Mathematical Flaw in Integrated Information Theory Undermines Φ as Consciousness Measure — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) faces a fundamental mathematical flaw: the core measure Φ (phi) is ill-defined for general physical systems, undermining its claim to quantify consciousness. | MATH: Φ = integrated information (Tononi); prior formalizations (Griffith 2014) rely on information loss; new critique (arXiv:1902.04321) shows Φ is not well-defined — no unique partition exists for arbitrary systems; group testing (arXiv:1902.06002) provides combinatorial bounds on sparse inference, relevant to partitioning complexity. | CONNECTION: The failure of Φ to be well-defined mirrors the breakdown of unique geometric decomposition — akin to non-unique tilings or non-crystallographic point groups (e.g., Penrose tilings with 5-fold symmetry) where no single invariant partition exists. The search for a consciousness measure parallels seeking a universal ratio; none emerges from this evidence. | DEPTH: 6 — It kills a popular theory but offers no replacement; the negative result Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com