The no-additional-components conjecture for outermost regions

Let $M'$ be an outermost region of a geometrostatic manifold, written as

$$M'={\mathbb R}^3\setminus\bigcup_{i=-n'}^n\Omega_i,$$

where each $\Omega_i$ is diffeomorphic to a three-ball, has stable minimal boundary $\Sigma_i=\partial\Omega_i$, and every component $\Omega_\alpha$ in the outermost-region description is one of these regions. The no-additional-components conjecture. For every $\Omega_\alpha$ there exists an index $i\in\{1,\ldots,n\}$ such that $p_i\in\Omega_\alpha$ and

$$M'={\mathbb R}^3\setminus\bigcup_{i=1}^n\Omega_i.$$

Thus every component removed from the outermost region should contain at least one distinguished point $p_i$, so no additional components with indices $i\leq 0$ occur. The claim concerns the topology of outermost regions in this setting and is stated without a resolution in the source.