[mckirk]

Unless somebody builds a kind of 'pseudo-random-generator' chain where the internal state is huge, changes substantially each tick and is very expensive to compute, so that it becomes infeasible to store or recompute (a large number of) previous states for anyone but the most powerful players.

You could then use that internal state as a private key to sign what you want and only keep the corresponding public key and a signed date+time to proof the veracity. The public keys themselves would need to form a blockchain in the traditional sense, so you can verify their integrity without the previous internal states.

If you wanted to go all-in with the verification, you'd probably also want to show something containing the date+time in the video, together with some complicated physical effects that are hard to fake.

Well, just thinking out loud here, but it seems like it might work :D