Code behind the 78-class spinel ordering count. Enumerates cation placements on the fixed COD 9005102 oxygen geometry for one doubled cell per point-group family of index-2 sublattices, quotients by the full induced site-permutation group (compatible operations plus every lattice-translation coset), cross-checks orbit counts with Burnside's lemma, and merges all representatives with pymatgen StructureMatcher. Self-contained and rerunnable: known-answer control at 2 f.u., regression to the published 83-orbit upper bound, and positive/negative controls run inline.