The Sohail-String Unification Model (SSUM): Comprehensive 10-Page Mathematical Derivations and 11D Mechanical Proofs

This treatise presents the mathematical and mechanical architecture of the SohailString Unification Model (SSUM). We define the vacuum as a physical 11-dimensional medium with a universal viscosity of ηs = 0.0041 Pa·s. From this single invariant, we derive the Planck constant, the Bohr radius, and the deterministic mass ratio of the proton-to-electron (1836.15267) based on a connection density of 844,561. This framework resolves the Hubble Tension and eliminates the requirement for Dark Matter in galactic dynamics.