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Which teacher model should be used, and in the case of self-distillation, which specific context should serve as the supervisory signal? Does the optimal choice vary from one token to the next? At present, addressing these questions typically requires costly training runs whose aggregate performance metrics obscure the dynamics at the level of individual tokens. We introduce a training-free diagnostic framework that operates at the highest resolution: per token, per question, and per teacher. We derive an ideal per-node gradient defined as the parameter update that maximally increases the student's probability of success. 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