The Möbius-Torus Continuum: Quantized Dark Vorticity and Spinorial Chirality in a 𝕋³ Universe

Extending the mechanical framework of a toroidal (𝕋³) universe and viscous dark fluid dynamics, this paper presents a topological bridge between macroscopic cosmic vorticity and microscopic spinorial fields. I hypothesize that while the universe exhibits a closed, orientable global topology (𝕋³), localized sub-manifold fiber bundles undergo non-orientable SU(2) double-cover twists, behaving structurally as microscopic Möbius strips. By projecting the continuous vorticity field ω onto these Möbius fiber bundles, I demonstrate that continuous dark sector fluid rotation naturally undergoes topological quantization into half-integer circulation states (Q = n + 1/2). This quantization offers a geometric explanation for spin-1/2 fermion behavior (720° rotational symmetry) and chiral parity asymmetry within embedded dark fluid solitons. This model unifies macro-scale cosmological stress mechanics with micro-scale quantum spin states within a single continuum-topological framework.