The Yang–Mills Existence and Mass Gap Problem and the Principle of the Threshold of Collective Emergence

This study presents a demonstration of the Yang–Mills existence and mass gap problem based on the Principle of the Threshold of Collective Emergence. The approach shows that a low-energy perturbation does not persist long enough for the self-interactions of the field to reinforce one another collectively. It establishes that beyond a critical energy threshold, these interactions can develop sufficiently to produce a distinct physical excitation, leading to the existence of a positive mass gap.