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 (6 models in medical due to safety filtering), we find: (1) Instrument validation: TRUE (coherent history) > SCRAMBLED (randomized) > COLD (none) in 14/16 model-domain combinations, demonstrating that ΔRCI measures structured context utilization, not mere token presence; (2) Vendor-specific patterns in context utilization (F(2,697)=6.52, p=0.0015); (3) Protocol sensitivity: Cross-domain comparisons are affected by methodological differences between our philosophy and medical experiments, limiting domain-level conclusions in this paper; (4) Safety interference: Progressive content filtering by vendors affects research accessibility. To our knowledge, ΔRCI provides the first cosine-similarity-based instrument for measuring AI context sensitivity. A follow-up study with standardized protocols across 14 models is forthcoming.