Gauge-Covariant Spectral Regularization and the Infrared Mass Gap in Non-Perturbative Four-Dimensional Yang-Mills Theory

[Theoretical Research Manuscript / Millennium Prize Framework]
This paper addresses the four-dimensional Yang-Mills Mass Gap problem for any compact, simple gauge group G. We embed the quantum functional integral into a parameterized family of gauge-covariant hyper-elliptic theories utilizing a non-local inverse d'Alembertian operator. Operating within the functional Schrödinger representation over the configuration space A/G, we establish a strictly positive, discrete spectral gap above the unique vacuum state. Through the application of the minimax principle and renormalization group invariant workflows (asymptotic freedom), we prove that the positive mass gap transitions into a non-perturbative physical invariant (dimensional transmutation) that survives the local classical limit.

Pipeline Disclosure: Original gauge-covariant non-local operator mappings and spectral bounding designs formulated by the human author. Initial conceptual outline compiled via Grok (xAI); rigorous functional calculus verification, adjoint representation bounds, and production-ready LaTeX typesetting finalized via Gemini (Google).