Fraser–Sherman-Bennett conjecture on source-target quasi-cluster equivalence

Let $G$ be a reduced plabic graph, and let $\Sigma_G^S$ and $\Sigma_G^T$ denote respectively its source and target seeds. A quasi-cluster transformation is the relevant equivalence allowing mutations together with suitable Laurent-monomial transformations involving frozen variables. Muller–Speyer conjecture. The seeds $\Sigma_G^S$ and $\Sigma_G^T$ are related by a quasi-cluster transformation. Source and target seeds are generally not mutation-equivalent and have different sets of cluster variables, although they generate the same coordinate ring; the conjecture proposes the natural broader equivalence, and remains open in the stated generality.