A Resonance-Based Field Framework for the Geometric Unification of Gravitation and Quantum Phenomena (Version 3)

This version presents a consolidated formulation of the resonance-field framework, in which physical phenomena are modeled as stability configurations of a single scalar field defined on a three-dimensional spatial manifold with an internal coherence parameter ζ. Compared to earlier preprints, the framework now includes a formally defined self-coherence operator governing stability, a mass functional expressed through ζ-directed curvature, an explicit dual-node stability criterion based on sequential gradient cancellation, and a unified interaction expression derived from resonance gradients. A clear structural distinction is established between lateral (spatial) and sequential (ζ-directed) coherence channels, together with a systematic classification of node types. The parameter ζ is treated not as an additional spatial dimension, but as an internal coherence coordinate governing stability, mass-generation, and interaction structure. Ongoing work aims to develop a minimal computational reduction of the framework through an effective wave–oscillator model of dual-node dynamics, enabling explicit treatment of binding thresholds, separation-dependent sequential excitation, and externally driven disruption regimes. The work forms part of an ongoing research program exploring resonance-based geometric foundations of matter and interaction.