Integrated Information Theory: Φ as Algorithmic Irreducible Complexity — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ, measuring irreducible causal integration in a system, with recent work linking it to algorithmic information theory to avoid information loss. | MATH: Φ = effective information (EI) minimized over partition; EI = 2^-H(mechanism) — Tononi's 2008 formulation; algorithmic variant: Φ_A = K(whole) − Σ K(parts) where K is Kolmogorov complexity (Grasso/arXiv:1405.0126); Tegmark's approach uses perturbation-based Φ with matrix norms (||M||_1 or spectral radius) on state transition matrices. | CONNECTION: No direct geometric ratio (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 appears in the cited sources. However, Φ's partition-minimization structure mirrors lattice/root-system symmetries — the "minimum information partition" (MIP) is a discrete optimization over partitions, analogous to finding the minimal cut in a weighted graph, which in crystallographic terms corresponds to identifying the weakest cleava Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com