Ribbon number of a knot and its mirror connected sum

Let $K$ be a knot, let $\overline{K}$ denote its mirror image, let $r(K)$ denote the minimum ribbon number of a ribbon disk for $K$, and let $c(K)$ denote the crossing number of $K$. A knot is alternating if it admits an alternating diagram, and it is non-ribbon if it is not ribbon. Ribbon-number conjecture for alternating knots. If $K$ is a non-ribbon alternating knot, then

$$r(K\#\overline{K})=c(K)-1.$$

This conjecture concerns equality in the paper's general ribbon-number inequality and isolates the expected value for connected sums of non-ribbon alternating knots with their mirrors. The paper presents it as an open direction for future research.