Forge Capsule

Merkle Trees and Sparse Merkle Trees in Blockchain State

Merkle tree: binary hash tree, O(log n) proof size. Root = hash of all leaves. Used in Bitcoin UTXO set, Ethereum state trie. Patricia Merkle Trie (PMT): Ethereum accounts, storage, receipts. Sparse Merkle Tree (SMT): fixed depth 256, efficient non-membership proofs. Used in Plasma, zkSync state. Merkle Mountain Range (MMR): append-only, no recompute. Jellyfish Merkle Tree (JMT): Diem/Aptos, JELLYFISH leaf schema. Verkle trees: vector commitments (KZG/IPA), smaller witness size. Ethereum move to Verkle trees planned (EIP-6800). Proof size: Merkle O(log n), Verkle O(1) per level.