∆-Coherence: A Field-Theoretic Framework for Identity Integrity in Cognitive Security Operations

This work introduces Δ-Coherence, a field-theoretic framework for modeling identity integrity in modern Security Operations Centers (SOCs). As cyber threats evolve toward the use of valid credentials, trusted infrastructures, and semantically legitimate actions, traditional detection paradigms—based on signatures, rules, and isolated anomalies—become increasingly insufficient. We propose a shift from event-based detection to field-based identity modeling. In this framework, identity is no longer treated as a static attribute, but as a dynamic trajectory evolving across behavioral, temporal, and relational dimensions. Stability emerges from the coherence of these interactions, while deviations accumulate as measurable coherence drift. To operationalize this concept, we introduce a set of observable features, including entropy-based behavioral metrics, graph-structured interaction patterns, and memory-aware temporal dynamics. These components allow the estimation of Δ-Coherence in real-world environments and enable the identification of early-stage identity degradation prior to explicit compromise. The framework is implemented within a SOC pipeline, demonstrating its compatibility with existing infrastructures such as SIEM platforms and its ability to complement traditional detection mechanisms. By reframing identity integrity as a stability problem in a relational field, Δ-Coherence opens a new direction for adaptive, cognition-aware cybersecurity architectures. This work contributes to the emerging paradigm of Cognitive SOCs, where security is understood not only as threat detection, but as continuous preservation of identity coherence in complex, distributed systems.