Dynamics of the Odero Field: A Persistence -Theoretic Framework for Cosmological Evolution

The Odero Field is proposed as a persistence-theoretic field that governs the emergence, maintenance, and evolution of structure across physical systems. Building upon the Odero Axiom, C(I) × E > D, the theory models persistence as the outcome of information-derived control acting through available energy against system decay. The resulting field formalism extends Persistence Science into a continuous dynamical framework and provides a basis for describing the evolution of persistence in cosmological environments. The field dynamics are formulated through a persistence potential and associated evolution equations that link information, energy, and decay to the emergence and stability of large-scale structures. Within this framework, regions of high persistence correspond to stable organizational configurations, while regions dominated by decay exhibit reduced structural longevity. The theory proposes that persistence gradients may influence system evolution across multiple scales, from local structures to cosmological domains. The Odero Field is presented as a phenomenological framework intended to complement existing physical descriptions while providing a persistence-centered interpretation of structure formation and survival. Mathematical definitions, governing relations, and falsifiability conditions are established, and potential observational consequences are outlined. The theory serves as a bridge between Persistence Science and cosmology, providing a foundation for future studies of observational signatures and cosmological persistence dynamics.