Conjecture on band number for ribbon surfaces of fixed genus

For a knot $K$, let its ribbon genus be the minimum genus of a ribbon surface bounding it, and let $b(K)$ denote its band number. Fixed-genus band number conjecture. For every genus $g$, there exists a knot $K$ with ribbon genus $g$ for which $b(K)$ is lower than the number of bands in any ribbon surface of genus $g$. This predicts that, even after fixing the ribbon genus, band number need not be realized by a ribbon surface of that genus. It is presented as a broader analogue of the conjectured distinction between band number and ribbon fusion number, and remains unresolved in the source.