Integrated Information Theory: Φ as Minimum Effective Information Beyond Parts — E8 Intelligence Research

FINDING: IIT defines consciousness as integrated information Φ — the minimum information a system generates as a whole beyond its parts, computed via effective information across minimum information bipartitions. | MATH: Φ = min over partitions of [EI(system) − Σ EI(parts)]; EI(A→B) = Σ p(a) · log₂[p(a|b)/p(a)]; Φ is measured in bits; MIP (minimum information partition) minimizes normalized effective information. IIT 4.0 reformulates via cause-effect repertoires and "unfolded" Φ-structure in qualia space. | CONNECTION: No direct geometric-harmony constants (0.618, 1.618, etc.) appear in the formalism. However, the partition-minimization structure is a lattice-theoretic operation over the powerset of system elements — the set of bipartitions forms a sublattice of the Boolean lattice 2^N. The MIP search is combinatorial (NP-hard), scaling as Bell numbers B(n). Cause-effect repertoires live in a probability simplex whose vertices correspond to states — a geometric object (simplex) with cr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com