Ribbon number additivity under connected sum

Let $K_1$ and $K_2$ be ribbon knots, and let $r(K)$ denote the minimum ribbon number of a ribbon disk for $K$. Ribbon number additivity conjecture. If $K_1$ and $K_2$ are ribbon knots, then

$$r(K_1 \# K_2)=r(K_1)+r(K_2).$$

The subadditivity inequality is immediate by taking the connected sum of minimizing ribbon disks, but equality is unknown in general. The conjecture is known when $g(K_i)=r(K_i)$ for both knots, including the examples $T_{p,q}\#\overline{T_{p,q}}$ discussed in the paper.