IIT 4.0 Lacks Quantum Collapse Link; Φ Defined via Minimum Partition — E8 Intelligence Research

FINDING: IIT 4.0 formalizes consciousness as integrated information (Φ), but the search results contain no experimental test linking Φ to quantum collapse rates; the only quantum result is a rate-distortion theorem for quantum channels, not brain dynamics. | MATH: IIT 4.0 defines Φ via the *minimum information partition* (MIP): Φ = min over partitions P of the *earth mover's distance* between the cause-effect repertoire of the whole system and the product of its parts. Formally: Φ = min_P ||CE(whole) − ⊗_i CE(part_i)||_W, where W is a Wasserstein metric. Quantum rate-distortion: R(D) = minρ, E I_c(ρ; E(ρ)) subject to distortion ≤ D, with coherent information I_c = S(ρ) − S(ρ, E). | CONNECTION: No direct geometric ratio appears. However, the Wasserstein metric in IIT is a *transportation cost* — its optimal solution on a line yields the 1/2 quantile, not golden ratios. The quantum rate-distortion bound uses *relative entropy* — no 0.618/1.618 structure. Base-60, crystallographic symm Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com