Christodoulou's trapped-surface conjecture for terminal indecomposable past sets

Let $(M,g)$ be the maximal future development of generic asymptotically flat initial data. A terminal indecomposable past set is a past set $\mathcal{P}$ in $M$ of the type described in the conjecture, and let $K$ be the compact closure of its trace on the initial-data hypersurface. For any open domain $D$ containing $K$, Christodoulou's trapped-surface conjecture. The domain of dependence of $D$ in $M$ contains a closed trapped surface. This conjecture is formulated as an essential intermediate step toward proving weak cosmic censorship. The supplied context states that weak cosmic censorship remains open, while related results are known for the Einstein–scalar field model in spherical symmetry and recent work has constructed vacuum spacetimes with naked singularities.