Data and code for: Extremal Threshold Decomposition, Exact Lower-Branch Asymptotics, and Vanishing-Kirchhoff Stability for a Singular Critical Fractional p-Kirchhoff Problem

This record contains the data and code supporting the PDE-level numerical consistency checks reported in the manuscript "Extremal Threshold Decomposition, Exact Lower-Branch Asymptotics, and Vanishing-Kirchhoff Stability for a Singular Critical Fractional p-Kirchhoff Problem". The package includes Python scripts for reproducing the regularized restricted-fractional PDE computations, generated CSV files, branch-certificate summaries, robustness checks with respect to grid size and singular regularization, figures used in the manuscript, and environment files for reproducibility. The numerical checks are intended as PDE-level consistency evidence for the theoretical predictions on lower-branch algebraic scaling and vanishing-Kirchhoff stability. They are not intended as a proof of the infinite-dimensional fractional p-Kirchhoff theory.