Topological Cosmology under BT-PEC Ontology: Singularity, Big Bang, Dimensional Emergence, Symmetry Breaking and Ten Falsifiable Predictions

This paper establishes a self-consistent topological cosmological model of cosmic evolution based on the BT-PEC ternary coupled topological dynamics ontological theory, utilizing Dirac constraint structures, a two-level critical bifurcation mechanism, and the principle of constraint submanifold homotopy-type jumping. The universe as a whole is defined as a closed topological dynamical system composed of a base-ontology second-order tensor field $B$, a temporal evolution 1-form field $T$, and an emergent constraint functional $\text{PEC}$. From first principles, this model rigorously derives the zero-dimensional topological singularity initial state of the universe, the second-level topological emergence event of the Big Bang, the hierarchical unfolding process of spacetime dimensions, the mechanism of spontaneous symmetry breaking at all levels of the universe, and the formation law of the four-dimensional macroscopic spacetime steady state. Distinguished from traditional explosive cosmologies, this theory defines the Big Bang as a topological structure mutation of the constraint submanifold rather than material expansion, and unifies the origin of dimensions, the emergence of time, and symmetry breaking as topological emergence effects of the ternary coupled system. Based on complete mathematical derivations, this paper presents ten strictly falsifiable, quantifiable, and observable scientific predictions in cosmology, providing a novel theoretical paradigm for early universe physics, the nature of spacetime, high-dimensional compactification, and cosmic topological structure research.