The positivity conjecture for cluster expansions

Fix an initial seed $t$, and write the Laurent expansion of a cluster monomial as

$$X(t')^{m}=X^{g}\cdot\left(\sum_{n\in\mathbb{N}^{I_{\mathsf{uf}}}}c_{n}Y^{n}\right),$$

where $t'$ is a seed, $m\in\mathbb{N}^{I}$, $g\in M^\circ(t)$, and the $Y$-variables are the associated Laurent monomials. In the quantum case, the coefficients belong to the Laurent polynomial ring in the quantum parameter $v$.

Positivity conjecture. The coefficients $c_n$ for cluster monomials are contained in $\mathbb{N}$ in the classical case, or in $\mathbb{N}[v^{\pm}]$ in the quantum case.

This is the positivity property expected for cluster expansions and was formulated in the classical setting by Fomin and Zelevinsky, with a quantum analogue expected. The supplied source gives no resolution status.