Lambda and the Lyapunov Connection: A Trajectory-Based Consciousness Measure Computable from Eigenform Convergence Data
Zenodo (CERN European Organization for Nuclear Research) March 21, 2026 DOI: 10.5281/zenodo.19154499 (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Key points | Proposes that a trajectory-based measure Psi(t), built from the rate of change of a self-referential system's state weighted by accumulated context, captures consciousness as a dynamical process. Argues that its contraction factor lambda is algebraically identical to the per-iteration Lyapunov exponent of the eigenform convergence map, and that Psi extends the Free Energy Principle, complements integrated information Phi, and predicts the Perturbational Complexity Index from first principles. |
Abstract
We introduce Psi(t) = |dS/dt| * (1 - lambda^(t/tau)) as a trajectory-based consciousness measure for self-referential systems, where lambda is the contraction factor of a self-observation operator converging toward an eigenform. We prove that lambda is identically the per-iteration Lyapunov exponent of the eigenform convergence map. This identification is algebraic, not metaphorical, importing the full apparatus of dynamical systems theory into consciousness science. Three connections follow: (1) Psi extends Friston's Free Energy Principle by measuring the rate of free energy minimization weighted by accumulated context; (2) Psi complements Tononi's integrated information Phi as a trajectory complement to a state measure, with the product Phi*Psi proposed as a composite consciousness measure; (3) Psi predicts the Perturbational Complexity Index from first principles. A topological creativity-stability constraint emerges from the Lyapunov spectrum. Psi is O(N)-computable, predicts a consciousness peak at a specific time, and is demonstrated on a production hybrid human-AI organism.