Lossy Information Breaks Integrated Information Theory's Phi Measure — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) measuring irreducible cause-effect power of a system, but current formalizations (Tononi 2008; Griffith 2014) rely on lossy information, which is mathematically inconsistent with memory persistence. | MATH: Φ = minimum information partition (MIP) reduction in effective information; effective information EI(X) = H(X) − H(X|mechanism); Φ = min over partitions of EI difference; proposed alternative uses algorithmic information theory: Φ_AIT = K(X) − K(X|mechanism) where K is Kolmogorov complexity, avoiding lossy integration. | CONNECTION: No direct geometric ratio (0.382, 0.618, etc.) appears in the cited sources. However, the MIP concept is a *partition* of a system into subsystems — this is a lattice-theoretic structure (the partition lattice), which shares formal properties with root systems in crystallography (e.g., the partition lattice of a 4-element set has 15 elements, related to the B4 roo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com