Conditional Dynamic Signatures in Large Language Models :

We present a methodological framework for measuring trajectory instability in autoregressive language models and characterise the conditional nature of such measurements. We define an amplitude-based ratio metric over hidden-state cosine distance and logit entropy, and we systematically audit its dependence on normalisation, layer choice, prompt category, and panel composition. Across 17 open-source models (parameter counts from 70M to 3B), we report four results that anchor the framework methodologically rather than as positive claims. First, three legitimate normalisation choices (RAW, CLIPPEDMAD, MINMAX) produce mean ratioₙorm values that differ by a factor of 2. 0 to 2. 4, with discrimination scores differing by a factor of 1. 93; the regime ordering is preserved only under CLIPPEDMAD. Second, variance decomposition across model identity, prompt category, and residual error attributes 7%, 17%, and 76% of total variance respectively architectural variance is a minority component and is exceeded by prompt-category variance. Third, 80% of token-level trajectories are non-stationary (mixed regime phases within a single generation), with only 13% remaining in a single regime throughout. Fourth, we report six small-panel hypotheses (V14-V15 audits) that did not survive scale-up to n=17 and are documented as explicit falsifications. We additionally describe a token-level COLLAPSE-RIVALRY cyclical structure (84% reopening rate after collapse on 638 cycles) and a fragmented topology in the canonical panel (fragmentation index 0. 65, Adjusted Rand Index 0. 11 against prior narrative families). The amplitude metric introduced here is presented as a complementary formulation to the token-level ctₜ metric of LIMENFourRegimes (Bosange Batuli, 2026, Zenodo, https: //doi. org/10. 5281/zenodo. 20348878) ; the two operationalise trajectory instability at different levels of the model (hidden-state amplitude versus token-level displacement) and require independent calibration. All claims carry epistemic labels I, II, III, or IV indicating measurement status, established concept, falsifiable conjecture, or interpretive framework respectively. Keywords: LLM hidden states · trajectory instability · variance decomposition · falsification · methodological discipline · normalisation audit · fragmented topology · LIMEN · IDChain · Unbind