The Invariance Maintenance Condition (IMC) - A Category 2 Translation for Computational Learning Theory

The Invariance Maintenance Condition (IMC) [Thomas, 2026a] is a framework for identifying and characterizing systems that maintain structural invariants under perturbation at measurable cost. The preceding companion translations applied the IMC to domains where all four applicability conditions are satisfied by the target system's internal logic: nonequilibrium thermodynamics, immunology, anesthesia, and ecological population regulation. This paper applies the IMC to computational learning theory (CLT) as a Category 2 case — one in which the applicability conditions are partially satisfied, the structural correspondence requires qualification at each step, and the primary contribution is identifying a theoretical gap rather than confirming a correspondence. The target system is not the trained model artifact but the learning pipeline: the coupled system of training, deployment, monitoring, and retraining. When the maintenance loop is operative, the IMC applies and generates predictions about generalization maintenance over deployment lifetime. When it is absent — in static deployments without monitoring or retraining — Condition X fails and the IMC does not apply; that failure is itself a structural finding. The central gap the IMC identifies: CLT is a theory of acquiring generalization, characterized by PAC and VC bounds on sample complexity. It has no native theory of maintaining generalization once acquired, no formalism for the maintenance sample rate required to hold generalization within tolerance under distribution shift, and no threshold predictions about when maintenance becomes infeasible. Four predictions follow from the IMC's threshold geometry applied to learning pipelines: a precursor degradation signal in subgroup and calibration metrics preceding aggregate accuracy decline; a maintenance sample rate bound not derivable from existing CLT formalism; structural asymmetry in recovery cost relative to initial training cost; and a hypothesis-class-sufficiency destruction threshold beyond which retraining cannot restore generalization. Deriving these quantities within CLT's existing formalism constitutes the research agenda the translation generates.