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I understand every transaction can be verified if it belongs to a block by a merkle path which is basically a set of hashes that finally end up at the merkle root.

I know the merkle root is stored in the block header, but where is the merkle path (set of merkle hashes) of a transaction stored within the block?

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The merkle path is not stored explicitly within the block. It is calculated from the transactions in the block when requested by a client.

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