Cognitive Rationalization Gap for Adaptive Systems

Adaptive systems may choose among direct inference, additional computation, external memory writes, and parameter updates. Whether these heterogeneous choices are explained by one linear exchange rate between quality and resource costs is an empirical question rather than an architectural assumption. This paper defines the Cognitive Rationalization Gap (CRG), a convex, deterministic diagnostic for fully observed action tables. The CRG is zero exactly when every selected action maximizes a specified linear quality-minus-cost index; it neither identifies a unique coefficient vector nor supplies a test under stochastic choice. We also derive a static comparison between compiling now and never compiling when compilation creates a fixed cost and an expected secondary-stream loss. A reproducible simulator illustrates the diagnostic under a shared versus context-dependent coefficient process and compares two static net-present-value heuristics. These illustrations use no language model, production trace, customer data, or deployment measurement. They do not establish the validity of the framework for real adaptive runtimes or solve a dynamic optimal-stopping problem.