arXiv:2609.26216v1 Announce Type: new

Abstract: A correct teacher solution becomes useful supervision when the receiving student can continue its reasoning. We measure this compatibility with prefix recovery: after revealing 25%, 50%, or 75% of a verified solution, we test whether the student completes it correctly. We connect recovery to the cosine conflict between cross-entropy and reverse-KL gradients over the full vocabulary. Across adjacent Qwen3 teacher-student pairs from 0.6B to 8B parameters, reverse-KL distillation delivers its most consistent mathematical and code improvements for the two students below 2B parameters. On a fixed cohort of 1,000 trajectories, average prefix recovery rises from 71.0% to 91.9% as student size increases from 0.6B to 4B, and the robust-fragile recovery gap contracts from 46.0 to 14.4 percentage points. With the teacher fixed at 8B, conflict separation falls from 0.993 to 0.233. An independent objective intervention finds the largest reverse-KL rescue on fragile trajectories. The three measurements locate the same capacity-dependent transfer regime: distribution matching has the greatest headroom when correct traces remain unevenly recoverable. Prefix recovery provides a practical diagnostic for selecting costly distribution-level distillation.