The Yang-Mills Mass Gap as a Topological Consequence of Finite Universe Geometry

The Yang–Mills Mass Gap as a Topological Consequence of Finite Universe Geometry The Yang–Mills existence and mass gap problem - one of the seven Millennium Prize Problems-has remained unresolved for over two decades. This work demonstrates that the problem's intractability stems not from mathematical difficulty but from an unphysical assumption embedded in its standard formulation: the treatment of spacetime as infinite flat R⁴. The Obstruction We identify three fundamental obstacles that render the mass gap unreachable within the conventional R⁴ framework: Infrared catastrophe: Long-wavelength modes proliferate without bound, leading to Gribov ambiguities and uncontrolled infrared behavior. Dimensional…