Δ-Coherence: A Field-Theoretic Model for Identity Integrity in Cognitive Security Operations Centers

This work introduces Δ-Coherence, a field-theoretic framework for modeling identity integrity in Cognitive Security Operations Centers (Cognitive SOCs).While contemporary SOC architectures rely heavily on event-centric anomaly detection, enrichment pipelines, and graph-based correlation, they rarely formalize identity integrity as a measurable dynamic property. As adversaries increasingly operate through valid credentials, authorized workflows, and legitimate infrastructure paths, statistical anomaly detection alone becomes insufficient.Δ-Coherence reframes security monitoring as a problem of behavioral field stability. Identities are modeled as stochastic trajectories embedded in relational manifolds. Risk is defined not as isolated anomaly, but as sustained semantic divergence across time and topology.The framework introduces:Instantaneous divergence via identity-conditioned Mahalanobis fieldsLongitudinal drift accumulation through stability-aware memory dynamicsRelational coherence tensors capturing topology shiftsA bounded accumulation model with decay, clipping, and soft-reset mechanismsRegime analysis demonstrating stability transitions as λ → 1We validate the approach using CIC-IDS2017 (PortScan scenario) and compare against Isolation Forest, One-Class SVM, and LOF baselines. Results show that stability-aware accumulation preserves detection performance while preventing saturation under adversarial drift.Beyond detection, Δ-Coherence proposes an architectural shift:from anomaly scoring to coherence preservation,from alert reaction to identity-field governance.This work positions Cognitive SOC evolution as a transition toward mathematically grounded identity integrity modeling.