Original question: When 51% or more of consensus participants validate any transaction for recording on-chain, against what evidence are they validating? Original Answer: Each transaction is broadcast, and the slot leader creates a block from all of the transactions in a given slot. That block is then broadcast to the rest of the network. The network relays the blocks until everyone has a copy, and each time a block is relayed, information about the sender is verified. See Ouroboros Praos for the set of properties tested when receiving a transaction.
Additional question related to original: What I really wanted to explore was whether the data required for truly validating the correctness of any transaction is viewable to the participants or if it’s held confidential (like it might be encrypted) would that validation really mean anything? With bitcoin, everyone can see whether you have enough coin to give away what you propose to give; but if there’s a scheme where information like that is confidential, then the validation means nothing and few would want to participate in a transaction that cannot be validated. There will be some contradictions that will find their ways into these new systems.