Vertical phase spirals are patterns visible in the positions and velocities of stars above and below the Milky Way's plane. These spirals indicate the galaxy is still recovering from a disturbance, such as a past collision with a smaller galaxy. A new preprint posted to arXiv has used computer simulations to investigate how these patterns evolve over time under realistic conditions. The study, titled "Phase spirals across galactic disks I: Exploring dynamical influences on winding," employed two different simulation approaches analyzed with basis function expansions to measure winding times (T_fit). The first was a test-particle simulation that does not include the gravitational influence of the stars on each other. The second was a fully self-consistent N-body simulation that does include those interactions. No sample size of real stars is involved, as this is purely simulation-based work. In the test-particle run, the phase spirals wound up at rates matching simple phase-mixing theory. In the N-body run, however, winding behaved differently: the start of winding was delayed, the overall winding rate slowed, and the rate itself oscillated with time. The strength of these effects depended on the azimuthal action (J_φ) of the stars. The researchers developed one-dimensional toy models of star groups traveling through evolving potentials to build intuition for the results. These models showed that winding is postponed until stars decouple from the perturbed midplane and that oscillations arise from breathing modes propagating through the disk. Changes to winding rates were strongest in the inner galaxy, where the disk's own gravity dominates. The authors conclude that all observational calculations of phase-spiral winding times in the Milky Way should be interpreted as lower limits on the time since the disturbance, with the most reliable values likely coming from the outer disk. This work is a preprint (arXiv:2603.23588) and has not completed peer review. Limitations include reliance on specific simulation setups that cannot capture every dynamical process present in the real Milky Way. Source: https://arxiv.org/abs/2603.23588