The LSC conjecture for families

Let $\varphi: Y \to T$ be a flat morphism, let $\mathfrak{a}$ be an $\mathbb{R}$-ideal sheaf on $Y$, and let $\tau: T \to Y$ be a section of $\varphi$. For a closed point $t \in T$, set $Y_t = \varphi^{-1}(t)$ and $\mathfrak{a}_t = \mathfrak{a}\mathcal{O}_{Y_t}$. Suppose that for all $t \in T$, $\mathfrak{a}_t \ne 0$ and $Y_t$ is a normal $\mathbb{Q}$-Gorenstein variety. LSC conjecture for families. The function

$$|T|_{\rm cl} \to \mathbb{R}_{\ge 0} \cup \{-\infty\}, \qquad t \mapsto \operatorname{mld}_{\tau(t)}(Y_t,\mathfrak{a}_t)$$

is lower semi-continuous, where $|T|_{\rm cl}$ is the set of closed points of $T$ with the Zariski topology. This conjecture is known when $\varphi$ is smooth and when all fibers have only quotient singularities, but the general statement is open.