> It's honestly embarrassing for the OP

I don't get this. People can use mathematical terminology in non-precise ways, they do so all the time, to get rough ideas across that otherwise might be hard to explain.

Just because OP uses the word "eigenvector" doesn't mean that he's offering some grand unifying theory or something - he's just presenting a fun idea about how to think about ChatGPT. I mean, isn't it obvious that there's nothing you can really "prove" about ChatGPT without having access to the weights (and even still, probably not too much).