A Kolmogorov-Complexity Reformulation of Integrated Information Theory — E8 Intelligence Research

FINDING: Consciousness quantification via integrated information (Φ) is formally linked to algorithmic information theory, with IIT's core measure shown to be lossy and replaced by a Kolmogorov-complexity-based formulation. | MATH: IIT 3.0/4.0 defines Φ as effective information over a system's cause-effect repertoire; the paper (arXiv:1405.0126) replaces lossy Φ with Φ_K = K(mechanism) − K(mechanism | partition), where K is Kolmogorov complexity (incompressibility measure). PyPhi implements discrete Φ via state-transition matrices; Kolmogorov complexity K(s) = min{|p| : U(p) = s} for universal Turing machine U. | CONNECTION: No direct geometric ratio (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 appears. However, the partition-based integration measure mirrors lattice/crystallographic symmetry breaking: Φ_K quantifies the *irreducible* structure across a partition — analogous to how a root system's Weyl group preserves lattice symmetries only if the partition respects the lattice's ge Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com