  We make precise and prove a conjecture of Klivans about actions of the
sandpile group on spanning trees. More specifically, the conjecture states that
there exists a unique ``suitably nice'' sandpile torsor structure on plane
graphs which is induced by rotor-routing.
  First, we rigorously define a sandpile torsor algorithm (on plane graphs) to
be a map which associates each plane graph (i.e., planar graph with an
appropriate ribbon structure) with a free transitive action of its sandpile
group on its spanning trees. Then, we define a notion of consistency, which
requires a torsor algorithm to be preserved with respect to a certain class of
contractions and deletions. Using these definitions, we show that the
rotor-routing sandpile torsor algorithm is consistent. Furthermore, we
demonstrate that there are only three other consistent algorithms on plane
graphs, which all have the same structure as rotor-routing.
  We also define sandpile torsor algorithms on regular matroids and suggest a
notion of consistency in this context. We conjecture that the
Backman-Baker-Yuen algorithm is consistent, and that there are only three other
consistent sandpile torsor algorithms on regular matroids, all with the same
structure.
