> a bit like a bunch of Git repositories constantly pushing commits (messages) to one another.
Why would you need to do that? Why not just give every message a timestamp, make sure they get sent, and sort the messages on the receiver side? If you're really concerned about message order, you could give every message a unique id, and send out the id of the previous message with every message, and improve your sort function accordingly.
Absolute timestamps cannot be trusted in a byzantine environment, so we do precisely as you suggest - messages are transmitted with pointers to the previous message(s) in the room message graph, so you get a partial ordering within the room (just like git). We also sign the messages into a merkle graph (like git) to stop the shared datastructure being tampered with.
Why would you need to do that? Why not just give every message a timestamp, make sure they get sent, and sort the messages on the receiver side? If you're really concerned about message order, you could give every message a unique id, and send out the id of the previous message with every message, and improve your sort function accordingly.