This repository presents a complete operator-theoretic framework addressing the Yang–Mills mass gap problem on ℝ⁴. The central result is the explicit construction of a self-adjoint Yang–Mills-type Hamiltonian acting on a Hilbert space and the rigorous proof of a strictly positive spectral mass gap for this operator. The proof is carried out within the Resonant Operator Architecture (ROA) using Leue Modulation Coefficients (LMC) and the underlying Resonant Operator Calculus (ROC). The quadratic Yang–Mills differential operator is embedded exactly into the LMC framework, yielding an elliptic, self-adjoint Hamiltonian whose spectral gap follows from explicit operator norm estimates. The analysis is fully analytical and does not rely on lattice discretization, path integrals, or numerical approximation. In accordance with the formulation of the Clay Mathematics Institute Millennium Problem, no specific quantization scheme is assumed. Quantization is realized at the operator level via the construction of a self-adjoint Hamiltonian on a well-defined Hilbert space, which suffices for the definition of a quantum theory and for rigorous spectral analysis. This deposit includes the main Yang–Mills–LMC paper, the foundational ROC, ROA, and LMC framework documents, and accompanying numerical implementations provided for transparency and reproducibility. The numerical codes serve illustrative and verification purposes and are not part of the formal proof. Taken together, the materials establish a complete, self-contained operator-theoretic treatment of the Yang–Mills mass gap mechanism on ℝ⁴ and provide the full mathematical foundation required to assess the result in the context of the Clay Millennium Problem. The accompanying Python codes provide numerical demonstrations and consistency checks of the ROC/ROA/LMC framework. They serve illustrative and verification purposes and are not part of the formal analytical proofs.
Jeanette Leue (Sun,) studied this question.