GCST Framework for Ocean Worlds, Galactic Stability, and Cosmological Complexity Limits Planets-Oceans as Long-Lived Resonators of Complexity in the Universe

Abstract Ocean worlds — including subsurface ocean moons and Hycean-type exoplanets — represent a special class of planetary systems with exceptional thermodynamic longevity. Within Global Complexity Stability Theory (GCST) and Optimal System Dynamics (OSD v1. 2), such worlds can be viewed as large-scale dissipative structures capable of sustaining complex self-organizing processes over extremely long timescales. The dynamics of instability are governed by the field equation: ∂Ψ/∂t = D ∇² Ψ + C α − γ Ψ with stability condition γ / (α C) > 1. Ocean planets operate in the deeply stable regime α ≪ 1, γ ≫ 1, making them natural attractors of long-lived complexity. Extending GCST to galactic and cosmological scales reveals hierarchical bounds on complexity: Cₘax ∝ γ / α at each level. A unified scale-invariant GCST equation emerges, while the variational principle, entropy law, evolution law, phase transitions, and information principle complete a self-consistent theoretical framework for the emergence and limits of complexity across cosmic scales.