The optimal bound for effective building of singularities

Let $(X,B)$ be a log variety, let $x\in X\setminus LCS(X,B)$ be a closed point, and let $H\in\operatorname{Div}(X)\otimes\mathbb{Q}$ be ample and normalized at $x$. Effective-building conjecture.

$$bld_x(B;H)\leq a(x;X,B).$$

Here $bld_x(B;H)$ is the infimum of the positive $c$ for which there is an effective $\mathbb{Q}$-Cartier divisor $D\sim_{\mathbb{Q}}cH$ with $a(x;B+D)=0$. The conjecture seeks the optimal local bound; the source proves a weaker universal bound, while the supplied text gives no resolution status.