A Long-Run Persistence Theory for AI Systems under the Redundancy-Adjusted Artificial Age Score (AAS)
Quick Answer
This paper introduces a long-run persistence framework for AI systems using the redundancy-adjusted Artificial Age Score (AAS), demonstrating that AI can operate indefinitely without unbounded structural aging.
Quick Take
The model defines a cycle-level age through a logarithmic penalty, establishing various persistence regimes and showing that structural age can remain bounded across infinite cycles.
Key Points
- Develops a framework for AI systems' long-run persistence using redundancy-adjusted AAS.
- Defines cycle-level age with a weighted logarithmic penalty on component consistency.
- Establishes persistence regimes: burdened, zero-burden, oscillatory, and cumulative terminal burden.
- Proves structural age can remain bounded across infinite operational cycles.
- Offers a formal basis for analyzing artificial persistence as bounded structural burden.
DeepSignal Analysis
What happened
The paper proposes a framework for assessing the long-term persistence of AI systems using a redundancy-adjusted Artificial Age Score (AAS). It argues that AI can function indefinitely without experiencing unbounded structural aging. The framework introduces a cycle-level age metric that remains bounded across infinite operational cycles.
Key evidence
- The model extends the AAS from a static measure to a functional that generates an age sequence across repeated operations.
- Structural age is defined through a weighted logarithmic penalty based on component consistency levels, ensuring that cycle-level age is uniformly bounded.
- The paper identifies various persistence regimes, including burdened persistence and zero-burden persistence, demonstrating that indefinite operation does not necessitate unbounded structural aging.
Why it matters
This research is significant as it challenges the notion that AI systems must deteriorate over time. By establishing a framework for bounded structural aging, it opens avenues for designing AI systems that can sustain performance across numerous cycles. This could have implications for the longevity and reliability of AI applications in critical areas.
Paper Resources
📖 Reader Mode
~2 min readAbstract: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)
— Originally published at arxiv.org
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