  We produce a flexible tool for contracting subcurves of logarithmic
hyperelliptic curves, which is local around the subcurve and commutes with
arbitrary base-change. As an application, we prove that hyperelliptic
multiscale differentials determine a sequence of Gorenstein contractions of the
underlying nodal curve, whose dualising bundle they descend to generate. This
is the first piece of evidence for a more general conjecture about limits of
differentials.
