Bounded discrepancy conjecture for divisors computing minimal log discrepancies

Let $d$ be a positive integer and let $\Gamma\subset[0,1]$ be a DCC set. There exists a positive real number $l$, depending only on $d$ and $\Gamma$, such that for every lc pair $(X\ni x,B)$ of dimension $d$, with $X$ $\mathbb{Q}$-Gorenstein and $B\in\Gamma$, there is a prime divisor $E$ over $X\ni x$ satisfying

$$a(E,X,B)={\rm mld}(X\ni x,B)$$

and

$$a(E,X,0)\leq l.$$

Bounded discrepancy conjecture. The divisor computing the minimal log discrepancy can be chosen with discrepancy for $(X,0)$ bounded uniformly in terms of $d$ and $\Gamma$. The claim is a general conjectural boundedness statement for minimal log discrepancy computations; the supplied excerpt gives no resolution status or further evidence.