This paper is the third in the Gravitype series. It derives strong constraints on admissible large-scale geometric organization in discrete SU(2)-valued substrates from locality, bounded valence, finite propagation, and conditional confinement stability. Broad classes of candidate geometries are excluded. The surviving admissible equivalence class is characterized by three-dimensional organization with triadic connectivity. The analysis is structural and pre-physical; no continuum limit, metric structure, or physical interpretation is assumed.
Nicholas Dean de St. Croix (Fri,) studied this question.