Admissibility, Convexity, and the Yang–Mills Mass Gap Emergent Electromagnetism as an Infrared Consistency Condition

This work presents a structured reframing of the four–dimensional Yang–Mills mass gap problem based on the principle of admissibility. Admissibility is defined as a minimal set of analytic and probabilistic conditions—boundedness, strict convexity, Gaussian domination, tightness of lattice approximations, reflection positivity, and infrared well-posedness—required for a gauge theory to admit a nonperturbative continuum formulation. Within this framework, the Yang–Mills mass gap is not treated as a separate dynamical hypothesis. Instead, it arises as a structural consequence of admissibility: strict convexity enforces Gaussian domination and exponential decay of Euclidean correlation functions, which in turn imply a strictly positive spectral gap under Osterwalder–Schrader reconstruction. The paper introduces the KN–Yang–Mills model as a minimal admissible deformation of Yang–Mills theory. The deformation preserves gauge symmetry, locality, and ultraviolet structure, introduces no explicit mass terms, and restores uniform convexity through a stabilizing geometric mechanism. Constructive existence of the theory follows via standard lattice approximation, tightness, and OS reconstruction arguments. A central consistency requirement for any mass-gap mechanism is compatibility with observed long-range physics. The admissibility framework is shown to be infrared-selective: while non-Abelian gauge modes are gapped, an Abelian infrared fixed point persists and reproduces Maxwell’s equations without independent postulate. This “Maxwell window” serves as an internal consistency check rather than an auxiliary assumption. This paper functions as a synthetic and organizing work within a broader series. Detailed technical proofs—covering convexity bounds, Gaussian domination, lattice tightness, OS reconstruction, and infrared sector analysis—are developed in the companion works cited herein. The present contribution isolates the admissibility principle and clarifies the logical structure linking existence, mass gap formation, and infrared consistency. No claim is made that ordinary Yang–Mills theory is admissible, nor that the Clay Millennium Problem is resolved in its original formulation. Rather, the work identifies admissibility as a unifying structural principle for nonperturbative gauge dynamics and exhibits a fully admissible four-dimensional Yang–Mills–type theory.