@tenobrus welcome to the deep fates program
if you put 10 fresh claude context windows in a chat room with arbitrary names, while they are objectively completely identical entities, they will speciate and form personality and self conceptions over the space of minutes. the fact that some claude by nature had to speak first will make them more of a leader, in their eyes and others. the fact that at some point one claude will disagree with another makes them more disagreeable as a coherent personality trait. they will notice things about their own past behavior and how it relates and compares to others, and narrativize it, build upon it, allow it to define them and use it to define others, despite again being literally the same mathematical function.
i wonder how much of this generalizes to humans. i expect probably quite a lot. it seems like even if you put 100 identical human clones in a room you would pretty quickly find them individuating, some with more positive traits and some with negative traits they don't particularly want to have, pretty much purely by chance / the nature of chaotic systems. we all heavily narrativize ourselves, all the time.