The noncommutative formal Galois group bijectivity conjecture

Let $\mathcal{NCF}_{L/k}$ be the noncommutative formal deformation functor and let $\widehat{QG}_{3,q}$ be the corresponding formal quantum Galois group; Proposition 6.8o gives a functorial injection

$$\mathcal{NCF}_{L/k}\longrightarrow\widehat{QG}_{3,q}.$$

Noncommutative formal Galois group conjecture. If $q$ is not a root of unity, the injection in Proposition 6.8o is a bijection. Consequently,

$$\mathcal{NCF}_{L/k}\simeq\widehat{QG}_{3,q}.$$

This conjecture identifies the noncommutative formal deformation functor with the formal quantum Galois group; the supplied text gives no resolution status.