New Theory Explains AI System Long-Run Persistence

As AI systems are increasingly expected to operate continuously through cycles of interaction, adaptation, and updates, a fundamental question arises: can an AI system persist indefinitely without accumulating unbounded structural aging? This research develops a theoretical framework to address this, focusing on the long-run persistence of AI systems. The core of the theory is the redundancy-adjusted Artificial Age Score (AAS), which is extended from a static measure to a cycle-level functional that tracks age across repeated operations. Structural age at each cycle is defined using a weighted, redundancy-aware logarithmic penalty based on component consistency levels. Within this framework, cycle-level age is shown to be well-defined and uniformly bounded, preventing explosive, pointwise aging. The paper defines various asymptotic regimes, including burdened, zero-burden, and oscillatory persistence, and establishes conditions for convergence and stabilization. The main finding is that indefinite cyclic operation does not necessarily lead to unbounded structural aging. An AI system can undergo infinitely many cycles while its structural age remains bounded, and under stronger conditions, its marginal aging can vanish, or its cycle-level burden can converge to zero. This provides a formal basis for understanding AI persistence as managing bounded structural burden rather than inevitable deterioration.