Superbrick conjecture for globally linked pairs in body-hinge graphs

Let $H$ be a multigraph, let $G_H$ be the body-hinge graph induced by $H$, and let $d\geq 3$. A $k$-superbrick is the graph-theoretic object defined in the source for the multigraph under consideration, and $(\binom{d+1}{2}-1)H$ is obtained by replacing every edge of $H$ by $\binom{d+1}{2}-1$ parallel copies. Body-hinge global linkedness conjecture. A pair $\{u,v\}$ is globally $d$-linked in $G_H$ if and only if there is a $\binom{d+1}{2}$-superbrick $S$ of $(\binom{d+1}{2}-1)H$ containing the vertices of the bodies of $u$ and $v$. This conjecture extends the body-bar cluster characterization to body-hinge graphs; the source introduces it after proving the corresponding body-bar result, and no resolution is supplied in the given text.