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I'd like to know how irreversible state is recorded in the blockchain, whether it's a moving pointer, or it's recorded in another way.

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Every block produced by a block producer includes a header field that indicates the highest numbered block that they confirmed. Using this information, each of the block producers are able to determine the highest number block that has received (2/3)+1 confirmations, making it the last irreversible block.

You can see here for more information from Dan Larimer about how this process works and why it was adopted.

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