Kauffman's genus-one slice derivative conjecture

Let $K$ be a smoothly slice knot and let $F$ be a genus-$1$ Seifert surface for $K$. An essential simple closed curve $d$ on $F$ is a simple closed curve that does not bound a disk in $F$.

Kauffman's conjecture. There exists an essential simple closed curve $d$ on $F$ such that

$$\operatorname{lk}(d,d^+)=0$$

and $d$ is a slice knot.

The conjecture was proposed by Kauffman in 1982 and was supported by work of several authors, but it was disproved by Cochran and Davis, who constructed a smoothly slice knot neither of whose derivatives is smoothly slice. The claim is therefore refuted.