The Wilson-SlabMix Architecture for the Yang-Mills Mass Gap

This manuscript presents the Wilson-SlabMix proof architecture, a proof-oriented research monograph aimed at deriving a positive physical gauge-invariant mass gap in non-Abelian Yang-Mills theory from the standard Wilson lattice gauge measure. The central objective is to extract the spectral gap without inserting a gluon mass term and without assuming confinement, an area law, exponential clustering, or a pre-existing mass gap. The proposed route proceeds through Wilson lattice gauge measure, gauge quotient construction, transverse curvature variables, a renormalized Wilson-Calderón-Zygmund kernel bound, physical cumulant control, Osterwalder-Schrader reconstruction on gauge-invariant observables, and a SlabMix transfer architecture. The key spectral target is a strict contraction of the physical slab transfer operator on the orthogonal complement of the vacuum. Once this contraction is obtained, the standard spectral representation yields a positive lower bound for the physical Hamiltonian above the vacuum. The manuscript isolates three Wilson-native mechanisms required for closure: renormalization-group irrelevance of non-local polymer remainders, large-deviation suppression of extended topological connectors, and absence of non-vacuum flat directions in the local physical gauge quotient. It further develops transverse parametrix control, non-Abelian Peierls estimates, cellular 2-tree construction, reflection positivity for renormalized physical observables, Dobrushin mixing, Kotecký-Preiss polymer bounds, and an explicit dictionary for Wilson-SlabMix constants. The Fractal Consistency Law (FCL) is not used as a mathematical premise of the Wilson-sector proof. It enters only as an interpretive layer: the Yang-Mills mass gap is read as a positive admissibility barrier in the physical gauge-invariant sector. In this reading, the gap is not a gluon mass inserted into the action, but the positive cost that every non-vacuum physical excitation must pay to remain coherent through scale, topology, and gauge quotient. The manuscript should be read as a rigorous proof architecture and conditional closure program, not as an officially verified solution of the Clay Yang-Mills problem. Its decisive mathematical burden remains the full Wilson-native verification of the bootstrap constants and closure inequalities identified throughout the text.