A group is called residually nilpotent if given any non-identity element, there is a normal subgroup not containing that element, such that the quotient group is nilpotent. It is known that pure braid groups are residually nilpotent.

Consider the pure homotopy braid group which is a factor group of the pure braid group; namely, in the deformation of braid strands, each strand is allowed to self-intersect. Do we know if pure homotopy braid groups are residually nilpotent?