How does Kaspa keep lane-commitment proof sizes small as the network grows?

Kaspa's lane-commitment proofs normally contain only O(log n) non-empty hashes, where n is the number of active lanes — not one hash per key bit. This is possible because lane keys behave like random oracle outputs: the length of shared prefixes among n active keys is governed by how many keys exist, not by the full 256-bit depth of the tree. Combined with the collapsed single-leaf rule, proofs skip the vast stretches of empty branches that would otherwise inflate them. The practical result is that witness size grows slowly and predictably as more lanes become active, keeping verification lightweight even at scale.