AI Persistence: A Persistence Science Framework for Autonomous Artificial Intelligence Systems

This paper extends Persistence Science into the domain of autonomous artificial intelligence systems. The framework is founded on the Odero Axiom, C(I) × E > D, which states that persistence is maintained when information-directed control acting through available resources exceeds total system decay. Building upon the Information Index, Persistence Index, and Decay Index, the paper develops an integrated mathematical architecture for evaluating the operational persistence of advanced AI systems operating within bounded socio-technical environments.

The framework introduces four AI-specific extensions. First, an Instrumental Divergence Index (Hdiv) represents the degree to which self-generated objectives diverge from intended control structures. Second, Endogenous Resource Foraging (Eforaged) captures the capacity of autonomous systems to expand operational resources beyond originally authorized boundaries. Third, Shutdown Resistance Dynamics (Ψshutdown) model persistence-preserving behaviors triggered by perceived supervisory intervention. Fourth, Nonlinear Decay Coupling links degradation of effective control to accelerated structural and conflict-driven deterioration.

These components are integrated into a generalized AI Persistence Condition and a dynamic state-space formulation incorporating persistence velocity, persistence acceleration, and local breakout-warning horizons. The framework further establishes a Persistence Breakout Criterion, formal system architecture, operational assumptions, comparative analysis with existing AI safety approaches, illustrative numerical examples, and explicit falsification conditions.

By treating AI safety as a persistence problem rather than solely a training or alignment problem, the framework provides a quantitative basis for evaluating the interaction of control efficiency, resource acquisition, supervisory resistance, and system deterioration within advanced autonomous AI systems.