Constructibility Control Theory: Viability, Optimal Intervention, and Feedback Stabilisation of Learning Systems From Passive Monitoring to Active Safety-Constrained Control

The Constructibility Framework monitors collapse proximity via the margin M(t). This paper introduces Constructibility Control Theory (CCT): a framework proposal connecting constructibility monitoring to active intervention design. CCT is presented as a structured operational sketch a foundation for future rigorous control-theoretic development not a closed theorem system in the sense of control theory (IEEE TAC, Automatica). All results are rst-order analytical arguments; formal viability proofs, CBF quadratic programs, and stochastic control closure are open problems. State: S(t) = (H(t),C(t),n(t)). Control: u(t) = (∆C,∆n) applied at discrete intervention times. Objective: min T 0 C(u(t)) dt subject to M(t) >εsafe. Three results: (1) the viability kernel Vis characterised as {(H,C,n) : L(S) > eεsafe R(S)}and is forward-invariant under the feedback law (Theorem 3.1); (2) the minimum-cost intervention from margin decit d satises ∆C∗ = C(e(d+ε)/β−1) (Theorem 3.4, consistent with Paper 6); (3) the feedback control law u∗(t) = κ(εsafe + δ−M(t))+ maintains E[M(t)] > εsafe/2 under bounded stochastic corruption (Theorem 3.6).