This work presents a unified model connecting mathematical compactification in the space of prime numbers with physical compactification of extra dimensions in string theory. It is shown that the imaginary unit i acts as a projection operator that reveals topological reduction defects, which are quantitatively expressed through the imaginary parts of Riemann zeta function zeros. The fundamental role of prime numbers 2, 3, 5 in the formation of three generations of Standard Model particles is substantiated. These defects determine the sectoral reduction coefficients κ, which govern the mass hierarchy of elementary particles and their magnetic moments. The theory establishes a bridge between number theory, topology, and particle physics.