Schubert-vanishing non-membership conjecture for coNP

Let $\operatorname{sc}_{\mathrm{SchubertVanishing}}$ be the decision problem asking whether a Schubert coefficient vanishes, for Schubert coefficients in the classical types $A$, $B$, $C$, and $D$. Schubert-vanishing coNP conjecture. $\operatorname{sc}_{\mathrm{SchubertVanishing}}$ is not in $\mathrm{coNP}$. The paper's main theorem places this problem in $\mathrm{coAM}$ assuming the Generalized Riemann Hypothesis, which suggests that the conjecture may be false. Conversely, membership of Schubert coefficients in $\#P$ would imply that Schubert vanishing is in $\mathrm{coNP}$; the paper therefore presents this conjecture as a deliberately opposing possibility.