Prove that one item belongs to a set using a short path of hashes.
LET’S PICTURE IT
A big family tree of fingerprints lets you check one leaf by carrying its siblings on the way to the top.
SEE IT FOR YOURSELF
Build a root and follow one membership proofStep 1 / 4
This example hashes UTF-8 A, B, C and D. The displayed hashes are abbreviated, and the tree uses the playground’s sorted-pair convention.
This example hashes UTF-8 A, B, C and D. The displayed hashes are abbreviated, and the tree uses the playground’s sorted-pair convention.Each pair of raw child hashes is sorted, concatenated and hashed. The resulting parent fingerprints commit to their children.Hash the two parents under the same rule to obtain one root commitment. Changing a leaf changes the hashes on its path.The highlighted siblings are B and hash(C,D). Starting with A, the verifier recomputes its path and compares the final result with a trusted root.
Animated local teaching model. No wallet, RPC or live blockchain data. Some labels and hashes are abbreviated for readability.
Build from the bottom
Hash each item to create leaves. Combine neighboring leaf hashes and hash them into parents. Repeat until a single root remains. Change one item and the hashes along its path change, including the root.
A proof carries siblings
To check a leaf against a trusted root, use the sibling hash at each level and recompute the path. With a balanced binary tree, this takes far fewer hashes than sharing every item. The proof only means something if you know which root you trust.
Conventions must match
Our Merkle playgroundhashesUTF-8 items, sorts each pair of hashes, concatenates the raw bytes and hashes the pair. An unpaired last node is promoted. This is an educational convention; it is not Ethereum’s state-trie format or a drop-in proof for every allowlist contract.
Roots are commitments
A successful proof shows membership under the chosen hashing and tree rules. It does not show that the data is truthful or that the root came from the right source. Ethereum uses more specialized authenticated structures for state; read the primary reference to explore that next.