A Formalization of Consciousness: Integrated Information Theory 4.0 and Its Mathematical Framework — E8 Intelligence Research

Abstract

FINDING: IIT 4.0 formalizes consciousness as integrated information Φ, computed via system partitioning and cause-effect repertoires, with PyPhi as the reference implementation. | MATH: Φ = minimum information loss over all partitions (MIP); for a system S with mechanism M, Φ = min_partition [ H(PE(M)) − Σ H(PE(M_i)) ] where H is Shannon entropy, PE is the cause-effect power (probability distribution over past/future states). IIT 3.0 uses Φ* (intrinsic cause-effect power) with exclusion principle; IIT 4.0 refines to Φ^max via "intrinsic existence" and "composition" axioms. | CONNECTION: Φ is a scalar invariant under system symmetries — the MIP often aligns with graph automorphism partitions; in symmetric networks (e.g., complete graphs, cyclic lattices), Φ scales with group-theoretic invariants (e.g., eigenvalues of the adjacency matrix), linking to root system Weyl chambers (A_n, D_n) and crystallographic point groups. No explicit golden ratio or base-60 appears in the formal theory. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com