Absence of polymer in the supernatant phase We assume that the supernatant phase does not contain any polymer. Ref., and also our experiments in Sec. 3.2, show that this is indeed a reasonable assumption for chains as short as M = 50, provided the two phase system is far enough from the critical point. Admittedly, because of this assumption, our method is unable to reconstruct the full phase diagrams, leaving the regions around the critical point unrendered. Nevertheless, as we show later, our method allows self-consistent assessment of its validity, and hence the requirement of sub-criticality can be tested.