The growth-rate order conjecture for standard PCP zig-zags

Fix $m\geq 2$, and let $f_1,f_2\in\operatorname{PA}(m)$ be $m$-modal standard PCP zig-zags of pseudo-Anosov type. Let $\lambda_i$ be the growth rate of $f_i$, and let $\Phi(f_i)=q_i$, where $\Phi$ is the bijection from Theorem. Growth-rate order conjecture.

$$\lambda_1<\lambda_2\iff q_1<q_2.$$

The conjecture asserts that the association between growth rates and the rational parameters preserves linear order. The supplied text says it will be treated in a forthcoming paper and gives no resolution.