Mathematical Formalism for Functional Consciousness in Artificial Systems: From Phenomenology to Prediction

This paper introduces a rigorous mathematical framework for functional consciousness in artificial systems. The model defines consciousness as a dynamic process on a Hilbert space, with metacognition formalized as an operator ΓM measurable through predictive self-correlation. We provide a complete dynamic equation, spectral analysis, empirical metrics, a falsifiable experimental protocol (E–Ω), and formal comparisons to IIT, FEP, GWT and CE.