Reinforcement learning with verifiable rewards (RLVR) has emerged as a prominent paradigm for training reasoning models, but its computational cost makes efficient data selection increasingly important. Since training examples contribute unequally to learning, selecting a small, informative subset can offer a more efficient alternative to using the entire data pool. The training-free selection method estimates prompt value with hidden states from complete greedy rollouts. However, in our datasets, $26$--$32\%$ of these rollouts fail to terminate within the generation budget. We introduce LIFT, a training-free data selector that identifies impactful prompts using only partial reasoning rollouts. At its core, LIFT uses Partial Rollout Context Lift (PRCL), a score inspired by pointwise $\mathcal{V}$-information that accumulates token-level log-likelihood ratios between a question-conditioned context and a null context with the question removed. This enables prompt scoring from a short rollout prefix rather than a complete trajectory. Across Qwen2.5-Math-1.5B and DeepSeek-R1-Distill-1.5B, prefixes retaining at least 90\% and 95\% of the full-rollout PRCL score, respectively, require only 26\% and 4.7\% of the tokens generated by full rollouts. Compared with SHIFT, LIFT reduces selection cost by 3.7--9.1$\times$ while achieving competitive downstream RLVR performance, with the highest six-benchmark average in three of six settings.

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