The ARC Operator: Spectral Regime Classification Across Scales

The ARC Operator introduces a spectral framework for identifying and classifying regime transitions across complex systems. At its core, the model operates on the principle that systems—whether physical, computational, or informational—exhibit coherent frequency structures that define their current state and govern their transitions. By mapping these spectral signatures, the ARC framework enables the detection of regime shifts, boundary conditions, and emergent structural patterns across scales. Rather than treating domains independently, this approach establishes a unified geometric logic of transformation, where structure, signal, and behavior are coupled through shared spectral dynamics. This allows for cross-scale interpretation, linking micro-level fluctuations to macro-level system states within a single analytical framework. The ARC Operator represents a formalization of this perspective, providing both a conceptual and operational model for analyzing coherence, disruption, and transition within adaptive systems. This work is licensed under CC BY-NC-ND 4.0. Attribution is required for any use.