A Long-Run Persistence Theory for AI Systems under the Redundancy-Adjusted Artificial Age Score (AAS)
arXiv:2608.04012v1 Announce Type: new 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 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, and 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, while 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.
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[Submitted on 22 Apr 2026]
Title:A Long-Run Persistence Theory for AI Systems under the Redundancy-Adjusted Artificial Age Score (AAS)
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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 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, and 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, while 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]
(or arXiv:2608.04012v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2608.04012
arXiv-issued DOI via DataCite
Submission history
From: Seyma Yaman Kayadibi [view email] [v1] Wed, 22 Apr 2026 01:39:35 UTC (387 KB)
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