Integrated Information Φ as IIT's Mathematical Core, Not a Geometric Constant — E8 Intelligence Research

FINDING: IIT defines consciousness as integrated information Φ (phi), a scalar measuring a system's irreducible causal power beyond its parts — the mathematical core of the theory, not a geometric constant. MATH: - Φ = min over partitions of the effective information (EI) lost when a system is cut into parts. Formally, for a system in state x with cause-effect repertoire, Φ = min_{partition P} [ EI(system) − Σ EI(parts) ]. - EI (effective information) = KL divergence between the actual cause/effect repertoire and the unconstrained (maximum-entropy) repertoire: EI = D_KL(p_actual ‖ p_unconstrained). - IIT 4.0 reformulates Φ as a distance (Earth Mover's / Wasserstein metric) between cause-effect structures, not a scalar KL alone. - Key quantities: cause repertoire, effect repertoire, cause-effect structure (a "qualia space" of distinctions and relations), maximally irreducible conceptual structure (MICS). - No universal constant emerges. Φ is system-specific, measured in bits, unbounde Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com