The finite-level ell-independence conjecture for unipotent fundamental groups

Let $X/F$ be a geometrically connected variety with base point $x\in X(F)$. For each $\u0**eell$, let $\hat{\mathcal{U}}_{\u0**eell,X,x}$ be the completed universal enveloping algebra of the Lie algebra of the ell-adic unipotent fundamental group, and let $\mathfrak{a}_{\u0**eell,X,x}$ be its augmentation ideal. Fix $k\geq 1$. Finite-level unipotent ell-independence conjecture. The system $\{\hat{\mathcal{U}}_{\u0**eell,X,x}/\mathfrak{a}_{\u0**eell,X,x}^k\}_{\u0**eell}$ of $W_F'$-representations is (weakly) ${\mathbb Q}$-compatible. This is presented as a weakening of the conjecture for the full unipotent fundamental group; the source does not indicate that it has been resolved.