A Resonance-Based Field Framework for the Geometric Unification of Gravitation and Quantum Phenomena (Version 4)

This preprint 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. The present version further introduces a minimal effective reduction of dual-node binding based on a two-channel separation between lateral coherence loading and sequential (ζ-directed) coherence locking. Representative parameter insertions using atomic and nuclear length scales are found to lie within binding energies in the expected eV and MeV ranges, and are sufficient to distinguish the unbound proton–proton configuration from the bound proton–neutron channel under a common sequential locking scale, differing only in effective lateral compatibility. This initial computational reduction provides a tractable bridge between the geometric stability principles of the framework and order-of-magnitude binding behavior across selected node classes, including electron-containing and neutrino-mode configurations. The work forms part of an ongoing research program exploring resonance-based geometric foundations of matter and interaction.