The Weak Generalized Property R Conjecture

An R-link is a link $L$ such that 0-surgery on $L$ yields a connected sum of copies of $S^1\times S^2$. A 0-framed unlink is an unlink whose components all have framing zero, and a split collection of Hopf pairs is a collection of split Hopf-link pairs. The Weak Generalized Property R Conjecture. For every R-link $L$, there is a 0-framed unlink $U$ and a split collection of Hopf pairs $V$ such that the split union $L\sqcup U\sqcup V$ is handleslide-equivalent to an unlink and a split collection of Hopf pairs.

This is a weaker variant of the Generalized Property R Conjecture. The source says that the GST links satisfy the weak conjecture, so this candidate is solved.