The Variational Principle of Persistence: Mathematical Foundations and Computational Validation in Biological, Physical, and Topological Systems

his record provides the archival, fully reproducible companion package for the manuscript “The Variational Principle of Persistence (VPP): Mathematical Foundations and Computational Validation in Biological, Physical, and Topological Systems.” VPP is presented as a domain-general structural framework for persistence under uncertainty: increasing structural closure/control can yield protective benefits while also incurring accelerating maintenance and coordination costs, producing an interior optimum and an “over-closure” failure regime (Systemic Reduction Paradox, SRP).

Validated domains (computational)

The manuscript and accompanying code validate the framework across three disjoint domains:

• Bacterial thermal performance (Sharpe–Schoolfield family): cross-species prediction and survival simulations under stochastic thermal stress.

• Statistical physics (2D Ising model): the VPP optimum localizes the critical region and remains stable under smooth monotone reparameterizations and finite-size checks.

• Complex networks (Watts–Strogatz model): an interior optimum emerges, and excessive closure reproduces the SRP pattern.

What is included in this record

This record is intended to be reproducible end-to-end (no manual patching required) and includes:

• Manuscript PDF 

• Overleaf-ready LaTeX bundle containing manuscript sources and the complete figure set.

• Reproducible code snapshot (Python scripts) used to generate the key figures and statistics, including sensitivity/robustness analyses.

• Supporting artifacts (generated outputs/archives) enabling full verification and quick inspection of results.

Reproducibility (quick start)

A minimal reproduction on a clean environment is:

1. Install dependencies from requirements.txt.

2. Run the full pipeline via run_all.py (if included in the snapshot), or execute the figure scripts individually as listed in the repository README.

3. The pipeline writes figures and summary artifacts to the designated output folders included in the bundle.

A Colab-friendly workflow is supported using the provided scripts bundle (unzip → install requirements → run). This record is designed so a reviewer can reproduce the figures using standard Python tooling in a fresh environment.

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