Shibata's refined multiplicity conjecture for log canonical complete intersection singularities

Let $X$ be an $n$-dimensional variety that is locally a complete intersection with log canonical singularities. For a closed point $x$ of $X$, let $\mathrm{emb}(X,x)$ be the embedding dimension at $x$ and let $\mathrm{lct}(\mathfrak m_x)$ be the log canonical threshold of the maximal ideal $\mathfrak m_x$. Write $e(\mathcal O_{X,x})$ for the Hilbert–Samuel multiplicity. Shibata's refined multiplicity conjecture.

$$e(\mathcal O_{X,x})\le 2^{n-\lceil\mathrm{lct}(\mathfrak m_x)\rceil},$$

and equality holds if and only if

$$\mathrm{emb}(X,x)=2n-\lceil\mathrm{lct}(\mathfrak m_x)\rceil.$$

The source presents this as a refinement of Watanabe's conjecture, allowing log canonical rather than canonical singularities and incorporating the log canonical threshold and embedding dimension. No resolution is supplied in the given text.