Intersection-dimension conjecture ID-2

Let $(A,\mathfrak{n})$ be a quasi-unmixed local ring with prime ideals $P$ and $Q$ such that $\sqrt{P+Q}=\mathfrak{n}$. ID-2 conjecture. If

$$e(A)<e(A_P)+e(A_Q)$$

and both $A/P$ and $A/Q$ are analytically unramified, then

$$\operatorname{dim}(A/P)+\operatorname{dim}(A/Q)\leq\operatorname{dim}(A).$$

This is presented as a conjectural generalization of Serre's Intersection Theorem. The supplied context gives a theorem under this same multiplicity inequality together with additional hypotheses, so it does not by itself establish the full conjecture in the stated generality.