Generalized Eulerian duality conjecture for holonomic Weyl-algebra modules

Let $K$ be a field of characteristic zero and let $A_n(K)$ be the $n$th Weyl algebra. Let $M$ be a non-zero left holonomic graded generalized Eulerian $A_n(K)$-module. Define its dual by

$$M^\dagger=\operatorname{Ext}^n_{A_n(K)}(M,A_n(K)),$$

and let $^\sharp M^\dagger$ denote the associated left $A_n(K)$-module after converting the right module $M^\dagger$ via the sharp operation. The notation $^\sharp M^\dagger(+n)$ denotes its grading shift by $n$.

Generalized Eulerian duality conjecture. The shifted module $^\sharp M^\dagger(+n)$ is a left generalized Eulerian $A_n(K)$-module.

The source presents this as another conjecture that would imply the graded Ext concentration conjecture. It applies to non-zero holonomic graded generalized Eulerian modules, but the source does not provide a resolution.