  We prove a conjecture of P. Guillon and G. Richard by showing that cellular
automata that eventually fix all cells to a fixed symbol 0 are nilpotent on
S^Z^d for all d. We also briefly discuss nilpotency on other subshifts, and
show that weak nilpotency implies nilpotency in all subshifts and all
dimensions, since we do not know a published reference for this.
