A Merkle tree organizes data hashes into a tree whose top hash, the Merkle root, summarizes the committed collection. Each parent is calculated from its children according to specified rules. Altering a leaf generally changes the hashes along its path to the root.
Verifying one item
An inclusion proof supplies the neighboring hashes needed to recompute that path, rather than every item in the collection. In a balanced binary tree with eight leaves, proving one leaf typically requires three sibling hashes plus its position information. The verifier also needs the item or its hash and a trustworthy root.
Use in Bitcoin
Bitcoin commits transaction identifiers to a Merkle root in each block header. Its construction specifies transaction ordering, pair hashing and duplication when a level has an odd number of entries. Other systems can use different tree structures and encoding rules.
What a proof establishes
A valid proof shows that an item belongs to the collection represented by the reference root, under the hash assumptions. It does not independently prove transaction validity, current unspent status or chain finality. Nor does the root reveal all underlying data: those data must still be available elsewhere for full checking.