One-shot on-policy distillation works, and long chain-of-thought length is the driver.

1-shot on-policy distillation was consistently effective across every sampled training example, with harder examples yielding larger gains (arXiv 2609.05198). The analysis attributes the improvement to the longer CoT paths hard problems naturally generate, which keep the student aligned with the teacher over long horizons and teach reflection patterns absent from short CoTs, not to high token entropy. A hard-example-only selection method, including "unsolvable" examples exceeding the teacher's own capability, trained successfully with 8 selected examples across four models from 1.5B to 7B.