Conjecture on the greenness of the mutation sequence for $\Gamma_{\overline{w}}$

Let $\Gamma_{\overline{w}}$ be the quiver associated with the word $\overline{w}$, and let $\mu_\bullet$ be the mutation sequence specified in the paper. A sequence of vertices is green with respect to a framed quiver when, at each step, the mutated vertex is green in the quiver obtained after the preceding mutations.

Greenness conjecture. The sequence of vertices of $\Gamma_{\overline{w}}$ mutated by $\mu_\bullet$ is a green sequence with respect to $\Gamma_{\overline{w}}$.

This conjecture concerns the compatibility of the explicitly constructed mutation sequence with the theory of green sequences. The supplied text gives no evidence that it has been resolved.