Install the supplied branch and position as the navCache and return it.
Overrides: Abraham
Overrides: Abraham
Overrides: Abraham
Overrides: Object
Lookup the anchorTrace to find the branch hanging off it. If there isn't one,
then install branch as that branch. Otherwise walk a balanced walk down the
binary tree of branches to find a place to hang the new branch.
This should really create a new root, but that's harder to draw!.
re-initialize the non-persistent part
Overrides: Abraham
Return all the successors of the receiver in the trace tree.
Return the first used positions on all the successors of trace.