Merkle root

The Merkle root is the final hash at the top of a Merkle tree. It's computed by pairwise-hashing leaves, then pairwise-hashing those hashes, level by level, until a single 32-byte value remains. That value commits to every leaf: change any leaf and the root changes.

For LearnCoin, the Merkle root is what gets written to Base L2 as the anchor transaction's calldata. One 32-byte value commits to every credential in a batch, regardless of how many credentials are in the batch. The verification path from a specific credential to the root is logarithmic in batch size — about 13 hashes for a 10,000-credential batch.

The root alone isn't a valid "proof of inclusion" for any specific credential — you need the path too. The root proves the batch exists; the path proves a specific credential is in the batch. Together they close the verification loop.