Integrated Information Theory: Consciousness as Maximally Irreducible Cause-Effect Structure — E8 Intelligence Research

FINDING: IIT formalizes consciousness as integrated information Φ, computed via cause-effect structure over a system's state space, not as a single scalar but as a maximally irreducible conceptual structure. | MATH: Φ = minimum information partition (MIP) of effective information — Φ = min over partitions P of [EI(x; MIP)] where EI = 1/|Ω| Σ_p D(p(mechanism state | cause) || p(mechanism state | effect)); IIT 4.0 replaces scalar Φ with a *cause-effect structure* (CES) — a lattice of distinctions and relations, with intrinsic existence = Φ^max over all subsets. PyPhi implements exact Φ for small systems (state-space explosion: O(2^n) states, O(2^(2^n)) partitions). | CONNECTION: The CES is a *poset* — its maximal elements form a *lattice* (crystallographic-like symmetry in state space). The "exclusion" principle picks a unique maximal Φ — analogous to selecting a *root system's highest weight* in Lie algebra representations. No direct golden-ratio or base-60 link appears in the core form Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com