Strong denominator-vector support conjecture

Let the strong $\mathbf g$-vector support conjecture be the assertion concerning equal $\mathbf g$-vectors, supports, and mutation sequences that do not exchange variables in the common support. For cluster monomials, replace $\mathbf g$-vectors by denominator vectors. Strong denominator-vector support conjecture. The strong $\mathbf g$-vector support conjecture holds with $\mathbf g$-vectors replaced by denominator vectors. The source later states that this holds for finite Cartan type, but gives no general resolution.