The isolated-singularity conjecture for cyclic invariants of quantum affine space

Let $A:=\Bbbk_{-1}[\mathbf{x}]$ and let $G:=C_n$ act as in the paper. A graded isolated singularity means that the invariant ring has the isolated-singularity property in the graded noncommutative sense used here. The isolated-singularity conjecture. $A^G$ is a graded isolated singularity if and only if $n$ is not divisible by $3$ and $5$. The preceding results establish this when $n=2^ap^b$ for a prime $p$, distinguishing the cases $p=3,5$ from the other primes; the assertion for general $n$ is left open.