The width bound for orientable surface knots

Let $F \subset \mathbf{R}^4$ be an orientable surface knot. Here $w(F)$ denotes the width of $F$, and $\operatorname{Braid}(F)$ denotes its braid index. Width bound conjecture. Then

$$w(F) \leq 2\operatorname{Braid}(F).$$

The bound is motivated by a local deformation near simple branch points of a surface braid, which can decrease the width by $2$. The source presents it as plausible; no resolution is supplied here.