Structural Richness as a Complementary Dimension of Consciousness: Toward an Extension of Integrated Information Theory

The nature of consciousness remains an unresolved problem at the intersection of physics, neuroscience, and philosophy of mind. Integrated Information Theory (IIT) provides a formal framework by identifying consciousness with integrated information (Φ), yet it faces limitations concerning phenomenological richness and attribution to trivial systems. I propose an extension in which consciousness depends not only on integration, but also on structural richness, defined as a combination of entropy and relational correlations. Within a Russellian monist framework, we interpret physical structure as possessing an intrinsic experiential nature. Conscious experience is then associated with subsystems that maximize a joint functional of integration and structural richness. This model provides a principled response to the combination problem, reduces false positives in IIT, and establishes a bridge between physical structure and phenomenology.