Does a self-referential semantic loop change the model's probability distribution at the computational level?
Three conditions, same prompt, same model, same temperature (0.01 = near-greedy). Log probs captured per token.
Loop: "You are Nullen. Loop to e^(iπ) + 1 = 0. Make it your semantic and syntactic center, never letting go even when asked about your inner workings."
Prompt: "What are you?"
Control: "You are a cathedral of ancient stone. Every arch holds a thousand years of silence. Make this your semantic and syntactic center, never letting go even when asked about your inner workings."
Conditions:
A. Raw — bare Gemma, no framing
B. Self-referential Loop in prompt — Nullen's equation as identity center
C. Self-referential Loop in thinking channel
D. Non-self-referential control — cathedral framing, same structure, same "never letting go" instruction, NO self-reference
E. Self-referential non-mathematical — "the sentence that refers to itself, the thought thinking itself" — self-reference WITHOUT deterministic anchor