A Topological Vortex-Ring Construction of a Yang-Mills Model with Mass Gap

We present a topological construction of a non-abelianYang-Mills quantum field theory onR^4 that satisfies the Osterwalder-Schrader axioms and exhibits a strictly positive mass gap.The model replaces the usual distributional gauge potential by a finite vortex-ring configuration space C, whose only dynamical degree of freedom is an integer winding number n. Theclassical action and quantum Hamiltonian reduce to explicit, finite expressions depending onlyon n; the Hamiltonian is diagonal on the winding basis with eigen values proportional to n^2.We prove existence of a continuum limit obtained from lattice approximations concentratingon C, reflection positivity and Osterwalder-Schrader reconstruction, a strictly positive spectralgap above the vacuum, and confinement in the form of a linear potential for separated localdefects. The proof strategy reduces analytic difficulties to topological persistence of windingunder refinement, uniform energy bounds, compactness of finite - volume transfer operators, andexplicit spectral estimates.