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Is it correct to say that in the bitcoin network, there are different versions of ledgers (although the longest chain is the correct one)?

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No, there is only one blockchain which is Bitcoin. There are no different versions or different blockchains that other people are using that are also Bitcoin. Such things do not exist. Such other blockchains that are forked from Bitcoin are not Bitcoin but rather altcoins.

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  • There are some orphaned blocks, sure, but as you say there is only one blockchain. – Willtech Apr 15 '18 at 7:51
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No, there is only a single ledger in the Bitcoin system. We call Bitcoin's ledger the UTXO set (Unspent Transaction Output set).

The point of a money is to track the purchasing power of its participants. Bitcoin does this by recording all transactions that ever occurred in the Bitcoin blockchain, it's "transaction journal". As long as all nodes enforce the same consensus rules, the mining process will cause a single "best chain" to emerge which means that the whole network converges on a single ground-truth. Bitcoin nodes replay and verify the complete blockchain to calculate the current UTXO set and thus synchronize with the network.

For a different ledger to emerge, there would need to be a disagreement in the consensus rules. However, when someone changes the rules their node follows unilaterally in an incompatible manner, they are departing the Bitcoin network. This new network that their node creates is incompatible and thus would be a new forkcoin, not Bitcoin.

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