The silting form of the Auslander–Reiten conjecture

Let $k$ be a field, let $A$ be a finite-dimensional $k$-algebra, and let $\mathsf{D}^{\rm b}(\mathsf{mod} A)$ be its bounded derived category. An object is presilting if it has no positive self-extensions; write $\mathsf{add}X$ for the additive closure of $X$, and let $\mathsf{proj} A$ be the category of finitely generated projective $A$-modules. The silting form of the Auslander–Reiten conjecture. $\mathsf{D}^{\rm b}(\mathsf{mod} A)$ has no presilting object $X$ such that $\mathsf{add}X$ contains $\mathsf{proj} A$ as a proper subcategory. This is posed as a silting-theoretic reformulation of the Auslander–Reiten conjecture, and the source does not state whether it is resolved.