The Structure and Trajectory of Context Sensitivity in Large Language Models: Content-Order Decomposition and Variance Dissociation

Context sensitivity in large language models (LLMs) is typically treated as a single dimension — models either "use context" or they do not. We challenge this view by decomposing context sensitivity into two measurable, independent dimensions: structure and trajectory. Using the Relational Coherence Index (RCI) framework and TRUE/SCRAMBLED/COLD experimental conditions, we analysed the conservation-validated model subset from Paper 6 (N = 8 Medical, N = 6 Philosophy) using TRUE/SCRAMBLED/COLD experimental conditions. Content-Order decomposition demonstrates that medical reasoning is 61% content-driven while philosophical reasoning is 59% order-driven (Mann-Whitney U = 45, p = 0.0047, Cohen's d = 1.59). Both content and order increase ΔRCI but have opposite effects on variance: content amplifies variance 4–6× while order suppresses it to ~30% of baseline. This variance machinery is domain-invariant (p = 0.463; p = 0.867), with domain specificity residing entirely in ΔRCI. Exploration Arc analysis reveals complete domain separation: philosophy expands conceptual diversity over conversation (mean Arc = 15.2) while medical responses remain stable (mean Arc = 1.7), with zero overlap between domains. A pilot analysis of Context Utilization Depth (CUD) is reported in Supplementary Material S1; three of four tested models show full recency dominance (CUD = 1), with Llama 4 Maverick as the sole exception (82%→98% K-curve). These findings provide a structural account of how LLMs process conversation, with direct implications for RAG design, prompt engineering, and clinical AI safety.