Much of systems neuroscience posits that emergent neural phenomena underpin important aspects of brain function. Studies in the field variously emphasize the importance of distinct emergent phenomena, including weakly stable dynamics, arrhythmic 1/f activity, long-range temporal correlations, and scale-free avalanche statistics. Few studies, however, have sought to reconcile these often abstract phenomena with interpretable properties of neural activity. Here, we developed a method to efficiently and unbiasedly generate model data constrained by interpretable empirical features in long neurophysiological recordings. We used this method to ground several major emergent neural phenomena to time-resolved smoothness, the correlation of distributed brain activity between adjacent timepoints. We first found that in electrocorticography recordings, time-resolved smoothness closely tracked transitions between conscious and anesthetized states. We then showed that a minimal model constrained by time-resolved smoothness, variance, and mean, captured dynamical and statistical emergent neural phenomena across modalities and species. Our results thus decouple major emergent neural phenomena from network mechanisms of brain function, and instead couple these phenomena to spatially nonspecific, time-resolved changes of brain activity. These results anchor several theoretical frameworks to a single interpretable property of the neurophysiological signal and, in this way, ultimately help bridge abstract theories of brain function with observed properties of brain activity.