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I am reading about the Merkle tree, I've read that in a block we store just the root of the tree. To check if a ttransaction is included in the Merkle tree we need to use the transaction's Merkle path. The question is where the Merkle tree is stored? How would a node given a path check if the leaf belongs to the Merkel tree?

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The Merkle tree is not stored anywhere.

It is implicitly defined by the transactions in a block. Whenever needed, the portion of it that is needed is computed on the fly using the transaction identifiers.

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