Ontological Basic Wavefield Theory (OBWT): Complete Formulation with Mathematical Consistency Checks

We present the complete formulation of the Ontological Basic Wavefield Theory (OBWT), a flat-spacetime gravitational framework rooted in a single foundational postulate: wave-vector conservation under gravitational modulation, expressed as u^2 + v^2 = Phi c^2. Matter is described as localized wave-packet configurations of a fundamental scalar wave field, photons as delocalized excitations, and gravity as modulation of wave-field propagation by a scalar potential. The theory derives a global mass-energy relation, a scalar field equation from variational principle, an effective metric, and all five classical tests of general relativity in the weak-field limit. In the strong-field regime, OBWT predicts a black hole shadow radius b_c = 6.75 GM/c^2, approximately 30% larger than the general relativistic prediction. The framework introduces a three-tier hierarchy of coordinate, physical-ruler, and light-measured distances, as well as coordinate, background, and locally measured light speeds. The theory resolves the black hole singularity and information paradox via a propagation-freezing boundary at r_g = GM/c^2, where matter wave packets dissolve into radiation as their effective rest energy vanishes. All mathematical derivations, dimensional checks, coordinate transformations, and weak-field expansions are provided in full in the appendices. OBWT offers a parameter-free, falsifiable alternative to general relativity, with strong-field predictions testable by current and near-future observations.