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"In a Bitcoin, the signatures are an integral part of the chain. Carol can only verify the complete chain of ownership if all the signatures exist because if even a single signature is missing, the chain breaks down…there’s no way to follow it through. A Segwit coin is different because the signatures are all outside of the chain. If even none of the signatures exist, or maybe none of the signatures were even real to begin with, Carol can still validate the chain of custody. I’m using the word custody instead of the chain of ownership, because Segwit really only shows custody.”
https://news.bitcoin.com/segregated-witness-removes-one-of-bitcoins-data-integrity-checks/