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If not, then why is it often claimed that the blockchain scaling issue is due to the fact that all tx has to be verified by all full nodes?
As long as a mining node found the correct nonce, the tx will be added to the block and the blockchain advances. It does not matter if the tx is not yet verified by some full nodes in the network.
(Yes, it will most probably get verified by all full nodes after it got into the block and the block propagates throughout the network. But this is not relevant as the blockchain already advanced (assuming there is no fork).)
Thanks. I know everything you said here, but still think it doesn't really answer the question. Indeed all tx will eventually get verified, but when there is no fork, blockchain do advance before the latest transactions get verified by all full nodes, right? When there is fork – Danny – 2018-11-08T06:59:18.177
Indeed the blockchain grows for any nodes that know about the new block. But, it does not grow for the nodes who do not know about it. Each nodes stores a copy of the longest blockchain that they know about. – JBaczuk – 2018-11-08T12:51:47.923