Training a model on long worked-out solutions teaches it to reason, but those solutions come from other models and contain wrong turns and padding, which the model learns along with the good parts.
Each step of a solution is scored by how much it favours the correct final answer over a paired wrong one. Steps where that score falls, or that keep drifting after the answer is all but settled, are hidden from training while staying readable in the text.
Across three model sizes, models trained this way scored about 5.5% higher than those trained on full solutions, measured relative to that baseline, and wrote 8.8% shorter answers.