Cosmological Update Dynamics: Structural Field and Instability Geometry

Cosmological Update Dynamics (CUD) v3. 3 provides a structural formulation of the universe based on the accumulation of distinguishability. In this framework, the universe is described as a continuous structural field, from which geometric quantities such as gradients, curvature, and instability naturally emerge. This version establishes the structural space of possible configurations, introducing: • a structural field representation u (x) = log A (x) • a geometric instability measure φ • a path-dependent structural distance dₛ • a coherence relation C = exp (−dₛ / ℓα) • a ψ-network representation derived from continuous structure • a global criticality parameter Γ Importantly, this formulation does not specify outcome realization or selection mechanisms. Instead, it defines the space of structurally possible configurations. For the selection mechanism governing outcome realization, see: Cosmological Update Dynamics v4 Selection-Driven Probability https: //doi. org/10. 5281/zenodo. 19945673