Kobayashi's pseudo-Riemannian space-form conjecture

Let a pseudo-Riemannian space form of signature $(p,q)$ be a pseudo-Riemannian manifold with constant sectional curvature $\kappa$, where $p,q\neq 0$. Kobayashi's pseudo-Riemannian space-form conjecture. There exists a compact space form with signature $(p,q)$ and sectional curvature $\kappa$ if and only if one of the following holds: $\kappa<0$ and $(p,q)$ is one of $(1,2n)$, $(3,4n)$, or $(7,8)$; $\kappa=0$ and $(p,q)$ is arbitrary; or $\kappa>0$ and $(p,q)$ is one of $(2n,1)$, $(4n,3)$, or $(8,7)$. This conjecture proposes a precise classification of compact pseudo-Riemannian space forms by signature and curvature; the supplied text does not indicate that it has been resolved.