Goussarov–Habiro conjecture for finite type invariants of string links

Let string links be proper tangles without closed components, and let two string links have the same number of components. They are Goussarov–Habiro conjecture. Two string links of the same number of components share all finite type invariants of order less than $k$ if and only if they are $C_k$-equivalent. The theorem of Goussarov and Habiro establishes the analogous statement for knots, while for links the only-if direction fails in general. This conjecture asks whether the characterization extends to string links.