Complete Closure and Minimality in a Natural Class of Marked Rank-Four Two-Probe Configurations

We study marked rank-four two-probe configurations M_g = [a_1, ..., a_g, b, c], g >= 2, in the class A0, which fixes the ambient rank and probe roles and varies only the number g of base generators. For g = 4 we obtain a complete marked closure of the mixed-volume deficit: complete formal Gale equality, exact pruning by rank-four realizability, rank-boundary completion, the all-rank pointwise equality set, and finite/general measure equality. The all-rank zero set has four disjoint rank-stratified branches; its full-base-rank branch is exactly the known support-disjoint parallelotope equality criterion. To exclude exact but inactive closures, we introduce a candidate-independent fully active complete-closure criterion (FACC-v1a). The g = 2 model fails deficit activity because its deficit is identically zero, whereas the g = 3 model fails realizability-pruning activity because a one-dimensional Gale space has no nonzero intermediate rank boundary. Consequently g = 4 is the unique FACC-v1a minimum in A0.