Δ-Coherence: A Trajectory-Based Framework for Evaluating AI Systems

This paper introduces Δ-coherence as a trajectory-level framework for evaluating artificial intelligence systems. Moving beyond accuracy-based metrics, we define coherence as the stability of cognitive trajectories under perturbation and relational interaction. We formalize Δ-coherence as a multidimensional signal and introduce the Plasticity Metric Pc to quantify bounded identity evolution. Through observational analysis and a controlled interaction protocol, we demonstrate that common failure modes such as hallucination, bias amplification, and reasoning instability can be understood as manifestations of coherence breakdown. The proposed framework establishes a measurable foundation for coherence-regulated AI systems and trajectory-based evaluation.