The mixed twistor structure conjecture for relative higher Malcev completion

Let $X$ be a projective variety, and let $\rho$ be a reductive representation of its fundamental group, assumed reductive after restriction to the fundamental group of the normalization. Let $Malc(X_B,\rho)/\mathbb C$ be the relative Malcev completion of the higher homotopy type. Mixed twistor structure conjecture. The completion carries a natural mixed twistor structure. This is presented as a generalization of the preceding mixed Hodge structure claim, with the relevant twistor notion cited externally; no resolution is given.