A Long-Run Persistence Theory for AI Systems under the Redundancy-Adjusted Artificial Age Score (AAS)

基于冗余调整后人工智能年龄评分（AAS）的 AI 系统长期持久性理论

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?

摘要： 人们日益期望人工智能系统能够在交互、适应和更新的重复循环中运行，而非仅仅提供孤立的一次性输出。这提出了一个根本性的理论问题：AI 系统能否在不产生无限结构性老化的情况下无限期地持续运行？

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.

本文基于冗余调整后的人工智能年龄评分（AAS），开发了一个 AI 系统长期持久性框架。该模型将 AAS 从一种静态评估指标扩展为一种循环级函数，能够在重复运行过程中生成年龄序列。在每个周期中，结构年龄通过对组件一致性水平进行加权且具备冗余感知能力的对数惩罚来定义。

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.

在该框架内，循环级年龄被证明是定义良好且一致有界的，从而排除了爆炸性的点状老化。在此基础上，本文定义了一系列渐近机制，包括负荷持久性、零负荷持久性、振荡持久性以及累积终点负荷。

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.

此外，本文还建立了比较排序、敏感性界限、组件级稳定下的收敛性、有限总变差下的持久性、周期间阻尼扰动下的几何稳定性，以及非退化冗余条件下的零负荷特征。

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.

主要研究结果表明，无限的循环延续并不需要无限的结构性老化：AI 系统可以在经历无限多个周期时保持结构年龄有界；在更强的正则性条件下，其边际老化会消失；而在最强的机制下，其循环级负荷会收敛于零。因此，该框架为将长期人工智能持久性分析为“有界结构负荷问题”而非“不可避免的累积恶化问题”提供了形式化基础。