Extremal-ray conjecture for homological data of squarefree complexes

Let $C(\operatorname{SqFree},n)$ be the positive rational cone generated by homological data triplets of free squarefree complexes over $\Bbbk[x_1,\ldots,x_n]$. A pure free squarefree complex is a free squarefree complex with the pure degree data described by the source, and $F_{\bullet}[s]$ denotes its shift by $s\in\mathbb{Z}$. Extremal-ray conjecture. The extremal rays of $C(\operatorname{SqFree},n)$ are precisely generated by the homology triplets of shifts $F_{\bullet}[s]$ of pure free squarefree complexes $F_{\bullet}$ belonging to a triplet of pure free squarefree complexes. If true, this would combine with the realization conjecture to imply the isomorphism between the coherent-sheaf and squarefree-complex cones. The supplied context does not establish whether it has been resolved.