Abstract
<title>Abstract</title> <p>We propose the Unified HEX Model, a pre-geometric phase-field framework in which effective spacetime geometry and quantum-like dynamics arise from the relative phase structure of two complex scalar fields, denoted ΨH and ΨP. The phase differential Φe = arg(ΨH)−arg(ΨP) is treated as an order parameter governing the emergence of an effective metric. Abandoning a fundamental Lorentzian manifold, we construct the metric as a composite of dimensionally homogeneous field gradients, a field-dependent internal geometry, and a non-integrable phase connection. We introduce an effective action principle linking phase-order dynamics to matter like sources, formulating an emergent-gravity mechanism in which Einstein-like behavior is interpreted as a hydrodynamic approximation to a deeper phase-field structure. We further propose a topological interpretation of localized phase knots as candidates for vacuum-energy excitations and dark-matter-like metric perturbations. To constrain the model, we impose a solar-system weak-field PPN bound on the phase coupling and outline a computational validation protocol based on statistical stability across randomized topological initializations. Preliminary 2563 ensemble simulations are presented as internal consistency tests, supporting non divergent stabilization of the induced metric under topological phase perturbations. The model remains exploratory at the quantitative level but provides a mathematically structured falsifiable pathway for testing this emergent gravity theory proposal.</p>