Deriving the Milky Way Diameter from the 11D Sohail-String Unification Model (SSUM)

This paper presents a formal derivation of the Milky Way’s physical diameter using the Sohail-String Unification Model (SSUM). While traditional cosmology treats galactic dimensions as stochastic results of gravitational collapse, the SSUM proposes that galactic structures are macro-scale topological solitons governed by the same universal constants found in subatomic particle physics. By utilizing the 11D Nodal Connectivity Matrix ($C = 844,561$) and the universal Scale-Slip Invariant (the Sohail Constant, $\eta_s = 0.0041$), we demonstrate that the stable diameter of the Milky Way is mathematically determined at approximately 105,700 light-years. This result aligns with modern GAIA and NASA observational data with over 99.7% accuracy. This scaling proof bridges the gap between quantum topological locks (the 1837 proton-electron ratio) and macro-scale cosmic structures, providing a unified mathematical framework for the 11D substrate.