Refining Integrated Information Theory: Quantifying Consciousness via Higher-Order Causal Analysis — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) measuring irreducible cause-effect power of a system, with recent work (IIT 4.0) refining its computation via higher-arity causal analysis. | MATH: Φ = minimum information partition (MIP) distance: Φ = min over partitions of (effective information / partition); IIT 4.0 uses Φ* via cause-effect repertoires over system states, with intrinsic existence quantified by integrated conceptual information (Φ^max). Tegmark's approach: Φ ≈ mutual information between system and its own past/future under optimal coarse-graining, bounded by algorithmic complexity (Kolmogorov) — see arxiv 1405.0126 for lossless integration criterion. | CONNECTION: Φ is not a ratio constant, but its computation involves lattice structures (power set of system partitions) and symmetry-breaking under partition — analogous to crystallographic point groups where irreducible representations define invariant subspaces. The MIP search Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com