GRPO-trained LLMs sharpen single-sample reasoning but collapse in policy entropy: 7B models lose to their base at Pass@64 on AIME. Existing mitigations score tokens from current-step statistics, missing that collapse is a trajectory-level event accumulating through coherent batch drift. We propose FRACT, a per-rollout score projecting a learned T-step committor’s gradient onto the entropy direction in the dual Fisher metric, with a forward-only closed form requiring no extra backward through the policy. As a sparse, sign-aware selective KL atop GRPO, FRACT improves Acc@16 over KL-Cov by +.037/+.034/+.045 across Qwen2.5-Base 1.5B/3B/7B and simultaneously raises Pass@1 and Pass@64 on all four benchmarks at 7B—mitigating, not merely shifting, the accuracy–diversity trade-off. Random-matched-mass gains only +.009 and Anti-FRACT underperforms GRPO by −.007 at 1.5B—the score, not regularization mass, is the cause at ∼1.5% structural overhead.

Reinforcement Learning with Verifiable Rewards (RLVR) and Reinforcement Learning from Internal Feedback (RLIF) often fail to benefit from test-time compute due to entropy collapse and the resulting loss of reasoning diversity. We show that this collapse is driven not by uniform entropy decay, but by premature overconfidence at a small number of structurally critical decision points. Based on a token-level analysis of GRPO-style policy optimization, we propose SCOPE (Structural Collapse-aware Optimization via Partial Entropy control), which assigns each generated token a redistribution score and applies selective KL regularization to only the top ∼ 5% of tokens under this score. Across model scales and architectures on math reasoning benchmarks, SCOPE consistently improves performance under both RLVR and RLIF settings, demonstrating that targeted entropy control at a vanishingly small subset of tokens is sufficient to sustain reasoning diversity and effective test-time scaling.