Supplementary Appendix: The Persistence–Governance Principle and the Nuclear Many-Body Limit

This record contains the supplementary appendix for “The Persistence–Governance Principle and the Nuclear Many-Body Limit.” The appendix introduces the Persistence–Governance Principle (PGP), a scale-invariant framework that classifies complex systems according to the ratio of relationship persistence time to interaction timescale. Applied to nuclear many-body systems, the framework provides a quantitative explanation for the observed domains of validity of ab initio methods, shell-model approaches, and density functional theories. The appendix formalizes persistence ratios for nuclear systems, analyzes their connection to computational complexity, and derives testable predictions for structural transitions, drip-line behavior, and the island of stability in superheavy elements. Rather than proposing new nuclear forces or interactions, the framework explains why exact solutions fail beyond specific mass thresholds as a consequence of physical encoding limits, not merely computational constraints. The accompanying PDF provides a complete, readable version of the supplementary material, while the included LaTeX source enables full reproducibility and regeneration of all figures and tables. Although developed in a nuclear physics context, the principle is formulated in a scale-invariant manner and may be applicable to other many-degree-of-freedom systems such as turbulence, plasma confinement, and cognitive dynamics.