Thue–Morse continued-fraction algebraicity conjecture

Let $a,b$ be two distinct elements of $\mathbb{F}_2[z]\backslash\mathbb{F}_2$, and let $\mathbf{u}(z)$ be the $(a,b)$-Thue–Morse sequence. Thue–Morse continued-fraction algebraicity conjecture. The continued fraction $\operatorname{CF}(\mathbf{u}(z))$ is algebraic of degree $4$ over $\mathbb{F}_2(z)$. This conjecture concerns the algebraicity and exact degree of continued fractions whose partial quotients are generated by a Thue–Morse sequence over $\mathbb{F}_2[z]$; its status is not resolved in the supplied source.