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 d_s • a coherence relation C = exp(−d_s / 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