Mathematical Implementation of Cyclic Cosmology with Closed Spatial Geometry

This paper provides the global geometric and mathematical foundation for the Unified Cyclic Cosmology (UCC) toy model introduced in “Cyclic Cosmology via Global Topological Identification of Black Hole Singularities.” The original toy model focuses on physical intuition: linking black hole interiors, Planck-scale regions, and cosmological origins into a single cyclic picture, while deliberately avoiding heavy formalism. That approach clarifies what the idea is, but leaves open a crucial question: can such a universe be made mathematically consistent and observationally constrained? This companion paper addresses that question directly.