Mesons and Tetraquarks as Topological Strings: Geometric Unification in QCD Phase Transitions

We present a geometric model of mesons and tetraquarks as topological strings emerging from curvature dynamics in quantum chromodynamics. Mesons correspond to closed strings (S1) with quark-antiquark singularities, while tetraquarks form knotted vortex configurations stabilized by non-local torsion. Key results: (1) Mass-radius relation m = σL + ℏcRp⟨K⟩, (2) Exotic state classification via knot polynomials,(3) Predictive decay patterns from critical curvature κcrit = 2πmπ c/ℏ. Experimental verification throughquantum simulation shows 89% fidelity for π+ and 87% for Zc(3900).