A Long-Run Persistence Theory for AI Systems under the Redundancy-Adjusted Artificial Age Score (AAS)
Seyma Yaman Kayadibi
Submitted on 22 Apr 2026
Abstract
Artificial intelligence systems are increasingly expected to operate over repeated cycles of interaction, adaptation, and update, rather than through isolated one-shot outputs. This shift raises a fundamental theoretical question: can an AI system persist indefinitely without incurring unbounded structural aging? This paper develops a long-run persistence framework for AI systems based on the redundancy-adjusted Artificial Age Score (AAS).
The model extends AAS from a static evaluative measure into a cycle-level functional that generates an age sequence across repeated operation. At each cycle, structural age is defined through a weighted, redundancy-aware logarithmic penalty over component consistency levels. Within this framework, cycle-level age is shown to be well-defined and uniformly bounded, thereby excluding explosive pointwise aging.
On this basis, the paper defines a hierarchy of asymptotic regimes, including:
- Burdened persistence
- Zero-burden persistence
- Oscillatory persistence
- Cumulative terminal burden
It also establishes comparative ordering, sensitivity bounds, convergence under componentwise stabilization, persistence under finite total variation, geometric stabilization under damped inter-cycle perturbations, and a zero-burden characterization under nondegenerate redundancy conditions.
The main result is that indefinite cyclic continuation does not require unbounded structural aging: an AI system may pass through infinitely many cycles while its structural age remains bounded. Under stronger regularity conditions, its marginal aging vanishes, and in the strongest regime, its cycle-level burden converges to zero. The framework thus provides a formal basis for analyzing long-run artificial persistence as a problem of bounded structural burden, rather than inevitable cumulative deterioration.
Comments: 38 pages, no figures; theoretical paper with theorems and proofs.
Subjects: Artificial Intelligence (cs.AI)
MSC Classes: 93C10, 40A05, 37N40, 93D20
ACM Classes: I.2; F.0; G.3
Cite as: arXiv:2608.04012 [cs.AI] (v1)
This paper contributes to the growing body of research on long-lived AI systems, particularly in the context of 2026's emphasis on continuous deployment and lifecycle management. By formalizing persistence as a bounded structural burden, it offers a rigorous foundation for future work on sustainable AI architectures.
via ArXiv AI