A Constructive Level-0 Foundation for Emergent Order, Information, and Physics in the Balance-Field Framework

This work presents a constructive Level-0 formulation of the Balance-Field Framework (BFG), introducing a minimal pre-mathematical substrate from which order, information, process time, and physical structure emerge. Instead of assuming spacetime, geometry, or physical laws as fundamental, the framework derives them from five primitive ingredients: distinguishable units, admissibility relations, polarity-marked transitions, recurrence structure, and identity retention. From this minimal ontology, the paper constructs structured information, microscopic order parameters, and a pre-temporal feedback mechanism that gives rise to an emergent notion of process time. Through explicit coarse-graining and continuum-admissibility conditions, the framework recovers macroscopic BFG variables and demonstrates how dynamical stability, feedback operators, and effective geometry arise as regime-dependent closures. In particular, geometric structure is shown to emerge from gradients of the order parameter, while the balanced regime appears as a dynamical attractor supported by a Lyapunov stability structure. The work does not claim empirical completeness but establishes a mathematically explicit and falsifiable research program for deriving physical law from a minimal structural substrate. It contributes to ongoing efforts in emergent spacetime, information-theoretic physics, and complex systems by providing a constructive bridge from discrete relational primitives to continuous physical descriptions.