Hash ladders from leaves to root.

A Merkle tree takes every tx id, hashes it, then hashes pairs of hashes, and keeps going until only one hash remains. That top hash, the root, represents the entire set. Change one leaf and every parent above it, including the root, flips.

To prove a leaf is included, you don’t send the whole tree—just the sibling hashes along the leaf’s path. Anyone can rebuild the root from the leaf + proof and check it against the published root.

Building a tree costs work, but checking a proof is fast: hash the leaf, mix in siblings in order, and compare the result to the root. If it matches, the leaf belonged to the original set; if not, the data was tampered with.