Wavefront set conjecture for generic local Langlands parameters

Let $F$ be a local field of characteristic zero, let $G$ be a classical group over $F$, and let $\pi\in\Pi_F(G)$ have a generic local $L$-parameter. For each symbol $\square$, let $\operatorname{WF}_{\square}(\pi)^{s-\mathrm{max}}$ denote the maximal members of the corresponding wavefront set under the $F$-stable topological order over $\mathcal{N}_F(\mathfrak{g})_\circ$, and let $\operatorname{WF}_{\square}(\pi)^{r-\mathrm{max}}$ denote the maximal members under the $F$-rational topological order. Wavefront set conjecture. The identities

$$\operatorname{WF}_{\mathrm{tr}}(\pi)^{s-\mathrm{max}}=\operatorname{WF}_{\mathrm{ari}}(\pi)^{s-\mathrm{max}}=\operatorname{WF}_{\mathrm{wm}}(\pi)^{s-\mathrm{max}}$$

and

$$\operatorname{WF}_{\mathrm{tr}}(\pi)^{r-\mathrm{max}}=\operatorname{WF}_{\mathrm{ari}}(\pi)^{r-\mathrm{max}}=\operatorname{WF}_{\mathrm{wm}}(\pi)^{r-\mathrm{max}}$$

should both hold. This conjecture seeks to identify analytic, arithmetic, and generalized-Whittaker descriptions of maximal wavefront data for generic parameters; the paper presents substantial progress toward it for real classical groups.