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However, setting the token budget, as well as the threshold for adaptive reasoning, is a practical challenge that entails a fundamental risk-accuracy trade-off. We re-frame the budget setting problem as risk control, limiting the error rate while minimizing compute. Our framework introduces an upper threshold that stops reasoning when the model is confident (risking incorrect output) and a novel parametric lower threshold that preemptively stops unsolvable instances (risking premature stoppage). Given a target risk and a validation set, we use distribution-free risk control to optimally specify these stopping mechanisms. 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