The maximal-length conjecture for maximal green sequences of the n-cycle quiver

Let $\Gamma_n$ be the $n$-cycle quiver, and let $\Phi^1$ denote the corresponding root set, with $|\Phi^1|=\binom{n+1}{2}-1$. A maximal green sequence for $\Gamma_n$ has a well-defined length. Maximal-length conjecture. For $\Gamma_n$, the maximal length of a maximal green sequence is

$$\binom{n+1}{2}-1=|\Phi^1|,$$

and this length is achieved by the sequence described in part (b) of the conjectured factorization construction. The conjecture gives the proposed upper bound for the interval of lengths of maximal green sequences; the supplied text does not state whether it has been resolved.