Existence of non-commutative crepant resolutions for Gorenstein toric algebras

Let $R$ be a Gorenstein toric algebra, meaning the coordinate ring associated to a Gorenstein cone. An NCCR of $R$ is an algebra of the form $\Lambda=\operatorname{End}_R(M)$ for $M\in\operatorname{ref}R$ such that $\operatorname{gl}\dim\Lambda<\infty$ and $\Lambda\in\operatorname{CM}R$. Gorenstein toric NCCR existence conjecture. Every Gorenstein toric algebra has an NCCR. The source describes existence of NCCRs as unclear in general and subsequently proves existence for simplicial and almost simplicial affine toric Gorenstein algebras, so the unrestricted statement remains open.