Integrated Information Theory: Phi as Irreducible Cause-Effect Power via Earth-Mover Distance — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) — the irreducible cause-effect power of a system's mechanism over its own past and future states, measured via the earth-mover distance between probability distributions. | MATH: Φ = minimum over partitions of the earth-mover's distance (Wasserstein-1) between the system's full cause-effect repertoire and the partitioned (disconnected) repertoire. IIT 4.0 refines this via intrinsic existence, using the *intrinsic difference* (ID) measure, not KL-divergence. Key quantities: φ_max (for a mechanism), Φ (for the whole system), and the "cause-effect structure" (CES) — a set of distinctions and relations, each with its own φ value. No universal constant emerges; Φ is system-specific, scale-free, and not a scalar but a structured object. | CONNECTION: The earth-mover distance is a metric on probability spaces — it induces a geometry where the "distance" between system states is measured by minimal work Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com