Dye–Kaestner–Kauffman conjecture on slice genera of classical knots as virtual knots

Let $K$ be a virtual knot. Its smooth slice genus is denoted by $g_s(K)$, and its topological slice genus by $g_s^{\rm top}(K)$. If $K$ is classical, let $g_4(K)$ and $g_4^{\rm top}(K)$ denote its smooth and topological slice genera as a classical knot.

Dye–Kaestner–Kauffman conjecture. For every classical knot $K$,

$$g_s(K)=g_4(K) \quad\text{and}\quad g_s^{\rm top}(K)=g_4^{\rm top}(K).$$

The conjecture asks whether allowing virtual knot representatives can reduce either the smooth or topological slice genus of a classical knot. It was posed as an open problem by Dye, Kaestner, and Kauffman, and remains open according to the source.