Gluonic Spectra through Knotified Correlators in Yang–Mills Theory

A mathematically rigorous construction of the Euclidean Yang–Mills measure is presented, based on a tensorized knot invariant \(I(K)\). By discretizing the space of framed knots and controlling topological fluctuations, a continuum limit is obtained that satisfies gauge invariance, ultraviolet finiteness, and reflection positivity. All Osterwalder–Schrader axioms are verified, leading to a self-adjoint transfer operator whose spectrum exhibits a strictly positive gap \(\Delta\ge\kappa\,\delta\), where \(\delta=\min_{K\neq\mathrm{trivial}}|I(K)|\). Analytic continuation to Minkowski space yields Wightman functions with an isolated one-particle glueball pole at mass \(m=\Delta\), thereby establishing a nonperturbative mass gap in pure Yang–Mills theory. Exponential clustering and infrared suppression are demonstrated via topological minimality, and the resulting glueball spectrum is expressed in terms of the minimal knot invariant and group-theoretic factors.