Intersection-dimension conjecture ID-1

Let $(A,\mathfrak{n})$ be a quasi-unmixed local ring with prime ideals $P$ and $Q$ such that $\sqrt{P+Q}=\mathfrak{n}$. ID-1 conjecture. If

$$e(A)=e(A_P)$$

and $A/P$ is 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, alongside the symbolic-power conjectures. The supplied context states a theorem proving the analogous inequality under a stronger multiplicity condition, but does not resolve ID-1.