I-Todorov's conjecture on longest maximal green sequences

Let $\Lambda$ be a cluster-tilted algebra of finite type, and let $C$ be one of the associated tilted algebras. The Auslander–Reiten quiver of $\Lambda$ is used to order the $C$-modules from right to left. I-Todorov's conjecture. (a) These $C$-modules form a maximal forward hom-orthogonal sequence of $\Lambda$-modules, and their dimension vectors form the $c$-vectors of a maximal green sequence for $\Lambda$. (b) The longest maximal green sequence for $\Lambda$ is given in this way. The conjecture predicts that an associated tilted algebra determines both a maximal green sequence and the longest possible maximal green sequence for the cluster-tilted algebra. The supplied source does not establish whether the conjecture is resolved.