Cosmological Update Dynamics: Structural Dynamics and Emergent Wave Behavior

Cosmological Update Dynamics (CUD) v4.1 introduces a dynamical formulation of the structural field, extending the geometric framework established in CUD v3.3. In this work, the universe is described as an evolving structural field generated by the accumulation of distinguishability. The dynamics of this field is formulated through an evolution equation governing the structural quantity A(x, τ), incorporating generation, accumulation, and instability-driven reconfiguration. An energy-based formulation is developed using Lagrangian and Hamiltonian structures, providing a consistent description of structural evolution under the influence of instability and structural potential. Locally stable configurations emerge as structural excitations, forming a discrete representation of the underlying continuous field and connecting naturally to the ψ-network framework introduced in earlier versions. In the weak-structure regime, the dynamics admits an effective wave-like description corresponding to a Schrödinger-like equation, suggesting that quantum mechanical behavior may be understood as an emergent approximation of a deeper structural dynamics. Importantly, this formulation focuses exclusively on structural evolution and does not introduce any selection mechanism or outcome realization. Selection processes are addressed separately in CUD v4. Together with previous formulations, this work contributes to a layered theoretical framework in which: • structure defines the space of possibilities (v3.3) • dynamics governs structural evolution (v4.1) • selection determines realization (v4) This separation provides a robust and extensible foundation for further theoretical development, including future work on selection mechanisms and their possible connections to higher-order structures. For complementary formulations, see: CUD v3.3 (Structural Geometry)https://zenodo.org/records/20049155 CUD v4 (Selection-Driven Probability)https://doi.org/10.5281/zenodo.19945673