The strong openness conjecture for multiplier ideal sheaves

Let $X$ be a complex manifold and let $\varphi$ be a plurisubharmonic function on $X$. Define the right-regularized multiplier ideal sheaf by

$$\mathscr I_{+}(\varphi)=\bigcup_{\epsilon>0}\mathscr I((1+\epsilon)\varphi).$$

Strong openness conjecture. The following equality of sheaves holds:

$$\mathscr I_{+}(\varphi)=\mathscr I(\varphi).$$

This conjecture is the natural generalization of the openness conjecture for multiplier ideal sheaves. The supplied source does not establish its resolution, so its status is recorded as open.