Smooth-sliceness conjecture for zero-twisted Whitehead doubles

Let $K$ be a knot, and let $W_0(K)$ denote its zero-twisted Whitehead double. Smooth-sliceness conjecture for zero-twisted Whitehead doubles. The knot $K$ is smoothly slice if and only if its zero-twisted Whitehead double $W_0(K)$ is smoothly slice. This relates smooth knot concordance to Whitehead doubles; the source notes that Freedman's result makes every zero-twisted Whitehead double topologically locally flatly slice, while the supplied text gives no resolution of the smooth equivalence.