  Covtree - a partial order on certain sets of finite, unlabeled causal sets -
is a manifestly covariant framework for causal set dynamics. Here, as a first
step in picking out a class of physically well-motivated covtree dynamics, we
study the structure of covtree and the relationship between its paths and their
corresponding infinite unlabeled causal sets. We identify the paths which
correspond to posts and breaks, prove that covtree has a self-similar
structure, and write down a transformation between covtree dynamics akin to the
cosmic renormalisation of Rideout and Sorkin's Classical Sequential Growth
models. We identify the paths which correspond to causal sets which have a
unique natural labeling, thereby solving for the class of dynamics which give
rise to these causal sets with unit probability.
