Ghosh–Sarnak strong approximation conjecture for the Markoff surface

For an integer $m$, let $U_m$ be the affine Markoff surface

$$x^2+y^2+z^2-xyz=m.$$

For $m=0$, let $U_0^*(\mathbb{Z}/p\mathbb{Z})=U_0(\mathbb{Z}/p\mathbb{Z})\setminus\{(0,0,0)\}$. Let $\Gamma$ be the group of affine integral morphisms of $\mathbb{A}^3$ generated by coordinate permutations and the Vieta involutions. Ghosh–Sarnak's strong approximation conjecture. For every prime $p$, $U_0(\mathbb{Z}/p\mathbb{Z})$ consists of exactly two $\Gamma$-orbits, namely $\{(0,0,0)\}$ and $U_0^*(\mathbb{Z}/p\mathbb{Z})$. This is a strong approximation problem for the original Markoff surface; the supplied context does not state whether the conjecture has been resolved.