String Solutions in Topological Phase Transitions: Geometric Approach to Confinement and Mass Spectrum

We present a geometric mechanism for string emergence from topological phase transitions inquantum chromodynamics. Unlike fundamental string theories, our model derives relativistic stringsdynamically through sphere-torus (S2 ⇌ T 2) transitions. Key results include: (1) Confinement as topological closure (π1(T 2)̸ = 0), (2) Tachyon-free mass spectrum(3) Minimal length Lmin = 2π√α′ ≈ 1.3 fm. Quantum simulations show 92% fidelity for J/ψ stringimplementation. The framework naturally incorporates gravity when ⟨K⟩ = 0.