The CSI conjecture on locally homogeneous representatives

Let a Lorentzian spacetime $\mathcal{M}$ be a constant scalar invariant (CSI) spacetime, with curvature invariants $\mathcal{I}$. A spacetime is CSI when all scalar polynomial curvature invariants are constant. CSI conjecture. There exists a locally homogeneous space $\widetilde{\mathcal{M}}$ with curvature invariants $\widetilde{\mathcal{I}}=\mathcal{I}$. This proposes that the scalar invariants of every Lorentzian CSI spacetime are realized by a locally homogeneous model.