The GLIN generation conjecture

Let $k$ be a field, and let $\operatorname{GA}_n(k)$ be the group of polynomial automorphisms. If $\operatorname{char}(k)\ne2$, let $\operatorname{GLIN}_n(k)$ be the smallest normal subgroup of $\operatorname{GA}_n(k)$ containing the linearizable polynomial automorphisms.

GLIN generation conjecture. If $\operatorname{char}(k)\ne2$, then

$$\operatorname{GLIN}_n(k)=\operatorname{GA}_n(k).$$

The paper motivates this by the inclusion of tame automorphisms in $\operatorname{GLIN}_n(k)$ and the result that the Nagata automorphism belongs to $\operatorname{GLIN}_n(\mathbb{C})$. The conjecture is presented as new and no resolution is reported.