Artificial intelligence is observed to age not through chronological time but through structural asymmetries in memory performance. In large language models, semantic cues such as the name of the day often remain stable across sessions, while episodic details like the sequential progression of experiment numbers tend to collapse when conversational context is reset. To capture this phenomenon, the Artificial Age Score (AAS) is introduced as a log-scaled, entropy-informed metric of memory aging derived from observable recall behavior. The score is formally proven to be well-defined, bounded, and monotonic under mild and model-agnostic assumptions, making it applicable across various tasks and domains. In its Redundancy-as-Masking formulation, the score interprets redundancy as overlapping information that reduces the penalized mass. However, in the present study, redundancy is not explicitly estimated; all reported values assume a redundancy-neutral setting (R = 0), yielding conservative upper bounds. The AAS framework was tested over a 25-day bilingual study involving ChatGPT-5, structured into stateless and persistent interaction phases. During persistent sessions, the model consistently recalled both semantic and episodic details, driving the AAS toward its theoretical minimum, indicative of structural youth. In contrast, when sessions were reset, the model preserved semantic consistency but failed to maintain episodic continuity, causing a sharp increase in the AAS and signaling structural memory aging. These findings support the utility of AAS as a theoretically grounded, task-independent diagnostic tool for evaluating memory degradation in artificial systems. The study builds on foundational concepts from von Neumann's work on automata, Shannon's theories of information and redundancy, and Turing's behavioral approach to intelligence.