Strong-coupling supports of SU(3) lattice gauge theory and a mirror-energy formulation of the mass gap: derivations, enumeration, weights and a conjec

We study the strong-coupling (character) expansion of four-dimensional SU(3) lattice Yang-Mills theory with the Wilson action, organized as a gas of plaquette supports. We derive step by step the Haar-integration rules, the weight of closed sheets, of discs and of three discs glued along a circle. We enumerate the translation classes of even plaquette sets and of \mathbb{Z}_{3} two-cycle supports through area 14. At area 11 there are 66 branched supports and at area 14 there are 224; the latter form a single orbit of 96 elements under the hypercubic group and decompose into three discs of 2, 4 and 8 plaquettes glued along a hexagon. We compute their weights and add them to a per-plaquette Kotecký-Preiss-type indicator, which holds up to \beta\simeq4.0 and fails from \beta=4.05 when all computed families are included. We also state the mass gap as \Delta=E_{1}-E_{0}, introduce the notation E\mathbb{H}_{0}=m_{0}^{2} in which the rest energy faces its mirror image, and formulate a conjecture on the role of the non-abelian self-interaction. All numerical results are computer-assisted and reproducible from the supplied code.