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Educational systems often require inspectable and editable knowledge states: educators want to know what a system assumes the learner knows, and learners benefit when the system can justify actions in terms of explicit skills, misconceptions, and strategies. Inspired by cognitive architectures, we propose Cognitive Agent Compilation (CAC), a framework that uses a strong teacher LLM to compile problem-solving knowledge into an explicit target agent. CAC separates (i) knowledge representation, (ii) problem-solving policy, and (iii) verification and update rules, with the goal of making bounded problem solving more inspectable and editable in educational settings. 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