Kauffman's Weak Conjecture for genus-one Seifert surfaces

Let $K$ be a slice knot, and let $F$ be a genus-one Seifert surface for $K$. For a simple closed curve $d$ on $F$, write $d^+$ for its positive push-off and define its self-linking by $\operatorname{lk}(d,d^+)$. Kauffman's Weak Conjecture. There exists an essential simple closed curve $d$ on $F$ such that

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

and the Arf invariant of $d$ vanishes. The theorem in the paper constructs slice knots and genus-one Seifert surfaces for which no surgery curve has vanishing Arf invariant, so this conjecture is refuted.