Towards a Unified Theory of Dynamic Cybernetic Stability: Con- structibility Erosion as the Common Downstream of Variety, In- formation, and Relevance Failure

Four prior papers establish necessary conditions for adaptive system function: requisite variety [Paper 1], effective information flow under channel degradation [Paper 2], temporal relevance of feedback [Paper 3], and reachable future state space [Paper 4]. Paper 1 further proves that variety matching is insufficient — an irreducible epistemic deficit 𝜀𝑡 > 0 drives a stress process 𝑆𝑡 whose long-run behavior is governed by the threshold 𝜇𝜑 ≶ 𝜆𝑆crit (Stress-Bounded Control Theorem), independently of controller variety. This paper provides the unifying layer. We show that the failure modes across all four papers — variety erosion, epistemic stress accumulation, effective information collapse, source-intrinsic decorrelation, and constructibility erosion — are not independent phenomena but analytically separable drivers of a single downstream quantity, the Constructibility Erosion Rate CER(𝑡) = −𝑑𝒞/𝑑𝑡. We formalize Dynamic Cybernetic Stability (DCS) as a two-tier joint condition: a stress feasibility gate (Paper 1’s threshold 𝜇𝜑 < 𝜆𝑆crit, a necessary condition no variety argument can replace) and a constructibility maintenance condition (𝒞(𝑡) ≥ 𝒞min, CER(𝑡) ≤ CERmax). The stress gate acts as a hard feasibility filter; only when it is satisfied does the constructibility layer become the operative diagnostic. We establish an implication hierarchy — each upstream failure is sufficient for CER(𝑡) > 0 — and show, via Paper 1’s Proposition 4.1, that CER(𝑡) > 0 can arise with all upstream conditions nominally satisfied. We propose a unified monitoring architecture, five cross-paper empirical predictions (including the predicted lead-time extension from Paper 1’s accumulation alarm), and five open problems whose resolution would convert the synthesis into a quantitative theory.