The $F$-rational structure conjecture for wavefront sets of enhanced $L$-parameters

Let $F$ be a local field of characteristic zero, let $G_n^*$ be an $F$-quasisplit classical group of the form $\operatorname{Isom}(V,q)^\circ$ for a non-degenerate $\epsilon$-Hermitian space $(V,q)$, or let $G_n^*$ be the metaplectic double cover $\operatorname{Mp}_{2n}(F)$ of $\operatorname{Sp}_{2n}(F)$. For a triple $(\varphi,\chi,q)\in\mathfrak{T}_a(G_n^*)$, let $\mathrm{WF}_a(\varphi,\chi,q)^\mathrm{max}$ be the maximal part of the arithmetic wavefront set, and let $\mathcal{Y}_a(\varphi,\chi,q)$ be the set constructed inductively from $\mathcal{L}_a(\varphi,\chi,q)\subset\mathcal{T}_a(\varphi,\chi,q)$. The $F$-rational structure conjecture. The $F$-rational structure of $\mathrm{WF}_a(\varphi,\chi,q)^\mathrm{max}$ can be completely determined by the inductive process defining $\mathcal{Y}_a(\varphi,\chi,q)$ by means of $\mathcal{L}_a(\varphi,\chi,q)$. This conjecture asserts that the consecutive-descent construction contains all the information needed to recover the rational nilpotent-orbit structure of the maximal arithmetic wavefront set; the paper does not establish it in full generality.