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It's the Problem, Not the Path: Budget and Difficulty Confounds in LLM Reasoning Trajectories

arXiv · AI, language, vision and robotics · article · Sep 3, 2026 · UTC

Reasoning traces of large language models are widely read as containing "breakthrough" moments and early-legible fates. Both readings rest on measurements missing a counterfactual control at the level of the claim; we supply both controls. First, a restart-controlled truncation probe separates when a solution fits the continuation budget from when a prefix carries value that fresh computation cannot buy, comparing per-anchor continuation solve rates against from-scratch restart curves at matched total generated-token budget. Applied to 178 problem-model cells (89 MATH problems x two small open

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