Derivative-State Drift: A Continuous-Time Model of Constraint Erosion in Elite and Artificial Optimization Systems

This working paper develops the Derivative-State Drift (DSD) framework as a unified structural model explaining cumulative misalignment in both elite institutional environments and artificial optimization systems. The model formalizes agents as operating in continuous-time state space, selecting actions based on expected first-order state change rather than absolute state levels. When constraint enforcement is soft, probabilistic, or compensable, normative sensitivity parameters decay endogenously, producing gradual threshold erosion. The analysis establishes three core results:(1) bounded incremental optimization can generate unbounded long-run drift;(2) resource buffering amplifies constraint erosion dynamics;(3) institutional insulation and artificial optimization share structurally isomorphic misalignment mechanisms. The framework contributes to contemporary debates on elite governance risk, moral hazard in insulated systems, and AI alignment theory by providing a formally tractable continuous-time account of constraint erosion.