Reinforcement learning with verifiable rewards (RLVR) enhances reasoning in large language models (LLMs) but typically depends on human-annotated answers or curated reward specifications. Label-free alternatives such as majority voting or LLM-as-a-Judge remove this cost but introduce false positives that destabilize training. We introduce JURY-RL, a label-free RLVR framework that decouples answer proposal from reward disposal: rollouts matching the plurality-voted answer receive positive reward only when that answer is verified in Lean. When verification is inconclusive, ResZero (Residual-Zero) discards the unverified plurality and redistributes a zero-mean, variance-preserving signal over the residual answers, keeping the optimization gradient stable without reinforcing unverifiable consensus. Across three backbones trained on math data, JURY-RL outperforms label-free baselines on mathematical reasoning, transfers to code generation and general benchmarks, and surpasses a majority-vote baseline in the test-time RL (TTRL) setting; it matches supervised ground-truth training on pass@1 and beats it on pass@k and response diversity.

Reinforcement learning with verifiable rewards (RLVR) has recently advanced the reasoning capabilities of large language models (LLMs). We investigate RLVR from a sample-centric perspective and introduce LPPO (Learning-Progress and Prefix-guided Optimization), a framework of progressive optimization techniques. Our work addresses a critical question: how to best leverage a small set of trusted, high-quality demonstrations, rather than simply scaling up data volume. First, motivated by how hints aid human problem-solving, we propose prefix-guided sampling, an online data augmentation method that incorporates partial solution prefixes from expert demonstrations to guide the policy, particularly for challenging instances. Second, inspired by how humans focus on important questions aligned with their current capabilities, we introduce learning-progress weighting, a dynamic strategy that adjusts each training sample’s influence based on model progression. We estimate sample-level learning progress via an exponential moving average of per-sample pass rates, promoting samples that foster learning and de-emphasizing stagnant ones. Experiments on mathematical-reasoning benchmarks demonstrate that our methods outperform strong baselines, yielding faster convergence and a higher performance ceiling, with these gains proving robust across diverse model architectures, scales, and reinforcement learning optimizers.