Ribbon–symmetric union conjecture for ribbon knots

A knot $K$ is a symmetric union if it is obtained from the connected sum $J\#-J$ of a knot $J$ with its mirror $-J$ by replacing trivial 4-tangles intersecting the symmetry axis with 4-tangles twisted along the axis. Ribbon–symmetric union conjecture. Every ribbon knot is a symmetric union. Symmetric unions are a broad class of ribbon knots and include all ribbon 2-bridge knots, but it remains open whether every ribbon knot admits a symmetric union diagram.