Weak Cosmic Censorship conjecture in the regularity class $\mathcal{B}$

Consider spherically symmetric initial data for the Einstein-scalar field equations in the regularity class $\mathcal{B}$, and let their maximal globally hyperbolic development (MGHD) be the corresponding spacetime. A singularity is naked if it is not hidden inside a black hole region. Weak Cosmic Censorship conjecture in $\mathcal{B}$. For generic spherically symmetric initial data in the regularity class $\mathcal{B}$, singularities arising in the MGHD of the Einstein-scalar field equations are not naked. This is a refined formulation of weak cosmic censorship whose content depends on the underlying functional framework. In the setting discussed by the paper, the relation between the regularity of the background and that of the perturbations motivates distinguishing this formulation from the rough BV-based instability results.