Strong growth-order conjecture for valence sequences

Let $\sigma_1$ and $\sigma_2$ be valence sequences with $\sigma_1<\sigma_2$, and let $\underline{\lambda}_\sigma$ and $\overline{\lambda}_\sigma$ denote the lower and upper bounds of growth rates among face-homogeneous tessellations with valence sequence $\sigma$. Strong growth-order conjecture.

$$\overline{\lambda}_{\sigma_1}\leq\underline{\lambda}_{\sigma_2}.$$

This is proposed as a sharper version of the paper's growth-order conjecture. The source does not state whether it has been resolved.