A Coherent Vacuum‑Phase Framework (P1–P2–P3) for Galactic Dynamics: A Superconductivity‑Analog Model of Vacuum Phase Rigidity Without Dark Matter

This work proposes a P3 coherent vacuum‑phase framework that reproduces

galaxy rotation curves without invoking dark matter, using superconductivity analogies,

vacuum phase coherence, and a logarithmic gravitational term emerging from a coherent

vacuum‑phase gradient. The paper includes a mathematical appendix and a set of

predictive observational tests linking the P3 model to real data.