Cancellation conjecture for doubly slice knots

Knots are considered up to connected sum, and a knot is doubly slice if it is the cross-section of an unknotted $2$-sphere in $S^4$.

Cancellation conjecture. If knots $J$ and $K\#J$ are doubly slice, then $K$ is doubly slice.

This conjecture asks whether doubly sliceness admits cancellation under connected sum. It is presented as unanswered and concerns the structure of the double concordance group.