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.本数据集包含支持下述论文中报道的偏微分方程（Partial Differential Equation，简称PDE）层面数值一致性验证工作的数据与代码：《Extremal Threshold Decomposition, Exact Lower-Branch Asymptotics, and Vanishing-Kirchhoff Stability for a Singular Critical Fractional p-Kirchhoff Problem》。本数据包涵盖可复现正则化受限分数阶PDE计算的Python脚本、生成的逗号分隔值（Comma-Separated Values，简称CSV）文件、分支证书摘要、针对网格尺寸与奇异正则化的鲁棒性验证实验、论文所用图表，以及用于保障结果可复现性的环境配置文件。本数值验证工作旨在为低分支代数缩放与基尔霍夫消失稳定性相关的理论预测提供PDE层面的一致性支撑证据，而非作为无限维分数阶p-基尔霍夫理论的正式证明材料。