Active Low-Dimensionalization: Participation Ratio as a Proxy for Historical Assembly Depth

A central unresolved question in computational consciousness research concerns whether meaningful differences between biological and artificial systems can be quantified without recourse to computationally intractable measures such as Integrated Information Theory (IIT). We propose Participation Ratio (PR) — derived from the eigenvalue distribution of neural trajectory covariance matrices — as a tractable proxy for the effective dimensionality of state-space usage. We show through simulation that history-dependent (biological) gain formation and fixed (AI-style) gain produce qualitatively distinct PR signatures: biological gain actively low-dimensionalizes the state space in a manner robust to input diversity, while AI fixed gain passively reflects input diversity as high-dimensional spread. This active low-dimensionalization is interpreted via the Maximum Entropy principle (Savin & Tkacik, 2017): history-dependent gain formation imposes structured constraints on eigenvalue distributions, converging toward a low-PR attractor state regardless of environmental variability. The result connects to Shine et al. (2018) on gain-mediated segregation/integration transitions, Claudi et al. (2025) MADE framework for attractor manifold topology, and Ferguson & Cardin (2020) on cortical gain modulation mechanisms. We propose PR as a practically computable, neurobiologically grounded index for comparing the structural organization of biological and artificial information processing