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Abstract: Persistent language model agents require memory that changes behavior without turning the active context into an unbounded record of past interactions. Retrieval based and summarization based memory improves recall, but it does not by itself enforce verified action boundaries. This paper develops a formal framework for compiling verified failures into compact symbolic patches. Each patch separates an online control plane, defined by a guard and an action mask, from an offline audit plane that records evidence, provenance and scope. The framework recasts adaptation as a cycle of assimilation, disequilibrium, accommodation and equilibration, and uses program search under a minimum description length constraint followed by integer linear programming to admit non redundant patches. Under stated assumptions, the model yields covered failure elimination, bounded active schema growth and bounded incremental drift outside the failure region. The paper also specifies a three tier evaluation protocol and a reference runtime design for controller level action gating.
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