AAS framework proves AI systems can run indefinitely without unbounded aging

Artificial intelligence systems increasingly operate through repeated cycles of interaction, adaptation, and updates—not one-shot outputs. This raises a fundamental question: can an AI system persist indefinitely without its internal structure degrading? In a new theoretical paper on arXiv (2608.04012), Seyma Yaman Kayadibi argues yes, provided we measure aging correctly. The paper extends the Redundancy-Adjusted Artificial Age Score (AAS) from a static metric into a cycle-level functional that tracks how a system's structural age evolves across repeated operation. Each cycle's age is computed via a weighted, redundancy-aware logarithmic penalty over component consistency levels. The key result: this cycle-level age is well-defined and uniformly bounded, ruling out explosive pointwise aging.

The paper then maps out a hierarchy of asymptotic regimes—burdened persistence, zero-burden persistence, oscillatory persistence, and cumulative terminal burden—and proves several convergence and stability properties, including geometric stabilization under damped inter-cycle perturbations and zero-burden characterization under nondegenerate redundancy conditions. The central takeaway is that indefinite continuation does not require unbounded structural deterioration: an AI system can pass through infinitely many cycles while its structural age stays bounded, and under the strongest assumptions its cycle-level burden converges to zero. This gives researchers a formal toolkit for analyzing long-run AI persistence as a problem of bounded structural burden rather than inevitable decay. For engineers building self-updating or lifelong-learning systems, the framework offers theoretical guardrails: persistence is achievable if aging is measured—and managed—cycle by cycle.