Equality of rational and Zariski wave-front sets

Let $F$ be a nonarchimedean local field, let $G$ be a reductive algebraic group over $F$, and let $\pi$ be an irreducible admissible representation of $G(F)$. Let $\operatorname{WF}^{rat}(\pi)$ and $\operatorname{WF}^{Zar}(\pi)$ be the rational and Zariski wave-front sets, and let $\overline{\operatorname{WF}}^{rat}(\pi)$ and $\overline{\operatorname{WF}}^{Zar}(\pi)$ be their corresponding geometric wave-front sets. Equality of rational and Zariski wave-front sets. We have

$$\overline{\operatorname{WF}}^{rat}(\pi)=\overline{\operatorname{WF}}^{Zar}(\pi)$$

or equivalently

$$\operatorname{WF}^{rat}(\pi)=\operatorname{WF}^{Zar}(\pi).$$

The paper presents this statement as equivalent to the singleton formulation in the relevant setting, and the first counterexample to the geometric singleton conjecture also refutes it. Thus it is not open in the generality considered here.