The denominator-vector conjecture for cluster variables

Let $\mathcal{A}$ be a cluster algebra with initial seed at $t_0$, initial cluster $(x_{1;t_0},\dots,x_{n;t_0})$, and let $\mathbf{d}_{\ell;t}^{B^0;t_0}=(d_1,\dots,d_n)$ be the denominator vector of a cluster variable $x_{\ell;t}$ not in the initial cluster. Denominator-vector conjecture. (1) Every $d_i$ is nonnegative. (2) $d_i=0$ if and only if some cluster contains both $x_{\ell;t}$ and $x_{i;t_0}$. (3) Each $d_i$ depends only on $x_{\ell;t}$ and $x_{i;t_0}$, not on $t_0$ or $t$. The conjecture is proved for finite type in the cited results, but is open for general cluster algebras.