Integrated Information Theory: Φ as Irreducible Causal Information via Minimum Information Partition — E8 Intelligence Research

FINDING: IIT defines consciousness as integrated information Φ — the irreducibly causal information a system generates above its parts, formalized via cause-effect repertoires and the MIP (minimum information partition). MATH: - Φ = min over partitions P of [I(X;Y) − Σᵢ I(Xᵢ;Yᵢ)] — integrated information as the information lost under the minimum-information partition. - Cause-effect structure: a system in state x generates a "cause-effect repertoire" over its past/future states; Φ is the distance (Earth Mover's / Wasserstein) between the unpartitioned repertoire and the MIP-partitioned repertoire. - Φ_max (maximally integrated) is achieved by systems whose transition probability matrix is highly irreducible — e.g., a fully connected network with heterogeneous weights. - Tononi's "Φ" scales with the number of irreducible causal distinctions and their relations (Φ-structure = "qualia space"). - Algorithmic-information reformulation (arXiv:1405.0126): Φ_AIT = K(system) − K(parts) using K Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com