Definition
A merkle proof, also called an inclusion proof or merkle branch, is the compact set of hashes that lets anyone verify a single transaction is included in a block without possessing the block's entire transaction list. It is the mechanism that makes lightweight Bitcoin clients practical, because it converts what would be a multi-megabyte download into a few hundred bytes.
What the proof contains
In a merkle tree every leaf is the hash of a transaction and every parent is the hash of its two children, terminating in a single root stored in the block header. To prove a given transaction is a leaf, you supply only the sibling hash at each level of the tree, the "path" from leaf to root. For a block with thousands of transactions, that path is roughly log2(n) hashes, typically a dozen or so 32-byte values.
How verification works
The verifier starts with the transaction's own hash, repeatedly combines it with the supplied sibling hashes in order, and checks that the final result equals the merkle root already committed in the block header. If it matches, the transaction provably belongs to that block; if any hash is wrong, the recomputed root diverges and the proof fails. The verifier never has to trust the party that supplied the proof, only the proof-of-work securing the header.
This primitive underpins Simplified Payment Verification wallets and any system that audits Bitcoin without a full copy of the chain. It depends on the integrity of the merkle root and is closely related to the broader idea of a cryptographic accumulator.
In Simple Terms
A merkle proof, also called an inclusion proof or merkle branch, is the compact set of hashes that lets anyone verify a single transaction is…