LLM "curving" via prompting

Genuine question on methodology, not the prose: how are MAP 1–4 actually generated?

None of Gemini, Copilot, Claude, GPT, Grok, DeepSeek, Qwen, Kimi, GLM, Gemma, Step, or Nemotron expose hidden states, attention weights, or manifold geometry through a standard chat prompt closed APIs return text completions only. A prompt, however carefully worded, can’t reach activation tensors it has no access to. So “internal channel width” “phase space drift” and “gravity well density” have to be coming from somewhere outside the model itself: either (a) a script computing some proxy metric on the output text (embedding distances, token entropy, etc.) and relabeling it with physics terms, or (b) the model generating numbers that sound plausible because the prompt asked it to role-play having this internal structure in which case the chart reflects the model’s compliance with your framing, not a measurement of anything inside it.

Both could be interesting on their own terms, but neither is “perturbing the manifold.” The core terms self-attraction, self-organization, gravity well also don’t map to standard mechanistic interpretability vocabulary, so right now they’re doing rhetorical work, not measurement work.

Happy to be wrong here if there’s actual white-box access (open weights + hooks via transformers/TransformerLens/nnsight), that changes the whole picture. What’s actually behind the Colab script is it reading real activations, or post-processing text output?