The support tau-tilting enumeration conjecture for gentle arbor quivers

Let $t$ be an arbor, let $G_t$ be the associated gentle quiver-with-relations, and let $P_t$ be the associated poset. A support-$\tau$-tilting object is an object in the support-$\tau$-tilting theory of the algebra defined by $G_t$.

The support tau-tilting enumeration conjecture. The number of support-$\tau$-tilting objects for the gentle quiver-with-relations $G_t$ is equal to the number of elements of $P_t$.

The source explains that the mutation graph of these objects is finite and gives rise to a congruence-uniform lattice and a simple polytope, but presents the enumeration as an unresolved conjectural relationship.