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Through a controlled schedule sweep on Qwen3-8B, we establish that \\emph{isolation periods}, defined as complete teacher freezing between updates, are the key structural property enabling stable learning, not teacher age. To characterize these underlying training dynamics, we introduce a diagnostic framework of temporal KL structure, refresh shock, and length-tail risk. This framework further uncovers \\emph{state-oblivious collapse}: optimal short-horizon fixed schedules catastrophically fail under long-horizon training because a clock-driven refresh can copy a transiently drifting student into the teacher in a single, irreversible step. This failure mode is ","title":"When Should the Teacher Move? 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