  We prove that in the absence of topological changes, the notion of BV
solutions to planar multiphase mean curvature flow does not allow for a
mechanism for (unphysical) non-uniqueness. Our approach is based on the local
structure of the energy landscape near a classical evolution by mean curvature.
Mean curvature flow being the gradient flow of the surface energy functional,
we develop a gradient-flow analogue of the notion of calibrations. Just like
the existence of a calibration guarantees that one has reached a global minimum
in the energy landscape, the existence of a "gradient flow calibration" ensures
that the route of steepest descent in the energy landscape is unique and
stable.
