LexFlow: Code, Benchmark Data, and Reproducible Results for Deterministic Lexicographic Flow Allocation on Lossy, Capacitated Rooted Trees

This dataset and software package provides the reproducibility materials for a study of deterministic three-stage lexicographic flow allocation on lossy, capacitated rooted trees. It contains the Python implementation, mathematical model documentation, six deterministic benchmark instances, a scale-verification instance with up to 500 users and 1022 edges, automated tests, source tables, generated numerical results, and provenance metadata. The package also includes a bilingual Uzbek/English desktop graphical user interface based on the same computational core as the command-line analysis pipeline. The implementation verifies the closed-form Stage-1 max–min fairness value against a HiGHS linear-programming solution, checks the equivalence of the path operator and node-balance formulation using exact rational arithmetic, preserves higher-priority objectives through the three lexicographic stages, and minimizes temporal allocation variation at Stage 3. Five synthetic benchmarks isolate specific mathematical properties. The Gone Abat Jap benchmark is a deterministic controlled-scenario adaptation of openly cited input data and does not represent field calibration, historical scarcity validation, or operational performance. The results can be reproduced by installing the documented Python dependencies and running python main.py analysis. Mathematical and implementation checks can be executed with python -m pytest -p no:cacheprovider. The private manuscript, licensed journal template, and internal review files are not included in this public package.