Space form conjecture for compact pseudo-Riemannian manifolds

A pseudo-Riemannian manifold of signature $(p,q)$ is understood here to be compact and complete, with constant sectional curvature $1$. Space form conjecture. There exists such a manifold if and only if $(p,q)$ belongs to the list specified in Example (4) of the source.

This conjecture concerns the classification of compact pseudo-Riemannian space forms and is linked to compact standard quotients of reductive homogeneous spaces. The source records substantial classification results for irreducible symmetric spaces and an announced resolution in a class with simple $G$, but does not state that the full conjecture is resolved.