Algorithmic Phi Refines Integrated Information Theory of Consciousness — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible cause-effect power of a system's state, with recent algorithmic-information refinements addressing information loss. | MATH: Φ = minimum information partition (MIP) normalized; IIT 4.0 uses Φ* = effective information over cause-effect repertoires; algorithmic variant replaces Shannon entropy with Kolmogorov complexity: Φ_alg = K(system state) − K(system state | partition), avoiding lossy integration. | CONNECTION: Φ's partition structure mirrors lattice/root-system decompositions (e.g., A_n root systems in state-space partitions); the MIP is a graph cut — related to spectral graph theory where eigenvalues (λ) of Laplacian encode integration/segregation balance; no explicit golden-ratio or base-60 constants appear in IIT formalism. | DEPTH: 6 — mathematically rigorous but empirically unvalidated; the algorithmic-information correction is a genuine advance, yet Φ remains com Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com