Constructibility as a State Variable: Monitoring Reachability Loss in Adaptive Systems

Three foundational frameworks — Ashby’s Law of Requisite Variety, Shannon’s channel capacity, and Age of Information — each identify a necessary condition for adaptive system function, yet each is insufficient to predict failure: systems fail even when variety, capacity, and freshness are nominally sufficient. We propose that the quantity actually disappearing in such failures is constructibility — the system’s capacity to reach the future states it needs to reach, under its current runtime constraints. We formalize constructibility 𝒞(𝑡) as a runtime state variable distinct from (though related to) classical design-time reachability, with first operationalization Reach𝐹 (𝑡) = |𝑅(𝑡, 𝐻) ∩ 𝒢(𝑡)|/|𝒢(𝑡)|, the goal-relative reachable fraction under horizon 𝐻. We introduce the Constructibility Erosion Rate CER(𝑡) = −𝑑𝒞/𝑑𝑡 and decompose it into three analytically separable mechanisms: reachable-goal shrinkage, goal-set expansion, and compound erosion. We establish a conditional Early Warning Principle (Principle 4.1): for systems with accelerating erosion trajectories (Class I), CER acceleration provides detectable lead time before constructibility reaches critical levels, with a quantifiable lower bound on that lead time. We connect CER(𝑡) to a hazard-rate analog ℎ(𝑡) = CER(𝑡)/𝒞(𝑡), bridging to survival analysis and reliability theory. We propose four candidate observable proxies — entropy volatilitỹ 𝐻, inter-channel divergencê Ψ, signal coefficient of variation CV, and representation drift̂ 𝜆rep — satisfying explicit proxy criteria (P1–P4), and treat their relationship to CER(𝑡) as an open identification problem rather than an established result. We show that the failure modes of the three prior frameworks (variety erosion, effective information collapse, source-intrinsic decorrelation) are each drivers of CER(𝑡) > 0, unifying them as mechanisms of constructibility erosion. Existing KA Phase-2 empirical results (E1, E6, E7) are reinterpreted as candidate illustrations of the framework, and the experiments required to move from consistency to evidence are specified.