Processual AI: Technical Implementation of the Ψ Index

This paper introduces Ψ‑Core, a processual AI framework designed to measure continuity and resilience in complex digital systems. The model is based on a mathematical formulation of Ψ(t), integrating cooperation (T), need (N), cost (C), and erosion (M) into a unified continuity index. The framework provides a layered architecture including kernel, agents, cognition, metrics, simulation, governance, and domain-specific extensions. It aims to serve both academic research and real-world applications in areas such as healthcare, cybersecurity, ecological systems, and socio-political analysis. The paper has been submitted to Springer and is currently under peer review. This preprint is shared openly to support transparency, collaboration, and early adoption of the Ψ‑Core methodology.