Integrated Information Theory's Φ as Information Loss Under Partitioning — E8 Intelligence Research

FINDING: Integrated Information Theory formalizes consciousness as Φ (phi), a measure of irreducible cause-effect structure; algorithmic reformulation ties Φ to information loss under partitioning, not to lossless integration. | MATH: Φ = min over partitions P of [effective information of whole − Σ effective information of parts]; IIT 3.0 uses cause-effect repertoires over a discrete state space; the AIT critique (arXiv:1405.0126) argues Φ depends on lossy compression, so Φ ∝ information destroyed by partition, not integrated. | CONNECTION: Partition lattices are the underlying combinatorial object — the set of all bipartitions of a system forms a lattice under refinement (the partition lattice Π_n, order-theoretic, with Möbius function μ(Π_n) = (−1)^(n−1)(n−1)!). Symmetry breaking = selecting a minimal-information partition, i.e. a maximal element in the lattice. No direct 0.618/1.618 ratio appears in the cited sources. | DEPTH: 6 FINDING: Parity (P) and time-reversal (T) symmetry in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com