. Rz_all.csv — Numerical data for growth suppression analysis. code_forward_shoot.py — Forward integration + shooting solver. make_fig_Rz_multi.py — Figure regeneration script.