Conservation and Convertibility as Structural Necessities of Persistent Systems: From Noether's Theorem to a General Theory of System Persistence Across Physical, Biological, Cognitive, and Social Domains

Conservation laws and massenergy equivalence are foundational results in physics.This paper argues that they are instances of deeper structural necessities governingany complex system that persists through time in a changing environment. Twometa-principles are identied and formally derived from a minimal persistence ax-iom: (i) Conservation Necessitythat every persistent system must track andbalance a set of identity-constitutive quantities, and (ii) the Convertibility Prin-ciplethat structure and process must be interconvertible, with a domain-specicconversion factor γ that bounds the system's resistance to transformation. Thepaper introduces a state-space formalism accessible to researchers across disciplinesand proves that systems possessing conservation without convertibility become rigidand brittle, while those possessing convertibility without conservation become dis-sipative and identity-less; only systems satisfying both occupy a viable persistenceregion. These results are instantiated across physics, biology, cognitive science,economics, and social systems, with formal structural correspondences establishedrather than merely asserted by analogy. A comprehensive literature review con-nects the framework to Noether's theorem, autopoiesis, the free energy principle,ecological rationality, dissipative structures, and general systems theory, while iden-tifying what the present contribution adds to each. The framework is shown to be self-applicable: its own epistemic limitations are predicted by the constraints itidentifies.Keywords: conservation laws, persistence, complex systems, structureprocess du-ality, viability, self-organization, meta-principles, dynamical systems, cross-domainisomorphism