Shokurov's codimension bound conjecture for minimal log discrepancies

Let $(X,B)$ be a log variety and let $\eta \in X$ be a Grothendieck point. The invariant $a(\eta;B)$ is the minimal log discrepancy at $\eta$.

Shokurov's codimension bound conjecture. The following inequality holds:

$$a(\eta;B) \le \operatorname{codim} \eta.$$

Moreover, $X$ is nonsingular in $\eta$ if

$$a(\eta;B)>\operatorname{codim} \eta-1.$$

This conjecture proposes a sharp upper bound for minimal log discrepancies and includes a criterion detecting nonsingularity. The source says that it had been proved up to codimension three, but gives no complete resolution status.