In most cases, this is going to come back to third-party services – think about the history of things like mailing a copy of a document to yourself using registered mail or having it notarized so the timestamp would be admissable in court. I'd be surprised if we haven't already seen someone submit timestamps from something like Facebook in court but we could use a general notary-as-a-service for this kind of app as more and more of the world moves online.
That won't help with a determined fraud from the beginning but that's always been a challenge in the court system and so most of that will come down to continuing to break down the attitude that digital data is somehow immune to the same trust issues as every other human artifact.
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