The cluster monomial conjecture for the shifted category $\mathcal{O}^{sh}$

Let $\mathcal{A}_{\Gamma_\infty'}$ be the cluster algebra associated with the quiver $\Gamma_\infty'$, and let $\mathcal{O}^{sh}$ be the shifted category appearing in the isomorphism of Theorem

. Through this isomorphism, cluster monomials are elements of the Grothendieck ring $K_0(\mathcal{O}^{sh})$. **Cluster monomial conjecture.** All cluster monomials in $\mathcal{A}_{\Gamma_\infty'}$ correspond to classes of simple objects in $\mathcal{O}^{sh}$. This is proposed as a generalization of the corresponding result for the category considered in Theorem

; the source does not state whether the conjecture has been resolved.