I understand that, but what about the round itself? Surely there's a case where a given round can be submitted with a separate set of transactions, leading to a fork?
Btw, worldwide network propagation using gossip is on average 15s, that's why ETH's block time is around there.
We're trying to prove in the paper that actually there's no such case where a fork happens involuntarily.
That's the purpose of the synchronization phase, to make sure that forks happen only when nodes explicitly want them to happen. Nodes will keep making round proposals until they're sure that they've got a consensus. If nodes can't agree within a certain number of rounds, it's actually in their interest just to void the round.
If you're aware of a specific case when an involuntary fork can happen, please let us know.
Do you have any reference for the 15s gossip time? All of our testing showed much lower numbers in the order of a few seconds at most, if all you needed to gossip what in the order of a few hundred bytes. Blocks are much larger though, and that's why I'd imagine a disparity could come from.