Data and code for Critical Reduction from the Initial Time and Memory Effects on State Selection in Semilinear Caputo Equations

This record provides the numerical data, source code, supplementary figures, and reproducibility materials associated with the manuscript “Critical Reduction from the Initial Time and Memory Effects on State Selection in Semilinear Caputo Equations.” The archive contains the unrounded numerical data used for the computational diagnostics, the implicit L1 time-stepping implementation, scripts for figure generation, the dynamic graph-entrance diagnostic, environment specifications, and numerical reproduction checks. It also includes the supplementary analytical and numerical material accompanying the manuscript. The numerical experiments are designed to support the theoretical results on original-time critical reduction, Mittag–Leffler initial layers, dynamic entrance into the cubic critical graph, critical memory tails, and state selection in semilinear Caputo equations. In particular, the archive contains diagnostics for the reduction error, critical-tail scaling, stable-profile approximation, and the history-preserving graph-entrance mechanism. Reproduction instructions and software dependencies are provided in the README and environment files included in the archive. Numerical comparisons are verified with stated floating-point tolerances rather than by requiring byte-for-byte identity across software environments.