A Verified Transversal Corpus of 5,014,161 Nonextendible Pairs of Orthogonal Latin Squares of Order 10

This dataset provides explicit machine-readable data and reproducible verification for a reference corpus of 5,014,161 distinct ordered pairs of orthogonal Latin squares of order 10 (2-MOLS(10)). Exhaustive enumeration within the supplied corpus gives the following common-transversal distribution: • 12,472 pairs with no common transversal;• 1,489 pairs with exactly one common transversal;• 136 pairs with exactly two common transversals;• 5,000,064 pairs with exactly three common transversals. The maximum numbers of pairwise cell-disjoint common transversals are distributed as follows: • 12,472 pairs with packing number 0;• 1,539 pairs with packing number 1;• 5,000,150 pairs with packing number 2. No supplied pair has more than two pairwise disjoint common transversals. Consequently, none of the 5,014,161 pairs extends to a set of three mutually orthogonal Latin squares of order 10: such an extension would require the 100 cells to partition into ten disjoint common transversals. The deposit includes the complete reference corpus, all 12,472 zero-common-transversal records, a curated set of 150 packing-number-two witnesses, and two highlighted records with an exceptional three-transversal overlap pattern. For each highlighted record, every pair of its three common transversals intersects in exactly two cells, the triple intersection is empty, and the packing number is one. Reproducibility materials include two independent full-corpus verification programs, a selected-record verifier, recorded passing receipts, data-format documentation, SHA-256 checksums, citation metadata, and licensing information. Verification operates directly on the displayed arrays and does not require access to the method by which the corpus was produced. This release is intended as a reproducible benchmark and a source of explicit witnesses for research in Latin squares, mutually orthogonal Latin squares, transversals, finite nets, and computational combinatorial design. All numerical claims are relative to the supplied reference corpus. The release does not claim that the corpus is complete among all pairs of orthogonal Latin squares of order 10, nor that its records represent distinct isotopy or paratopy classes.