Multiplicity bound conjecture in terms of minimal log discrepancies

Let $x\in X$ be a point on a variety with log canonical singularities. Denote $e:=\dim m_x/m_x^2$ and $d:=\dim X$ at $x$. The minimal log discrepancy at $x$ is denoted by $\mathrm{mld}_x(X)$. Multiplicity bound conjecture. If $\mathrm{mld}_x(X)>k-1$ for some integer $0\le k\le d$, then

$$\mathrm{mult}_xX\le \binom{e-k}{d-k}.$$

Moreover, equality holds when $k=d-1$. This proposed bound generalizes the preceding multiplicity bounds for varieties with Du Bois and rational singularities. Its status is not established in the supplied text.