Knot-Based Gauge Fields and the Yang-Mills Mass Gap

This study proposes a knot‑based parameterization of non‑Abelian gauge fields is shown to enforce a nonzero Yang–Mills mass gap by embedding gluon self‑interactions into a fractal, space‑filling curve whose topological invariant \(\mathcal{I}(K)\) discretizes the configuration space. The resulting energy spectrum possesses a finite gap \[\Delta E \sim \frac{1}{\mathcal{I}(K)},\]with non‑perturbative QCD effects introducing only multiplicative corrections. This construction extends to all gauge theories in \(n\ge4\).