Grothendieck–Teichmüller conjecture

Let $\widehat{\operatorname{GT}}$ be the profinite Grothendieck–Teichmüller group and let $G_\mathbb{Q}$ be the absolute Galois group of $\mathbb{Q}$. Grothendieck–Teichmüller conjecture. Combining the conjecture that $\widehat{\operatorname{GT}}$ is the automorphism group of the profinite Grothendieck–Teichmüller tower with Grothendieck's conjecture yields

$$\widehat{\operatorname{GT}}\cong G_\mathbb{Q}.$$

The statement is derived in the source from the two preceding conjectures, so its status depends on those conjectures; no resolution evidence is supplied.