 the Stepanov criterion (see, e.g., [@LiNi00 Lemma 0.00]) we deduce that $\mathcal{S}_0^{{\ifm {{\sf wt}} {{$\sf wt$}}}_0}$ is an irreducible polynomial in ${\overline{{\mathbb F}}_{\hskip-0.0mm q}}(A_s {\ifm {,\ldots,} {$,\ldots,$}}A_0)[A_0,A_0]$. 