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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) View a PDF of the paper titled A Long-Run Persistence Theory for AI Systems under the Redundancy-Adjusted Artificial Age Score (AAS), by Seyma Yaman Kayadibi View PDF HTML (experimental) 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) Full-text links: Access Paper: View a PDF of the paper titled A Long-Run Persistence Theory for AI Systems under the Redundancy-Adjusted Artificial Age Score (AAS), by Seyma Yaman Kayadibi View PDF HTML (experimental) TeX Source view license Current browse context: cs.AI new | recent | 2026-08 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)