I've watched some parts of [1] on youtube, and it seems the riposte system is on the machines in the post office. if it is also used in headquarters, I don't know. they have messages that have incremental sequence numbers to identify the replicates messages.
messages are put into the message store where each message has a checksum. when a message is read and gives a CRC error, someone raises a call, and they rebuild the message store. which recalculates the checksums, I assume.
CRC errors can be caused by data corruption on the counters. so this implies data is stored on the counters. when they rebuild the message store it seems they can use data from the other counter which hopefully has no corrupted message (but the former software engineers can't quite remember if this was true, at least she says so). so it seems they have redundancy between these counters. when CRC erros happen often, they'll replace the counter.
I also assume they describe the Horizon system pre-2010.
[1] "Anne Chambers - Day 67 AM (26 September 2023) - Post Office Horizon IT Inquiry", https://www.youtube.com/watch?v=q72zvd9Iz3Q