I'm just trying to figure out under what circumstances we could consider a completely artificial entity a continuation of our existence. As you pointed out, merely containing our knowledge isn't enough. Human knowledge is a constantly growing edifice, where each generation adds to and build upon the successes of the past. I wouldn't expect an AI to find value in everything we have produced, just as we don't. But if our species were wiped out, I would feel comfortable calling an AI which traveled the universe occasionally writing McCartney- or Lennon-inspired songs "us." That would be survival. (I could even deal with a Ringo Starr AI, in a pinch.)