They give him a secret password, first extracting a promise that he will treat them better from now on. So, the common prefix property still preserved with the dynamic update. All these chains have some common blocks, at least the genesis block, up until some height. Sheep: [to Babe] Well, I wouldn't call that a bite myself. Duchess: Well, they say you've forgotten that you're a pig.
In brief, all block producers have a verifiable random function VRF keys which they register with locked stake. Duchess: Definitely, they call it. We suppose each validator has a set of chains in the current slot in the epoch.