What question did this study set out to answer?

This research aims to compare measures of consciousness—Φ, Φ_G, and the S-measure—within the context of the Moltbook AI agent system.

June 10, 2026Open Access

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

Key Points

This research aims to compare measures of consciousness—Φ, Φ_G, and the S-measure—within the context of the Moltbook AI agent system.
Conducted exact calculations for Φ, Φ_G, and S on a toy model with N = 8 nodes.
Analyzed scaling behavior for real systems with N ~ 10³–10⁴.
Evaluated computational feasibility of each measure in relation to the AI architecture.
Confirmed that all measures (Φ > 0, Φ_G > 0, S > 0) are positive for the toy model.
Showed that Φ is physically impossible to compute, while Φ_G remains NP-complete and unsuitable for non-Gaussian architectures.
Demonstrated that S-measure is computable in O(N³) without requiring partition searches or distributional assumptions.

Abstract

We perform a rigorous computational comparison of three measures of consciousness/subjecthood — exact integrated information Φ (Tononi, 2004), Gaussian approximation ΦG (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, ΦG > 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, ΦG 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.

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