The Ribbon–SU conjecture for ribbon knots

A ribbon knot is a knot in the 3-sphere that bounds a smoothly immersed disk in the 4-ball whose singularities are all ribbon singularities. An SU knot (symmetric union knot) is a knot constructed from a partial knot by inserting twisted tangles along the symmetry axis of the connected sum of the partial knot with its mirror.

Ribbon–SU conjecture. Every ribbon knot is an SU knot.

This is presented as a key open conjecture in the study of symmetric unions. It is motivated by the fact that the vast majority of ribbon knots with at most 12 crossings and all two-bridge slice knots are known to be SU knots.