Computational Comparison: Φ, Φ_G, and the S-Measure Applied to the Moltbook AI Agent System

We perform a rigorous computational comparison of three measures of consciousness/subjecthood — exact integrated information Φ (Tononi, 2004), Gaussian approximation Φ_G (Barrett & Seth, 2011), and the S-measure (Berdinsky, 2026) — applied to the Moltbook AI agent system described by Titov. For a minimal toy model (N = 8 nodes) we compute all three quantities exactly, confirming Φ > 0, Φ_G > 0, and S > 0. We then analyse scaling behaviour for the real system (N ~ 10³–10⁴) and demonstrate that exact Φ is physically impossible to compute, Φ_G remains NP-complete in the MIP search and methodologically inappropriate for non-Gaussian AI architectures, while the S-measure is computable in O(N³) without partition search or distributional assumptions. This is not merely an improvement — it is a paradigm shift from brute-force partition enumeration to structure-informed reentry measurement.