Teacher takeover in on-policy distillation (OPD) can produce incorrect responses even when the student and teacher independently answer the same problem correctly, a failure we quantify using Collaboration Failure Rate (CFR). To address it, we propose Contextual Digest for On-Policy Distillation (CD-OPD). CD-OPD structures the earlier context of teacher guidance through a teacher-generated dependency graph, curating the required problem conditions and preceding reasoning as node summaries alongside the unchanged guidance in a Contextual Digest before student continuation. We further develop online meta-reweighting, which compares Digest segment gradients with a task gradient from independent student responses to improve student-only performance, favoring updates predicted to reduce task loss. Across eight benchmarks, CD-OPD improves average accuracy by 1.32--7.05 percentage points over representative existing OPD methods. It also reduces CFR by 27.4\%--56.4\% relative to existing takeover-based OPD methods.

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