Axioms for Identity Preservation in Organized Systems

Identity in organized systems---biological, artificial, or computational---has historically been treated as a descriptive or domain-specific property. This paper presents a substrate-agnostic, axiomatic framework for identity preservation grounded in four irreducible invariants: identity-preservation, continuity, provenance, and $\Phi$-coherence. Together, these axioms define the necessary and sufficient conditions under which a system can be said to maintain identity across perturbations, state transitions, and self-modification. The framework provides a unified ontology for identity, enabling formal analysis, verification, and governance of complex systems.