The modified openness conjecture for plurisubharmonic functions

Let $\alpha$ and $\beta$ be plurisubharmonic functions on a complex manifold. Let $\mathcal{J}(\alpha)$ denote the multiplier ideal sheaf of $\alpha$, and let $\mathcal{J}_+(\alpha,\beta)$ be the maximal element, as $t\to0^+$, of

$$\{\mathcal{J}(\alpha+t\beta)\mid t>0\}.$$

Modified openness conjecture. Then

$$\mathcal{J}_+(\alpha,\beta)=\mathcal{J}(\alpha).$$

This is a sheaf-theoretic formulation of the openness phenomenon for multiplier ideals and is stated in the paper as a conjectural assertion; no resolution is supplied in the source.