What are the concrete costs of Kaspa's chain membership proof in practice?

In the current Kaspa parametrization, adding chain membership proof support increases each block header by just 32 bytes — the size of a single hash — and the worst-case proof itself is about 9.5 kilobytes. Validating a block under this scheme requires computing only 33 hashes, and that step can be skipped entirely for blocks that fall outside the selected chain. The proof size and verification time both scale as θ(log(N)loglog(N)), meaning they grow very slowly even as the blockchain gets longer. For a beginner, 9.5 KB and 33 hashes are tiny numbers — this is a compact, fast system, not a heavy burden on the nodes that keep the network running.