Theory of Compactified Manifolds and Arithmetic-Topological Algebra

This paper presents a unified theory connecting the compactificationof multidimensional Calabi-Yau manifolds with arithmetictopologicalalgebra based on prime numbers and zeros of the Riemannzeta function. We prove that:• Fermions correspond to prime numbers through homotopy groupsπk(CY 7)• Bosons are described by composite numbers as resonant statesin 8D space• Particle masses emerge from topological action Stop and zerosζ(1/2 + iγn)The theory predicts resonances at En = γnΛG (ΛG ≈ 1.218 TeV)and explains the Standard Model mass hierarchy without free parameters.Novel connections between von Neumann entropy, Betti numbersb3(CY 7) = 192, and prime distributions are established.