  We investigate a variant of the chip-firing process on the infinite path
graph: rather than treating the chips as indistinguishable, we label them with
positive integers. To fire an unstable vertex, i.e. a vertex with more than one
chip, we choose any two chips at that vertex and move the lesser-labeled chip
to the left and the greater-labeled chip to the right. This labeled version of
the chip-firing process exhibits a remarkable confluence property, similar to
but subtler than the confluence that prevails for unlabeled chip-firing: when
all chips start at the origin and the number of chips is even, the chips always
end up in sorted order. Our proof of sorting relies upon an independently
interesting lemma concerning unlabeled chip- firing which says that
stabilization preserves a natural partial order on configurations. We also
discuss some extensions of this sorting phenomenon to other graphs (variants of
the infinite path), to other initial configurations, and to other
Cartan-Killing types.
