Woo–Yong's conjecture on the Gorenstein locus of Schubert varieties

Let $X$ be a Schubert variety, and let $x\in X$. The Gorenstein-locus conjecture. The point $x$ lies in the Gorenstein locus of $X$ if and only if the generic point of every irreducible component of the singular locus of $X$ containing $x$ lies in the Gorenstein locus of $X$. This conjecture seeks a criterion for determining the Gorenstein locus from the irreducible components of the singular locus. It was proposed by A. Woo and A. Yong; the paper proves a special case for minuscule Schubert varieties, while the general statement is not resolved here.