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Abstract The brain generates diverse cognitive states while maintaining a stable functional architecture, a duality that remains difficult to reconcile. Prevailing views assume that flexible cognition necessitates correspondingly flexible architecture, in which different tasks demand distinct reconfigurations of functional networks. Here we introduce the intrinsic network flow (INF) framework as a complementary view. This framework is built on temporally coordinated signal flows across brain networks that constitute a universal scaffold, stable across diverse cognitive states and common across individuals. We show that a wide range of task-evoked activation patterns can be reconstructed by modulating only the temporal phase alignment of these flows, whose fixed structure determines functional connectivity topology, gradients, and large-scale networks, thereby preserving these properties across task states. This situates resting-state and task-state dynamics within a unified framework and suggests a generative relationship from flow-like dynamics to the full landscape of resting-state and task-state phenomena. Crucially, phase information, which neither existing brain state analyses nor eigenmode decompositions can extract, outperforms amplitude or activation-based markers in distinguishing cognitive states. These findings reframe task-evoked activation and deactivation as constructive and destructive interference among concurrent flows, rather than selective engagement or disengagement. This reconceptualization implies that the primary control variable for cognition is when intrinsic dynamics align in time, not where or how much the brain activates. Together, these results demonstrate that flexible cognition can emerge from retiming without reconfiguring functional architecture, offering a new path toward understanding the principled link between intrinsic dynamics and task-evoked cognition.