Geometric Origin of Electron Spin: Polar-Plane Sweep, the 720° Return, and the Structural Dissolution of the Superposition Mystery

The spin-1/2 property of the electron is one of the most fundamental yet least explained features of quantum mechanics. This paper — PP-03 in the META Physics preprint series — derives the spin-1/2 structure from the geometry of META Physics (Multi-dimensional Emergence Theory of Actuality). The key mechanism is the polar-plane sweep: when a 2-dimensional disk whose plane contains the rotation axis undergoes a full 2π rotation within a 3-dimensional ball B³ (R), the disk sweeps out the entire ball, and its boundary circle covers the full 2-sphere S² (R) twice — once per half-revolution. Consequently, orientational return requires 4π (720°), not 2π. This is the geometric content of the double cover SU (2) → SO (3). Within the META Physics framework, the Emergence System (ES) is S³ (R) ≅ SU (2). The two polar planes combine via the ES imaginary unit to form spin eigenstates: |↑⟩ = Dₓz + iDᵧz, |↓⟩ = Dₓz − iDᵧz. The equatorial plane, invariant under rotation, yields integer spin (spin-1). Detailed correspondence is established with the Dirac belt trick, SU (2) spinor representation theory, the fiber bundle SU (2) → SO (3), and the spin structure prerequisite on manifolds. The "superposition" of spin states is reinterpreted as the weighted geometric co-presence of two real polar planes in the ES — resolving the ontological mystery of quantum superposition as a structural limitation of the lower-dimensional WS₃ observer (DA-3). Five core results are established with zero free parameters: (I) the polar-plane sweep theorem; (II) spin eigenstates from ES imaginary structure; (III) integer spin from equatorial invariance; (IV) mass independence of spin; (V) geometric ORIGIN of quantum superposition. Mathematical formalization and documentation: Claude (Anthropic, Claude Opus 4. 6). The core insights, physical intuitions, and axiom system originate from the author's 30 years of independent research.