= Perfect rose tree
A <rose tree> is perfect when all its <leaves of a rooted tree> have the same depth. This permits unequal branching counts and unary branches; perfectness alone does not require every internal <vertex> to have the same number of children. A bottom-up certificate returns `Just 0` at a leaf, `Just (h+1)` when all child certificates are `Just h`, and `Nothing` otherwise. <Structural induction> proves that a certificate exists exactly when the tree is perfect: all root-to-leaf routes acquire one edge when attached to the new root.
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