coNP-hardness conjecture for Schubert vanishing

Let $\operatorname{sc}_{\mathrm{SchubertVanishing}}$ be the decision problem asking whether a Schubert coefficient vanishes. Schubert-vanishing hardness conjecture. $\operatorname{sc}_{\mathrm{SchubertVanishing}}$ is $\mathrm{coNP}$-hard. The conjecture is presented as a consequence of the preceding non-membership conjecture together with the paper's discussion of Schubert coefficients and vanishing. The main theorem gives an upper bound in $\mathrm{coAM}$ under the Generalized Riemann Hypothesis, but the source provides no resolution of this hardness claim.