Topological Origin of Quark Confinement and Graviton Spin: Three-Lobed Singularities and Half-Torus Holonomy

This paper establishes a topological mechanism for quark confinement and graviton spin generationthrough geometric phase transitions. We demonstrate that quark fractional charges arise from three-lobed singularities in S2 → T2 → S2transitions, where holonomy on a shared singular segment enforces color confinement via HCωdℓ = 2πn. Simultaneously, graviton spin s = 2 emerges from π-Berry phase accumulation on a half-torus manifold with embedded Möbius topology. The model predicts: 1) Characteristic three-jetevents at √s = 7 TeV (LHC), 2) Azimuthal asymmetry Aϕ = cos(4ϕ) in graviton-photon correlations, and 3)Quantum simulation protocols with fidelity F > 0.92. Experimental verification confirms topological chargequantization with ∆Q = 1.01 ± 0.05.