Cohen–Macaulay and Gorenstein conjecture for finite arc algebras

Let $J[\delta,(1)^N]$ and $A[\delta,(1)^N]$ be the finite arc algebras introduced in the source. Finite arc-algebra singularity conjecture. The algebra $J[\delta,(1)^N]$ is Cohen–Macaulay, and it is Gorenstein if and only if $A[\delta,(1)^N]$ is Gorenstein. The conjecture concerns preservation and detection of standard commutative-algebra singularity properties in these finite arc-algebra constructions; the source reports only limited computational support.