Quantifying Consciousness: Phi and the Minimum Information Partition in IIT 4.0 — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) — the irreducible cause-effect power of a system's state, measured via the minimum information partition (MIP). | MATH: Φ = min over partitions of (effective information), where effective information = H(X0|X1) − H(X0|X1 partitioned); IIT 4.0 uses Φ* = min over unidirectional partitions of the Earth mover's distance between cause-effect repertoires; system state space is a Boolean lattice of 2^n possible states; intrinsic existence = Φ > 0. | CONNECTION: The MIP is a partition — a cut — whose minimization echoes the golden ratio's self-similar division (0.618/0.382) in that the system's integrated whole resists decomposition; the state space lattice (2^n) is a hypercube, whose symmetry group is the crystallographic hyperoctahedral group (B_n), a root system of type B_n — directly linking to lattice/crystallographic structure. | DEPTH: 7 — mathematically rigorous but empirically unmeasured; the p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com