The finite-determinant conjecture for the associated F-isocrystal

Let $(V,\nabla,\mathit{Fil}^{\bullet},\Phi)$ be the Fontaine–Faltings module corresponding to a representation, and let $q'$ and $\lambda$ be as in the construction over $\mathbb{Q}_{q'}$. Consider the determinant object $(\det V,\det\nabla,u\det\Phi)$ for a unit $u\in\mathbb{Z}_{q'}^*$.

Finite-determinant conjecture. There exist elements $u\in\mathbb{Z}_{q'}^*$ such that $(\det V,\det\nabla,u\det\Phi)$ corresponds to a finite character of

$$\pi^{\mathrm{et}}_1\left(\mathbb{P}^1_{\mathbb{Q}_{q'}}\setminus\{0,1,\infty,\lambda\}\right).$$

Finite determinant is needed to apply the $\ell$-to-$p$ companion theorem to the associated $F$-isocrystal. The supplied text gives no resolution of this assertion.