Artificial Age Score (AAS): Proof-Theoretic Foundations and Axiomatic Uniqueness

An axiomatic and fully proved foundation is provided for the Artificial Age Score (AAS), a penalty-based metric designed to quantify output-level aging-like degradation in observable recall accuracy under redundancy-aware channel weighting. The score is analyzed as a separable aggregation of channel contributions, enabling transparent decomposition across subsystems and consistent comparison across sessions via normalization. Core analytical properties are proved, including well-definedness on the admissible accuracy domain, convexity, and Jensen-type coarsening bounds that quantify the cost of heterogeneity, finite additivity over disjoint index sets, and positive homogeneity of degree one in the effective weights. Sensitivity ceilings are derived to control worst-case perturbation effects, and the small-noise regime is characterized to clarify limiting behavior as the regularization vanishes. Interactions between weights and redundancy gates are formalized, yielding principled targeting rules on both raw and normalized scales. Finally, an axiomatic representation and uniqueness theorem is proved, showing that under weak functional requirements, the AAS form is uniquely determined up to bit calibration. Complete proofs are provided for all stated results.