The one-ended limit group profinite splitting conjecture

A limit group is a finitely generated subgroup of a group obtained from a free group by finitely many extensions of centralizers, and it is one-ended when it has one end. For a group $G$, write $\widehat{G}$ for its profinite completion and let a free profinite product be denoted by $\amalg$. One-ended limit group profinite splitting conjecture. The profinite completion of a one-ended limit group does not split as a free profinite product. This is posed as a direction for extending profinite detection results beyond fundamental groups of graphs of virtually free groups with virtually cyclic edge groups; the supplied text gives no resolution status.