Stable Kauffman Conjecture for Levine surfaces

Let $K$ be a slice knot. A Seifert surface $F$ stabilizes to a Seifert surface $F'$ if $F'$ is obtained from $F$ by finitely many trivial one-handle attachments. A Levine surface is a Seifert surface admitting a set of surgery curves that forms a slice link. Stable Kauffman Conjecture. Any Seifert surface for $K$ stabilizes to a Levine surface. The source presents this as a stable weakening of Kauffman's philosophy; no resolution is supplied in the paper.