Conservativity conjecture for realization functors of motives

Let $k$ be a base field and consider the diagram of categories of motives and realization functors described in the paper, with rational coefficients. A morphism of motives is tested by its image under each functor in this diagram. Conservativity conjecture. All functors in the diagram are conservative: a morphism between motives is an isomorphism whenever its image under one of these functors is an isomorphism. This conjecture concerns whether the listed realizations detect isomorphisms; it is presented as out of reach in full generality, although special cases can be proved.