We use the notations if a slot is empty, if is given to only one late honest party behind the current slot and if is given to only one synchronized honest party. In Ouroboros Genesis, the best chain can be the longest chain or the chain which is forked long enough and denser than the other chains in some interval. Liveness is the result of the chain growth and chain quality properties. Proof: We define two types of slot. Springer, Cham,
Having late parties in BABE influences chain growth. In this case, the epoch length has to be around 3. The next day, Hoggett sees Babe sort the hens, separating the brown from the white ones. In Ouroboros  and Ouroboros Praos , the best chain valid chain is the longest chain. Fly is so anxious to find out whether he is guilty or innocent that, instead of barking orders at the sheep, she talks to them to find out what happened.