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 EM (t) > εsafe/2 under bounded stochastic corruption (Theorem 3. 6).