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how does the zk proof work? what are the advantages of this approach over utreexo where you download (to verify) but don't save the transactions?
A merkle tree IS A ZK PROOF. You prove something (an item is a node/leaf of the tree) without revealing the whole knowledge (all leaves).
It's used in Bitcoin for transactions - a more zk-proof-esque usage is in web crypto. When you connect to a website, the exsistence of a certificate revocation can be proven without downloading all certificates - just a few nodes in the tree.
Cryptographers often consider things like merkle trees or signatures not ZK proofs but to be categories on their own ... but they totally do prove a statement without revealing all the knowledge.