Tensorized Knot Invariants and the Yang-Mills Mass Gap

This paper introduces a novel approach to the Yang-Mills mass gap problem through the development of tensorized knot invariants. A new topological invariant $\mathcal{I}(K)$ is constructed for gauge field configurations, establishing a complete classification of field configurations into discrete topological sectors. The tensor structure enforces vacuum stability through energy barriers between sectors, with transition probabilities exponentially suppressed for small coupling. This framework provides a rigorous mathematical foundation for understanding the mass gap through the relationship between knot topology and gauge field dynamics.