Monotone Defect-Deleting Trades in One-Factorizations

This preprint studies exact trades between labeled one-factorizations of complete graphs through their action on the binary defect graph, whose vertices are factor labels and whose edges record pairs of one-factors that do not form a Hamilton cycle. Starting from a finite trade on K16, three computer-certified stable seeds on K64 are obtained. Two symbolic signed-doubling successor operations generate infinite families of exact trades with setwise monotone defect deletion: no new binary defect edge is created. If a construction has order n and changes r factor labels, it deletes exactly 5rn/48 defect edges. In particular, one family changes only three factors and deletes 5n/16 defects, while another changes 3n/16 factors and deletes 5n^2/256 defects. The preprint also develops a transporter-based decomposition that interprets defect changes as closed-orbit cancellation and boundary-path transport. This Zenodo record contains the manuscript together with the finite certificates, exact verification scripts, independent verifier implementation, expected outputs, integrity hashes, and reproduction instructions supporting the computer-assisted seed assertions.