The Dynamic Good Regulator: Model Currency as a Viability Condition for Adaptive Regulation

The Good Regulator Theorem (Conant and Ashby, 1970) establishes that every good regulator of a system must contain a model of that system. This is an ontological condition — the model must exist — but it is silent on a distinct question: how long does an existing model remain valid for regulation? We show that model validity is not a permanent property but a dynamic one, governed by the same decorrelation and constructibility dynamics established in the preceding series. We introduce model currency ℳ(𝑡) as the fraction of the regulator’s internal model that remains epistemically valid at time 𝑡, and show that ℳ(𝑡) satisfies dynamics analogous to the Constructibility Erosion Rate:̇ ℳ(𝑡) ≤ 0 in general, with rate determined by the source-intrinsic decorrelation rate 𝜆(𝑠) and the model’s update frequency 𝜇. We prove the Dynamic Good Regulator Theorem: a regulator whose model exists but whose currency ℳ(𝑡) falls below a critical threshold ℳmin is not a good regulator in the dynamic sense — it satisfies Conant–Ashby’s static condition while failing the dynamic viability condition. We derive a Model Refresh Rate Condition (analog of Paper 1’s critical latency 𝜏 ∗): the minimum model update frequency required to maintain ℳ(𝑡) ≥ ℳmin. We connect model currency decay to CER(𝑡) > 0 (Paper 4) via a new mechanism — representational erosion — and position the Dynamic Good Regulator Theorem as the missing axiom beneath Papers 3–5: the condition that the model assumed by those papers to exist is in fact dynamically viable.