Addendum II to Model H: Multi-Scale Verification and Geometric Unification of Gravity

This addendum extends the "Model H" framework, presenting a unified solution for gravitational dynamics from the quantum scale to galactic structures without Dark Matter. Key Results: Tully-Fisher Derivation: We analytically derive the Baryonic Tully-Fisher Relation (M ∝ V^4) from the fluid dynamics of space-time, treating gravity as a tension in a superfluid medium. Precision Tests: The model is verified against independent galaxies (SPARC database) with predictive errors < 1.6%. Solar System Unification: We demonstrate that the anomalous precession of Mercury is explained by a specific geometric factor (K_G = 1.20) inherent to the orbital eccentricity, while spherical orbits follow a laminar regime (K_G ≈ 1.15). Fine Structure Constant: A thermodynamic link is proposed between the vacuum tension and the fine-structure constant (α ≈ 1/137). Methodology: The model introduces a "Geometric Coefficient" (K_G) modulating vacuum tension based on observed morphology, replacing Dark Matter halos with a shape-dependent gravitational response. Includes the complete unified derivation of the KG factor and the Master Equation. Model H: A Superfluid Mechanics Framework for Unified Cosmology https://zenodo.org/records/18436687 Addendum III to Model H: Connections with Fundamental Constants, Nuclear Forces, and Baryonic Mass https://zenodo.org/records/18350730 Addendum IV to Model H: Universal Derivations from a Single Parameter - From Fundamental Constants to Cosmology https://zenodo.org/records/18388914