  Mochizuki's work on torally crys-stable bundles has extensive implications
for the theory of logarithmic connections on vector bundles of rank 2 on
curves, once the language is translated appropriately. We describe how to carry
out this translation, and give two classes of applications: first, one can
conclude almost immediately certain results classifying Frobenius-unstable
vector bundles on curves; and second, it follows from prior results of the
author that one also obtains results on rational functions with prescribed
ramification in positive characteristic.
