Ganatra–Kuo–Li–Wu's positive-wrapping conjecture for sheaf kernels

Let $X$ and $Y$ be manifolds, let $\Lambda$ and $\Sigma$ be conic conditions defining the relevant microsupported sheaf categories, and let $L \in \Sh(X \times Y)$ be a constructible sheaf with perfect stalks. The sheaf $L$ need not be microsupported in $-\Lambda \times \Sigma$. Let $\mathfrak{M}^{+}_{-\Lambda \times \Sigma}(L)$ denote the positive wrapping functor applied to $L$. Ganatra–Kuo–Li–Wu's positive-wrapping conjecture. Certain geometric constraints on $\ssupp(L)$ guarantee that

$$\mathfrak{M}^{+}_{-\Lambda \times \Sigma}(L) \ast (-)$$

preserves compact objects. The supplied text does not specify those geometric constraints or state whether this more general conjecture has been resolved.