The Generalized Property R Conjecture for links

Let $L=K_1\cup\dots\cup K_n$ be an $n$-component link in $S^3$. A 0-framed surgery on $L$ means surgery with framing zero on every component, and let $\#_n(S^2\times S^1)$ denote the connected sum of $n$ copies of $S^2\times S^1$. The Generalized Property R Conjecture. If 0-framed surgery on $L$ yields $\#_n(S^2\times S^1)$, then $L$ is handle-slide equivalent to the $n$-component unlink.

This extends Property R from knots to links and connects 3-dimensional surgery with 4-dimensional handle calculus. The source describes the conjecture as an open problem; stable and weak variants are considered because the proposed GST links may be counterexamples.