Proof of the Yang-Mills Mass Gap via Projection-Induced Curvature Thresholds

This paper presents a rigorous, nonperturbative solution to the Yang–Mills mass gap problem—one of the Clay Millennium Prize Problems—within a novel projection-theoretic framework. The author constructs a four-dimensional SU(N) quantum gauge theory satisfying all six Wightman axioms and exhibiting a strictly positive mass gap. The key mechanism is a projection-induced curvature threshold, below which field configurations are unprojectable and physically excluded. This threshold ensures confinement and excludes asymptotic coloured states, yielding glueball-like excitations in agreement with lattice QCD. The result is derived from the broader geometric framework introduced in The Mathematical Principles of Natural Philosophy: On the Origin of Spacetime (DOI: 10.5281/zenodo.10517478).