Integrability of upper cluster algebra elements for recurrent quivers

Let $Q$ be a recurrent quiver and let $\mu_-\mu_+$ be its associated mutation map. Let the associated upper cluster algebra be the intersection of the Laurent polynomial rings of its seeds. Upper-cluster-algebra integrability conjecture. If $Q$ exhibits Zamolodchikov integrability, then every element of its associated upper cluster algebra also exhibits Zamolodchikov integrability. The conjecture is motivated by the fact that linearizability is preserved by addition and multiplication but not generally by division.