The mixedness conjecture for coefficient objects

Let $X_0$ be a smooth variety over $\mathbb{F}_q$, let $\ell$ be a prime, and let $\mathcal{E}_0$ be a $\overline{\mathbb{Q}}_{\ell}$-coefficient object on $X_0$. An object is $\iota$-mixed when its Frobenius eigenvalues satisfy the corresponding weight conditions under the chosen embedding $\iota:\overline{\mathbb{Q}}_{\ell}\hookrightarrow\mathbb{C}$.

Mixedness conjecture. Every $\overline{\mathbb{Q}}_{\ell}$-coefficient object on $X_0$ is $\iota$-mixed.

The paper states that this follows later from the Langlands correspondence, so the conjectural assertion is presented as known in the paper's subsequent development.