Weighted Erdős–Burgess equality conjecture for finite principal ideal rings

Let $R$ be a finite principal ideal ring with identity, and let $\boldsymbol{I}_{\Psi}(\mathcal{S}_R)$, $\boldsymbol{D}_{\Psi}(\mathop{\rm U}(R))$, ${\rm Ind}(P)$, and ${\rm St}(P)$ denote the weighted Erdős–Burgess constant, weighted Davenport constant, index of a prime ideal, and stabilizer of that ideal under the action of $\Psi$, respectively. Let $\Psi$ be a subgroup of the group ${\rm Aut}(R)$.

Weighted Erdős–Burgess equality conjecture.

$${\rm I}_{\Psi}(\mathcal{S}_R)={\rm D}_{\Psi}({\rm U}(R))+\sum\limits_{P\in \operatorname{spec}(R)} \frac {T\left({\rm Ind}(P);\ \frac{|\Psi|}{|{\rm St}(P)|}\right)} {\frac{|\Psi|}{|{\rm St}(P)|}}.$$

This conjecture asserts an exact formula for the weighted Erdős–Burgess constant of finite principal ideal rings, refining the preceding lower-bound conjecture. The source gives no evidence of resolution, so its status remains open.