Conway knot ribbon minimality conjecture

Let $C=11n_{34}$ denote the Conway knot. It has Alexander polynomial $1$ and is topologically slice but not smoothly slice. Conway knot ribbon minimality conjecture. The Conway knot $C$ is ribbon minimal. Computational experimentation provides evidence for this claim, but the source states no proof; a proof would also bear on a folk conjecture concerning crossing numbers under ribbon concordance.