Response to comment on "Quantum time crystals and interacting gauge theories in atomic Bose-Einstein condensates" by Syrwid, Kosior, and Sacha

In a recent comment [1] on our paper [2] Syrwid, Kosior, and Sacha (SKS) asserted that we did not correctly calculate the chiral soliton energy ${\cal E}_{LAB}$ in the lab frame, and further that the system we proposed is not capable of supporting a genuine quantum time crystal. We concede that we did not correctly calculate ${\mathcal{E}}_{LAB}$ but we illustrate below that our system can nonetheless display time crystal behavior with a ground state that is spatially localized and rotating.