Spacelike singularity conjecture for generic asymptotically flat black holes

Let a gravitational-collapse spacetime arise from one-ended initial data on a hypersurface $\Sigma$. For a point $p$ on a spacelike singularity $\mathcal{S}$, say that its causal past has relatively compact intersection with $\Sigma$ when this intersection is relatively compact. Spacelike singularity conjecture. The terminal boundary of a generic asymptotically flat black hole consists of a null piece emanating from infinity $i^+$, namely the Cauchy horizon $\mathcal{CH}_{i^+}$, together with a non-empty spacelike singularity $\mathcal{S}$ such that, for every $p\in\mathcal{S}$, the causal past of $p$ has relatively compact intersection with $\Sigma$. This conjecture describes the expected terminal structure of generic black-hole interiors in gravitational collapse; the supplied text gives no resolution status.