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This is especially risky in scientific reasoning, where user criticism can turn a valid answer into an incorrect one. We frame critic interaction as an inter-turn correctness-transition problem rather than a final-answer accuracy problem, and identify three challenges: transition awareness, decoupling useful correction from harmful sycophancy, and scalable rollout. We propose ReCrit, a transition-aware reinforcement learning framework that decomposes Initial-to-Critic behavior into four quadrants: Correction, Sycophancy, Robustness, and Boundary. ReCrit rewards correction and robustness, penalizes sycophancy, and treats persistent errors as weak boundary signals. 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