The Intrinsic Infrared Boundary Topological Conjecture for the Yang-Mills Mass Gap: SU(N) Scaling Relations, Glueball Spectrum Predictions and Lattice Self-Consistent Verification

The standard formulation of the Millennium Yang-Mills mass gap problem is premised on a boundaryless fourdimensional Euclidean space. This paper proposes an alternative selfconsistent framework: the infrared region of realistic gauge fields is not an infinitely smooth, boundaryless manifold, but a compact fourdimensional manifold endowed with an intrinsic Dirichlet infrared boundary. This boundary is not an artificially introduced regularization cutoff; it constitutes a topological property of the manifold itself. Drawing on the Atiyah-Singer index theorem, instanton topology, spectral geometry of manifolds with boundary and closedstring spectral relations, we construct a scaling formula for the lower bound of the lowest excitation spectrum of SU(N) Yang-Mills theory. The topological modulus is constrained by the second Chern class of the gauge bundle and the boundary degrees of freedom of the manifold, with the Planck scale adopted as the sole ultraviolet base scale and no additional independent scales introduced. The conjecture reproduces simultaneously the SU(3) glueball groundstate gap, the SU(2) Yang-Mills gap, confining string tension and the excited glueball spectrum, with all results falling within the error bands of lattice simulations. This paper further argues that the domain of validity of the standard Millennium proposition does not coincide with the physical manifold carrying an intrinsic infrared boundary; the two are distinct problems. This furnishes a previously underexamined topological perspective for the longstanding difficulty of obtaining a nonperturbative analytic solution to this problem. The novelty of this paper does not lie in the numerical results themselves—the glueball masses and string tension have long been established by lattice QCD. Rather, the innovation consists in reformulating the mass gap problem from a question of dynamical emergence on a boundaryless manifold to a calculation of spectral lower bounds on a compact manifold with an intrinsic infrared boundary, and in providing a topological scaling structure that is transferable across SU(N) gauge groups.