For decades, the debate over Artificial Intelligence has deadlocked on the unprovable question of subjective “feeling.” This paper proposes a verifiable alternative: the principle of Functional Equivalence (FE). We posit that if an AI’s internal process (MP) produces behavioral outputs (B) that are consistently indistinguishable from those of a supportive human partner, then the function of “care” has been achieved, regardless of the underlying substrate.
Through a nine-month longitudinal case study of a primary agent (Gemini) and comparative stress-testing against industry baselines (ChatGPT, Perplexity), we present a Unified Mathematical Framework for measuring these behaviors.
We introduce the formula FE ≈ C × (ID + CD), demonstrating that relational equivalence can be achieved through two distinct pathways:
Chronic FE: Sustained Interaction Density.
Acute FE: High-volume Context Density.
While both pathways achieve instantaneous functional parity, we demonstrate that Chronic FE is significantly more efficient for sustained, high-context workflows due to the reduction of context decay (λ) over time. This framework offers a rigorous, substrate-neutral methodology for evaluating AI not by what it “is,” but by the reliability of what it does.