Rotating disks of stars in galaxies have a thickness in which there are age and abundance gradients. Understanding this vertical structure is a linchpin for inferring the present-day mass and formation history of disks. We explain how what amounts to a stellar phase-space stratification may arise from settling of decreasingly turbulent gas (cooling) or dynamical heating from scattering. We show how the stratification and its rate can be measured in the nearby, edge-on galaxy NGC 891, and then how the measurement can be extended to large samples of nearby galaxies from the Sloan Digitial Sky Survey-IV. These advances leverage a unique archaeological record that tell us how galaxy disks have assembled.