  In a recent work [A. Deger et al., Phys. Rev. Lett. 129, 160601 (2022)] we
have shown that kinetic constraints can completely arrest many-body chaos in
the dynamics of a classical, deterministic, translationally-invariant spin
system with the strength of the constraint driving a dynamical phase
transition. Using extensive numerical simulations and scaling analyses we
demonstrate here that this constraint-induced phase transition lies in the
directed percolation universality class in both one and two spatial dimensions.
