Subtraction-free characterization conjecture for bounded cluster-variable ratios

Let $\mathcal{D}$ be a full-rank cluster algebra of finite type, and consider ratios of products of its cluster variables on the totally positive locus. Such a ratio is called bounded when it is bounded there. A ratio $p/q$ is subtraction free in cluster variables if $q-p$ can be expressed as a polynomial with positive coefficients in the full set of cluster variables. Cluster-variable subtraction-free conjecture. Every bounded ratio is subtraction free in cluster variables. The paper presents this as the natural cluster-algebra analogue of the determinantal-ratio conjecture, but supplies an explicit counterexample showing that it is false in general.