Context Curves Behavior: Measuring AI Relational Dynamics with ΔRCI

Current AI evaluation focuses on accuracy and safety benchmarks, neglecting relational dynamics—how models utilize conversational context. We introduce ΔRCI (Delta Relational Coherence Index), a novel metric measuring context sensitivity through a three-condition protocol (TRUE/COLD/SCRAMBLED). Across 1,000 trials (90,000 API calls) spanning 7 models and 2 epistemological domains, we find: (1) Vendor-specific patterns in context utilization (F(2,697)=6.52, p=0.0015); (2) Massive domain modulation (Cohen's d > 3.0) where models switch from SOVEREIGN in open-ended philosophy to CONVERGENT in structured medicine; (3) GPT-5.2 uniquely 100% CONVERGENT in both domains (150 trials, σ=0.014–0.021); (4) For CONVERGENT models, TRUE > SCRAMBLED > COLD, demonstrating ordered context outperforms mere token presence. We propose Epistemological Relativity: AI behavior curves based on knowledge structure. To our knowledge, ΔRCI provides the first cosine-similarity-based instrument for measuring AI context sensitivity, enabling evidence-based prompt engineering and model selection.