Universal Field Theory (UFT) Formalism v1.1: Scalar Field, Resolution Dynamics, and Emergent Force

This report presents UFT Formalism v1.1, the first mathematically closed realization of Universal Field Theory (UFT). Building on the foundational report Universal Field Theory (UFT): A Field-First Framework Beyond Time, Motion, and Probability (Zenodo, DOI: 10.5281/zenodo.18196974), this work develops a minimal scalar-field formalism capable of reproducing quantum-like, classical, and gravitational behavior as regime-dependent outcomes of a single equilibrium-seeking field. The formalism introduces a scalar deviation field Δ defined over a spatial manifold, a variational principle encoding the Law of Consequence (LOC), a functional definition of Alignment / Recognizability Threshold (ATT), frequency-layered resolution dynamics, condensation criteria for emergent mass, and interface-based derivation of force. Time, motion, probability, and force are treated as emergent descriptors rather than fundamental entities. This report establishes the mathematical backbone necessary for testability, simulation, and experimental engagement, while deliberately excluding cosmology, vector/tensor extensions, and quantum field interactions, which are reserved for future versions.