Conjecture on the non-Gorenstein locus of Schubert varieties

Let $X_w$ be a Schubert variety, and let $({\mathfrak S},\prec_I)$ be the poset of permutation intervals. The order ideal of intervals corresponding to points where Schubert varieties are not Gorenstein is denoted ${\mathcal I}_{\mathrm{not\ Gorenstein}}$. Non-Gorenstein locus conjecture. The order ideal ${\mathcal I}_{\mathrm{not\ Gorenstein}}$ is generated by families (1) and (2) in the stated characterization of Gorenstein Schubert varieties. This would determine the locus of non-Gorenstein points; the supplied text does not state a resolution status.