The chart simplification conjecture for branched covering surface-knots

Let $(F,\Gamma)$ be a branched covering surface-knot of degree $N$. The quantities $u(F,\Gamma)$ and $u_w(F,\Gamma)$ denote, respectively, the maximum and weak maximum numbers of 1-handles required in the relevant chart simplification processes.

Chart simplification conjecture.

$$u(F,\Gamma) \leq \max\{u_w(F,\Gamma),N-1\}.$$

This conjecture predicts that the simplification number is controlled by the weak simplification number and the degree. It is presented here as a conjecture previously given in the cited work; no resolution is supplied in the source.