Jamet, Popoli, and Stoll's maximum order complexity conjecture for the Fibonacci-Thue-Morse sequence

Let $\alpha=(1+\sqrt{5})/2$ be the golden ratio, let $\bf ftm$ be the Fibonacci-Thue-Morse sequence, and let $M_{\bf ftm}(n)$ denote its maximum order complexity at length $n$. Jamet, Popoli, and Stoll's conjecture.

$$M_{\bf ftm}(n)\sim\frac{n}{1+\alpha^2}.$$

This conjecture gives the expected asymptotic growth of the maximum order complexity of the Fibonacci-Thue-Morse sequence. The paper recalls a lower bound of order $n/(\alpha+\alpha^3)$, but the conjectured asymptotic equivalence is not resolved in the supplied context.