MUT v5.8.6: Effective Background Scalar Field Formulation and Derived Constants

MUT v5.8.6 presents a comprehensive formulation of the Effective Background Scalar Field (ΦA) framework, extending previous versions by incorporating atomic, gravitational, and galactic-scale derivations. This standalone supplement unifies the deterministic computation of the Fine-structure constant (α), the geometric phase factor (ξ), and the Newtonian gravitational constant (G) from a single scalar field substrate. The work demonstrates atomic-level resonance, field impedance alignment, and galactic rotation modeling without invoking dark matter. MUT v5.8.6 establishes a dimensionally consistent, mathematically rigorous, and physically unified framework for mass, electromagnetism, and gravitation, fully compatible with field-theoretic and quantum considerations.