Malec–O Murchadha conjecture on the TSS-CMC foliation of the Kruskal extension

Fix any constant mean curvature $H$. Let $C_H$ and $c_H$ be the parameter values defined by the four families of TSS-CMC hypersurfaces, and set

$$\{\Sigma_H\}=\tilde{\Sigma}_{H,0<c\leq C_H}^+\cup\tilde{\Sigma}_{H,C_H>c>-8M^3H}^-\cup\Sigma_{H,-8M^3H\geq c>c_H}^+\cup\Sigma_{H,c_H\leq c<0}^-.$$

Malec–O Murchadha conjecture. Given any constant mean curvature $H$, the Kruskal extension can be foliated by the TSS-CMC hypersurfaces $\{\Sigma_H\}$. The paper presents this as the summary of Malec and O Murchadha's conjecture; the supplied source does not state whether the full claim has been resolved.