Rational smoothness and smoothness conjecture for symmetric orbit closures

Let $K$ act on the ambient flag variety, let $Y_{\gamma}$ be the closure of the orbit indexed by $\gamma$, and let $\mathcal{O}_{\alpha}$ be the orbit indexed by $\alpha$ with $\alpha\leq\gamma$. Rational smoothness along $\mathcal{O}_{\alpha}$ means that the Kazhdan–Lusztig–Vogan polynomial satisfies $P_{\gamma,\alpha}(q)=1$. Rational smoothness conjecture. $Y_{\gamma}$ is rationally smooth on $\mathcal{O}_{\alpha}$ if and only if $Y_{\gamma}$ is smooth on $\mathcal{O}_{\alpha}$. The paper notes verification for $(p,q)=(2,2),(3,2)$; although global rational smoothness is known to coincide with smoothness, the local assertion is not established in general.