Repetition-threshold formula for rich sequences

Let $\mathcal{C}_d$ be the class of $d$-ary sequences rich in palindromes. For each $n\in\mathbb{N}$, let $\mathbf{u}_n$ denote the sequence defined in the paper by the corresponding morphism, and let $E^*(\mathbf{u}_n)$ be its asymptotic critical exponent. Repetition-threshold formula. The repetition threshold is

$$\mathrm{RT}(\mathcal{C}_d)=E^*(\mathbf{u}_{2d-1})$$

for every $d\in\mathbb{N}$ with $d\geq 2$. This is presented as a suggestion based on estimates and examples, rather than as an established result; its resolution is not given in the supplied text.