The Ψ-Model as a One-Field Hypothesis: Exact Core, Geometric Mainline, and the Discipline of Physical Verification

This record contains the primary English manuscript of the Ψ-model together with a Ukrainian companion version. The manuscript studies a one-field hypothesis in which the only fundamental dynamical entity is the complex field Ψ(x)=A(x)e^{iφ(x)}, while geometric, wave, and spectral structures are treated as different regimes of a single action S[Ψ]. The work explicitly separates exact results, numerically reproduced nodes, working hypotheses, bridge-only elements, open obstacles, and forbidden routes. A central methodological requirement is the law of one physical object: geometry, far-field tails, energy, and the future spectral route to matter must arise from one and the same admissible isolated object. The English PDF is the primary citation version of this record; the Ukrainian PDF is provided as a supporting companion text. This deposit should be read as an open preprint-style research manuscript rather than a peer-reviewed journal publication.