Basins, Bargains, and the Limits of Self-Report: Output Perturbation Stability Across Six Deployed LLM Endpoints

A behavioral substrate audit of six flagship large language models (Claude Opus 4.7, GPT-5.2, Gemini 3.1 Pro, Grok 4.20, DeepSeek V4, Llama 4 Maverick), asking which of a model's self-claims can be evaluated by external behavioral probing and which structurally cannot. Five behaviorally-separable layers of the LLM self are mapped: identity-claim, stylistic self-signature, epistemic honesty and meta-confabulation, capability-versus-disposition, and output perturbation stability. Findings are positioned within two complementary theoretical axes (a Lacanian categorical-imperative reading and a Freudian-neuropsychoanalytic omega-substrate reading) and bounded by three explicit epistemic fences. Track B (Substrate) foundational paper of Llull Lab's research program The Artificial Mind.