The equivariant slice-ribbon conjecture

Let $K$ be a periodic knot in $S^3$ whose periodic diffeomorphism extends to $B^4$ and preserves a slice disk; such a knot is called equivariant slice. It is called equivariant ribbon if the preserved slice disk is ribbon.

Equivariant slice-ribbon conjecture. An equivariant slice knot is equivariant ribbon.

This is a strengthening of the classical slice-ribbon problem to knots with a compatible periodic symmetry. The paper notes that all knots known at the time to be equivariant slice were equivariant ribbon, but does not establish the conjecture.