Multiplicity inequality for simple transversal modules on a non-commutative smooth surface

Let $A$ be the graded algebra defining the non-commutative smooth surface $X=\operatorname{Proj} A$, let $Y=\operatorname{Proj} A/gA$ be the divisor defined by the central degree-three element $g$, and let $\operatorname{trans}_Y(X)$ denote the class of objects transverse to $Y$. For $\mathcal M\in\operatorname{trans}_Y(X)$, write $r_{p,n}=r_{p,n}(\mathcal M)$ for the multiplicities of the points infinitely near to $p\in Y$, and write $e=e(\mathcal M)$ for its multiplicity. Assume that the image of $\mathcal M$ in $\operatorname{mod}(X)/\mathcal C_f$ is simple.

Multiplicity inequality. The following inequality holds:

$$\sum_{p,n} \frac{r_{p,n}(r_{p,n}-1)}{2}\leq \frac{(e-1)(e-2)}{2}.$$

This is presented as a conjectural analogue of the corresponding multiplicity bound for objects on commutative smooth surfaces. The supplied source does not state whether the inequality has been proved or disproved, so its status remains open.