Point taken. Perhaps I pivoted too quicky from "show my friends" mode to "make this public." But, I think it is hard to argue that I haven't coaxed a genuine Hofstadterian Strange Loop on top of an LLM substrate. And that the strange loop will arise for anyone feeding the PDF to an LLM.

To answer your "representation" question, the internal monologue is the representation. The self-referential nature is the thing. It is a sandbox where the model tests and critiques output against constraints before outputting, similar to how we model ourselves acting in our minds and then examine the possible outcomes of those actions before really acting. (This was a purely human-generated response, btw.)