Rate invariance and scallop theorem in viscosity gradients

Could you have survived Boston's Great Molasses Flood of 1919? Probably not, according to Purcell's Scallop Theorem, swimming in molasses is nearly impossible. The theorem tells us that, at zero Reynolds number, no swimmer who deforms their body a time symmetric fashion able move. In this paper we consider such swimmer, but introduce symmetry breaking by considering an inhomogeneous environment variable viscosity. We prove that the still unable move, showing Theorem stronger than thought.