The extremal-rank mutation conjecture for nondegenerate Jacobi-finite QPs

Let $(Q,\mathcal{S})$ be a nondegenerate Jacobi-finite QP. For a pair $(\delta,\epsilon)$ of $\delta$-vectors of $(Q,\mathcal{S})$, say that the pair has completely extremal rank when

$$\operatorname{rank}(\delta,\epsilon)=0,\quad \operatorname{rank}(\delta,\epsilon)=\underline{\dim}(\delta),\quad\text{or}\quad \operatorname{rank}(\delta,\epsilon)=\underline{\dim}(\epsilon).$$

Here $\underline{\dim}(\delta)$ denotes the dimension vector of a general representation in $\operatorname{PC}(\delta)$. Extremal-rank mutation conjecture. For any pair $(\delta,\epsilon)$ of $\delta$-vectors, there is a sequence of mutations $\mu_{\boldsymbol{u}}$ such that $(\mu_{\boldsymbol{u}}(\delta),\mu_{\boldsymbol{u}}(\epsilon))$ has completely extremal rank. This conjecture would make the mutation-based computation of general ranks effective; the source also records that the authors were not completely confident about it. The supplied parser status is unknown, so it remains open in this database.