This short note, on the mathematical part of version 2, proposes a spectral framework related to the Yang–Mills mass gap problem as formulated by Arthur Jaffe and Edward Witten. A coupled operator structure is introduced on a Hilbert space combining a Yang–Mills sector with a one-dimensional Schrödinger operator possessing a coercive potential. The resulting depth operator has purely discrete spectrum with strictly positive first excitation. A coupling condition excludes gauge excitations in the zero-depth sector. Together, these elements define a spectral mechanism in which all non-vacuum states are constrained to energy levels bounded below by a strictly positive constant. This yields a natural emergence of a mass gap within the Yang–Mills framework. The construction is formulated at the operator level and isolates the spectral mechanism independently of a full constructive quantum field theory. The remaining problem is the realization of the corresponding theory satisfying the Osterwalder–Schrader axioms.
Henrik Nilsson (Sun,) studied this question.