Continuity_ The Fractal Principle Underlying Physics, Life, Mind, Law, AI, and Society

This paper formalizes The Continuity Invariant: the structural requirement that any system—biological, physical, or artificial—must maintain an unbroken, verifiable lineage of state transitions to preserve identity and resist entropy. Continuity is presented not as a metaphor, but as a mathematically and structurally homologous phenomenon that governs the persistence of all complex systems. Key Contributions: The Four Invariants: Defines the foundational requirements for systemic stability: Lineage (L), Temporal Monotonicity (ω), Provenance (P), and Causal Consistency (F). Cross-Domain Mapping: Demonstrates how Continuity governs diverse systems, including: Physics: Conservation laws and causal order. Biology: DNA replication fidelity and homeostatic stability. Cognition: The maintenance of the "Self" and autobiographical memory. AI/NeuroAI: A new standard for "Safe AI" through reconstructable reasoning and identity horizons. Governance & Law: The "Veritas Ledger™" as a supra-institutional standard for evidentiary integrity. The Identity Horizon: Introduces the mathematical threshold where systemic "drift" leads to the irreversible collapse of identity and meaning. Conclusion: By defining Continuity as the "Meta-Law" of coherent existence, this work provides a unified framework for engineering persistence in artificial systems, auditing fragility in human institutions, and understanding the survival of biological life.