DFS Order Matters

The specific DFS order (which child you visit first) does not change correctness. Subtrees still map to ranges.

But if you want reproducible $tin$ values for debugging, use consistent child ordering (sorted by node number). In production, any DFS order works. Be consistent within a single run. This traversal order captures the tree structure in a way that makes range queries possible. If you change the DFS order, the timestamps change, but the technique still works. This property holds regardless of which child you visit first.