The 720° Rotation: Why Fermions Need Two Full Turns ✓ 0° Initial state boundary in phase with background core rotates 360° ✗ 360° Boundary anti-phased ψ → −ψ (half-turn of boundary phase) core rotates 360° ✓ 720° Boundary restored full boundary phase cycle complete core boundary 0° 360° 720° 1 full cycle 2 full cycles ½ cycle (anti-phase) 1 full cycle (restored) The counter-rotating boundary has half the rotational periodicity of the core — the physical content of SU(2) double cover.