Integrated Information Theory (IIT) begins with essential properties of consciousness and translates them into postulates that any physical system must satisfy to specify the physical substrate of consciousness. A recently introduced information measure captures three of these postulates—existence, intrinsicality, and information—and is unique. This work shows that the measure also satisfies the remaining postulates of integration and exclusion, creating a framework that identifies maximally irreducible mechanisms. These mechanisms can form maximally irreducible systems, which then specify the physical substrate of conscious experience.
Integrated information theory (IIT) proposes that consciousness is identical to the cause-effect structure generated by a maximally irreducible substrate (a Φ-structure). This work introduces a definition for system-integrated information (φs) grounded in IIT's postulates of existence, intrinsicality, information, and integration. It examines how determinism, degeneracy, and connectivity fault lines affect system-integrated information. The proposed measure identifies complexes as systems whose φs exceeds that of any overlapping candidate systems.