Larsen's Galois maximality conjecture for compatible systems

Let $K$ be a finitely generated field, let $X$ be a smooth projective variety over $K$, and consider a $\mathds{Q}$-compatible system of Galois representations

$$\{\rho_{\ell} \colon G_K \to \operatorname{GL}(\operatorname{H}^{i}_{\operatorname{\acute{e}t}}(X_{\overline{K}},\mathds{Q}_{\ell}))\}.$$

Let $\mathbf{G}_{\ell}^{\operatorname{sc}}$ be the simply connected cover of the adjoint algebraic monodromy group, and let $\Gamma_{\ell}^{\operatorname{sc}}$ be the inverse image of the adjoint Galois image in $\mathbf{G}_{\ell}^{\operatorname{sc}}(\mathds{Q}_{\ell})$. Larsen's Galois maximality conjecture. For all sufficiently large primes $\ell$, $\Gamma_{\ell}^{\operatorname{sc}}$ is a maximal compact subgroup of $\mathbf{G}_{\ell}^{\operatorname{sc}}(\mathds{Q}_{\ell})$. Moreover, it is hyperspecial: there exists a smooth affine group scheme $\mathscr{G}_{\ell}^{\operatorname{sc}}$ over $\mathds{Z}_{\ell}$ such that

$$\mathscr{G}_{\ell}^{\operatorname{sc}}(\mathds{Z}_{\ell})=\Gamma_{\ell}^{\operatorname{sc}}.$$

This is presented as a weaker form of the Galois maximality conjecture for arbitrary smooth projective varieties. The supplied text gives no resolution status for this assertion.