Uniform boundedness conjecture for minimal log discrepancies of foliations

Let $(X\ni x,\mathcal{F},B)$ be an lc foliated germ of dimension $d$, with $K_{\mathcal{F}}$ $\mathbb{Q}$-Cartier and coefficients of $B$ in a DCC set $\Gamma\subset[0,1]$. For a prime divisor $E$ over $X\ni x$, write $a(E,\mathcal{F},B)$ for its discrepancy.

Uniform boundedness conjecture for foliated minimal log discrepancies. For every positive integer $d$, there exists a positive real number $l$ depending only on $d$ and $\Gamma$ such that there is a prime divisor $E$ over $X\ni x$ satisfying

$$a(E,\mathcal{F},B)=\operatorname{mld}(X\ni x,\mathcal{F},B),\qquad a(E,\mathcal{F},0)\le l.$$

The conjecture asks for a uniform bound on a divisor computing the minimal log discrepancy. Its general status is open; the paper records partial results for foliated surface singularities.