Formalizing Consciousness: Integrated Information Theory 4.0 and Its Mathematical Framework — E8 Intelligence Research

FINDING: IIT 4.0 formalizes consciousness as integrated information (Φ), computed via the cause-effect structure of a physical system's state space, with PyPhi as the reference implementation. | MATH: Φ = minimum information partition (MIP) distance — formally, Φ = min over partitions P of (effect repertoire distance + cause repertoire distance), using Earth Mover's Distance (EMD) on probability distributions over system states; IIT 3.0 uses Φ = 2^-H(mechanism|partition) with Shannon entropy H; the state space is a directed graph of 2^n possible states for n elements, with transition probabilities forming a Markov chain. | CONNECTION: The cause-effect structure is a lattice (poset) of mechanisms — its maximal irreducible cause-effect structures form a "conceptual structure" whose geometry (in the space of probability distributions) is the core of Φ. No direct golden-ratio or base-60 link; but the lattice structure is a partially ordered set, analogous to root system posets (e.g., A_n, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com