Operationalizing Persistence Through Constraint Margins: A Domain-Independent Analytical Procedure Persistent structures exist throughout nature across a wide range of spatial and temporal scales, yet methods for analyzing persistence are typically developed independently within individual scientific disciplines. This manuscript introduces a domain-independent analytical procedure for operationalizing persistence using state spaces, governing constraints, viability regions, failure boundaries, constraint margins, and persistence times. Rather than proposing new physical laws or replacing established scientific theories, the procedure provides a common analytical workflow that can be instantiated using the existing knowledge, governing equations, and measurement practices of individual disciplines. The workflow intentionally separates domain-independent analytical structure from domain-dependent scientific implementation, allowing researchers to express persistence problems using a consistent methodological framework while preserving the established methods of their respective fields. The manuscript develops the mathematical formalism underlying the procedure and illustrates its application using representative examples from orbital mechanics and cellular biology, together with additional stress tests involving combustion, atmospheric dynamics, crystalline solids, and radioactive decay. These examples are intended to demonstrate the workflow's applicability while identifying the natural boundaries of the current formulation. This Version 1.0 release represents the initial public presentation of the methodology. It is intended to invite independent evaluation, application, and constructive feedback from researchers across scientific disciplines. Future work will explore adaptive margin dynamics, stochastic extensions, moving viability boundaries, nested persistence, and additional domain-specific applications. Version: 1.0 (Frozen Release) Status: Public preprint License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Charles Carroll (Sat,) studied this question.