Generalized property R conjecture

Prove that every smooth R-link is handleslide equivalent to a zero-framed unlink.

Background

An R-link is a link whose integral surgery yields a connected sum of copies of S1×S2. The generalized property R conjecture would imply that handle-ribbonness equals ribbonness, but the paper emphasizes that the conjecture and its stabilized variants remain unresolved.

References

The generalized property R conjecture asks whether every $R$-link is handleslide equivalent to a $0$-framed unlink, veracity of which would prove that handle-ribbon implies ribbon. This conjecture is wide open, as are various weaker "stabilized" versions .

— Derivative links in contact topology  (2609.30182 - Breen et al., 24 Sep 2026) in Section 1, subsection “Tight R-links”

Is every transverse $R$-link stably equivalent to a max-sl unlink?

— Derivative links in contact topology  (2609.30182 - Breen et al., 24 Sep 2026) in Question 1.3, subsection “Tight R-links”