The Sohail–String Unification Model (SSUM): A Deterministic Mechanical Framework from an 11D Physical Vacuum

The Sohail–String Unification Model (SSUM) proposes a deterministic physicaldescription of nature in which the vacuum is not an empty geometric backgroundbut a mechanically active, viscous, higher-dimensional string matrix. Elementaryparticles are interpreted as stable topological knots formed within this matrix, withobservable physical constants emerging from internal connectivity and resonanceharmonics. A universal vacuum viscosity, termed the Sohail Invariant (ηs ≈ 0.0041Pa·s), is derived from baryonic mass topology and leptonic resonance ratios. Usingthis invariant, the proton–electron mass ratio, Planck constant, and atomic lengthscales are obtained through deterministic relations. At astrophysical and cosmological scales, SSUM provides mechanical explanations for flat galactic rotation curvesand the observed Hubble tension without invoking non-baryonic dark matter ormodified gravity. The framework yields testable predictions for early galaxy formation and gravitational-wave dispersion.