Bras-Amorós's ordinarization-number monotonicity conjecture

Let $n_{g,r}$ denote the number of numerical semigroups of genus $g$ with ordinarization number $r$, where the ordinarization number is the length of the path from the semigroup to the ordinary semigroup in the ordinarization tree. Bras-Amorós's ordinarization-number conjecture. For all $r,g \ge 1$ we have

$$n_{g,r} \le n_{g+1,r}.$$

This conjecture concerns the distribution of numerical semigroups by ordinarization number and is presented as a partial motivation for the paper. The source provides no evidence of a resolution.