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 (εₘax) and growth suppression R (z). Evidence of temporal localization: the linear correlation between R (z) and εₘax 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 darkₛectorₚreprintfinal22. pdf — Full manuscript. allgateₛurvivors. csv — List of all viable parameter points. Rzₐll. csv — Numerical data for growth suppression analysis. codeforwardₛhoot. py — Forward integration + shooting solver. makefigRzₘulti. py — Figure regeneration script.
masaki okada (Sun,) studied this question.