* receive all the transactions (or their hashes) that occurred
* sign this with some HMAC, and publish it
* then we know that the transactions occurred by X time
of course, the question is how do we know transaction A really occurred after X time? Perhaps some will claim it occurred before X, but just wasn't included by anyone in the network for X because they are discriminating against that transaction's participants, or something.And what if it was included by some in the network but not others? How do we know some are not cheating?
That's where proof-of-work comes in. You can also have proof-of-stake and other mechanisms, by which to solve the Byzantine Generals problem. How do we know that the signers aren't cheating? Who watches the watchers?