The Variational Principle of Persistence: Mathematical Foundations and Computational Tests Across Biological, Physical, and Topological Regimes.

This record provides the manuscript and reproducibility package for version 2.4.1 of The Variational Principle of Persistence: Mathematical Foundations and Computational Tests Across Biological, Physical, and Topological Regimes. The manuscript introduces the Variational Principle of Persistence (VPP), a variational framework for self-organizing systems in which boundary closure is treated as a structural optimization variable. Viability is represented through an operational landscape over closure, allowing interior optima, marginal loss under overclosure, and risk-asymmetry conditions to be analyzed within a common mathematical setting. The framework is evaluated across three complementary regimes. The biological regime tests whether a VPP viability score can organize empirical thermal-performance data. The Ising regime anchors the framework against an exactly characterized physical transition. The topological-dynamical regime measures viability directly as stochastic metapopulation persistence on variable graph structures, providing a less constructed viability landscape than gain–cost scores. The reproducibility package includes scripts, numerical outputs, generated figures, manifests, and audit documentation for the reported computational analyses. The topological analysis uses a discovery–holdout design across five graph families. The risk-asymmetry condition is presented as an open theoretical prediction rather than as an empirically validated result.