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We propose a cosmological model in which the universe is fundamentally a spinor- like entity—a topologically nontrivial structure that requires two complete traversals of spacetime to return to its original state. In this framework, the apparent asymmetry between matter and antimatter arises not from imbalance or broken symmetry, but from a topologically necessary dual-phase evolution: the first traversal of the universe generates the matter-dominated phase; the second, an antimatter-dominated mirror, evolves in a reversed temporal orientation. Together, these form a unified spinor-cycle in which the global CPT symmetry is preserved.