We further the classification of rational surface singularities. Suppose $(S, \mathfrak{n}, \mathcal{k})$ is a strictly Henselian regular local ring mixed characteristic $(0, p > 5)$. classify functions $f$ for which $S/(f)$ has an isolated singularity at maximal ideal $\mathfrak{n}$. The such are used to show that if $(R, \mathfrak{m}, excellent, Henselian, Gorenstein dimension $2$ and 5)$, th...