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The human brain integrates diverse cognitive processes into a coherent whole, shifting fluidly as a function of changing environmental demands. Despite recent progress, the neurobiological mechanisms responsible for this dynamic system-level integration remain poorly understood. Here we investigated the spatial, dynamic, and molecular signatures of system-wide neural activity across a range of cognitive tasks. We found that neuronal activity converged onto a low-dimensional manifold that facilitates the execution of diverse task states. Flow within this attractor space was associated with dissociable cognitive functions, unique patterns of network-level topology, and individual differences in fluid intelligence. The axes of the low-dimensional neurocognitive architecture aligned with regional differences in the density of neuromodulatory receptors, which in turn relate to distinct signatures of network controllability …