Finality in a Proof-of-Work (PoW)
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In a proof-of-Work (PoW) system, finality is typically achieved through the use of confirmations, which refer to the number of blocks that have been added to the chain after a particular block. The more confirmations a block has, the more secure it is considered to be. From the :
"The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of CPU power."
A chain can split into two different forks when two different miners mine a block at the same time. When that happens, it is quite difficult to determine which fork is the valid chain. Once one of the chains validates a block before the other chain completes it becomes the longest chain. The longest chain is the one with the longest most valid blocks attached.
The longest chain becomes officially the accepted chain and the transactions mined on the shorter chain are rejected. However, it is possible the transactions rejected on the shorter chain have been included in other blocks on the longest chain.