∆-Coherence: A Trajectory-Based Framework for Evaluating AI Identity Stability

Δ-Coherence is a trajectory-based evaluation framework for measuring identity stability in AI systems across time, adaptation, and perturbation. While current benchmarks focus on pointwise performance, Δ-Coherence introduces a structured approach to quantify whether a system remains coherent with itself as it evolves. The framework decomposes coherence into four axes—logical consistency, temporal stability, robustness to perturbation, and identity invariants—and proposes a coherence-aware regulator that modulates system plasticity based on coherence signals. This work highlights identity drift as a critical failure mode not captured by standard evaluation metrics and outlines a path toward trajectory-aware evaluation and identity-preserving AI systems.