Additive Conflict Obstructions in Group-Labeled Matroids

We study abelian-group labelings of a finite matroid that distinguish one basis sum from every other basis sum. An incidence conflict graph bounds the number of nonroot values, and an exact unsaturated integer-lattice criterion characterizes realization of a prescribed class partition. Uniform-matroid controls separate graph coloring from additive realization and show why torsion must be retained. Explicit ternary rank-six and binary rank-eight non-SI constructions attain the full-rank chromatic bound; the latter has a 47-vertex, join-indecomposable 8-critical core and no K5 joined to an odd cycle anywhere in its full original-root conflict graph. The binary six-forbidden proximity theorem supplies strict-density and full-value slice conditions for a hypothetical rank-eight obstruction. The universal five-forbidden and binary seven-forbidden proximity conjectures remain open. The supplement supplies exact inputs, certificate checkers, source, claim dependencies and additional adversarial tests.