Abstract

We study whether a modular recurrent classifier receives the information required to identify a changing decision rule, and whether its reported switching statistics distinguish old-rule responses from generic response repetition. For an explicitly specified uncued task, the point sequence is independent of a stationary four-ID rule process. We prove that neither recurrent history nor any other rule-independent processing reveals the active rule. Two rule IDs implement the same label function. The resulting population classification optimum is exactly three quarters and is attained by a memoryless classifier; oracle rule access instead gives accuracy one. We calculate the distinction between rule-ID changes, label-function changes, and informative disagreements. Cued, delayed-cue, erased-cue, and causally ordered feedback tasks are separately declared protocols. A feedback elimination argument identifies effective rule functions while retaining the indistinguishability of duplicate IDs. Old-function response fractions, repeated-response fractions, flexibility ratios, and censored recovery-pattern summaries receive distinct definitions and sequence-level certificates. For structural repair, the masked-gradient identity explains why stored derivatives can be zero at inactive linear weights while effective-weight derivatives remain available. Reference-preserving restoration and score-allocation propositions separate mask reopening from recovery of a pre-pruning parameter. Executed matching, bracketed surrogate estimates, and unsupported targets are distinguished, with conditional interpolation and isoacute calibration bounds. A subordinate finite quantum cue pilot demonstrates retention and conditional rule execution without overcoming an absent observation channel. The supplied development brief and public implementation record are separated from independently proved objects and from unexecuted numerical claims. No cognitive-construct validation, treatment ranking, biological mechanism, quantum advantage, or inherited analytic admission is asserted.