  We study indigenous bundles in characteristic p>0 with nilpotent p-curvature,
and show that they correspond to so-called deformation data. Using this
equivalence, we translate the existence problem for deformation data into the
existence of polynomial solutions of certain differential equations with
additional properties. As in application, we show that P^1 minus four points is
hyperbolically ordinary (in the sense of Mochizuki. We also give a concrete
application to existence of deformation data with fixed local invariants.
