Gabbard's equivariant sliceness conjecture for a strongly invertible 2-knot

Let $(J,\tau)$ be the strongly invertible $2$-knot referred to in Gabbard's Theorem 5.8. Gabbard's equivariant sliceness conjecture. The knot $(J,\tau)$ does not bound an equivariant $3$-ball. This conjecture arises from an example of a cyclic action on $S^1\times B^3$ with no evident invariant parting $3$-ball; an equivariant $3$-ball would yield a $3$-sphere with unusually strong properties. Its resolution is left open in the source.