The Space Form Conjecture

Let $(p,q)$ denote the signature of a pseudo-Riemannian manifold, with $p,q$ as in the displayed classification table.

Space Form Conjecture. There exists a compact, complete pseudo-Riemannian manifold of signature $(p,q)$ with constant sectional curvature $1$ if and only if $(p,q)$ lies in the following list:

$$\begin{array}{c|ccccc} p&\mathbb{N}&0&1&3&7\\ q&0&\mathbb{N}&2\mathbb{N}&4\mathbb{N}&8 \end{array}$$

This is presented as a special case of the standard quotient conjecture. The supplied text gives no resolution status.