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Integration-to-boundary is a prominent normative principle used in evidence-based decisions to explain the speed-accuracy trade-off and determine the decision-time. Despite its prominence, however, the decision boundary is not directly observed, but rather is theoretically assumed, and there is still an ongoing debate regarding its form: fixed vs. collapsing. The aim of this study is to show that the integration-to-boundary process extends to decisions between rapid pairs of numerical sequences (2 Hz rate), and to determine the boundary type by directly monitoring the noisy accumulated evidence. In a set of two experiments (supplemented by computational modelling), we demonstrate that integration to a collapsing-boundary takes place in such tasks, ruling out non-integration heuristic strategies. Moreover, we show that participants can adaptively adjust their boundaries in response to reward contingencies. Finally, we discuss the implications to decision optimality and the nature of processes and representations in numerical cognition.