Geometric Foundation for a Hardcore Poisson Cut-off of SU(3) Yang-Mills in Four Dimensions - Degree bound, interaction graph, Reflection Positivity and strong-coupling confinement at fixed cut-off (no claim of continuum limit or mass gap)

This note constructs a well-defined ultraviolet regularisation of pure SU(3) Yang-Mills theory on R4 based on a Matérn-II hardcore Poisson point process of range ℓ > 0. The interaction graph is the Gilbert R-graph GR(P) with R = 4ℓ and deterministic degree bound degG(x) ≤ 6560, Tmax ≤ 6559, N ≤ 19677, uniform in the realisation of P. We define a finite-range local triangle action, establish Reflection Positivity in a minimalist version discarding Π-intersecting triangles, and, in the strong coupling regime β < β0 with explicit β0 ≈ 7.8×10⁻7, obtain via Kotecký-Preiss a unique infinite-volume Gibbs measure, exponential clustering and an area law. All results hold at fixed cut-off ℓ > 0. The continuum limit ℓ → 0, the weak-coupling regime β → ∞, full Reflection Positivity including TΠ, and the existence of a continuum mass gap are left open. The text makes no claim to solve the Clay Millennium Problem.