The α-Complexity Hypothesis: A Proposed Information-Theoretic Metric for Subjective Richness

"This work is a component of the Phase-Dependent Scaling Program (2026) and is theoretically grounded in the 1.91x Critical Scaling Gap identified in Omandac (2026, Paper 1)." "This is a theoretical/speculative framework & Background Philosophy" A fundamental challenge in consciousness research is the quantitative characterization of subjective experience. While Integrated Information Theory (IIT) proposes metrics such as Φ, a gap remains in connecting these to the physical dynamics of collective quantum substrates. We propose the α-Complexity Hypothesis, a theoretical framework suggesting that the scaling exponent $\alpha$—identified in noisy Dicke-type systems—may serve as a proxy for the information-carrying capacity of a conscious state. We hypothesize that 'consciousness richness' is functionally related to the system's proximity to the coherent scaling regime (α ≈ 0). In this state, the Dicke Hamiltonian supports maximal collective integration, potentially providing the physical substrate for unified experience. Conversely, as α approaches the fragmented limit (approximately -1.1 to -1.4), the resulting information disintegration corresponds to a loss of subjective depth. This framework offers a mathematical bridge between the physics of collective dephasing and information-theoretic measures like mutual information. By framing consciousness as a state-dependent scaling phenomenon, we provide a testable basis for investigating altered states and clinical disorders of consciousness through the lens of quantum information fragmentation."