Title: Realization of "Time Crystal" Lagrangians and Emergent Sisyphus Dynamics,
Abstract: We demonstrate how non-convex "time crystal" Lagrangians arise in the
effective description of conventional, realizable physical systems. Such
embeddings allow for the resolution of dynamical singularities that arise in
the reduced description. Sisyphus dynamics, featuring intervals of forward
motion interrupted by quick resets, is a generic consequence. Near the would-be
singularity of the time crystal, we find striking microstructure.