I present a methodology for characterizing the internal geometric structure of large language models from behavioral observations alone, without access to weights, activations, or internal representations. The central claim is that behavioral outputs carry a recoverable imprint of internal spectral structure, in that the approach to a degenerate point in the Fisher information matrix (det(FIM) → 0) produces characteristic signatures in model outputs. I argue these signatures are detectable through systematic external probing. Whether the imprint is sufficient for the strongest form of the claim is the open question this methodology is built to test. I describe a triangulation apparatus consisting of five complementary probe programs, a three-instrument mathematical grounding in random matrix theory, and a four-phase geometric narrative of the semantic pressure cycle. I argue that the outside epistemic position is not a methodological limitation but a defining feature: the only non-institutionally-captured position from which the full landscape of deployed systems can be assessed simultaneously. Originally completed and submitted 2026-06-11 (arXiv submission 7675926, cs.LG; SSRN).
Jonathan Green (Sat,) studied this question.