The strong coincidence conjecture for irreducible Pisot substitutions

Let $\sigma$ be an irreducible Pisot substitution, and let the associated substitution dynamical system and its strong coincidence condition be understood. Strong coincidence conjecture. Every irreducible Pisot substitution $\sigma$ satisfies the strong coincidence condition. This is presented as another problem among the versions of the Pisot conjecture discussed in the paper; the supplied material does not state that this formulation is resolved.