{"paper":{"title":"Quantum Latin Squares of Order Six with Cardinalities Nineteen, Twenty-One, and Twenty-Three","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zhipeng Xu","submitted_at":"2026-07-13T16:51:12Z","abstract_excerpt":"We give three explicit quantum Latin squares of order $6$ with cardinalities $19$, $21$, and $23$, where vectors differing only by a global phase are counted as identical. The first two examples arise from normalized Schur products of columns of complex Hadamard matrices. For cardinality $19$, a Butson-type matrix over eighth roots of unity has the unique nontrivial coincidence $v_{01}=v_{25}=v_{34}$. For cardinality $21$, an explicit member of Karlsson's three-parameter family has $21$ pairwise inequivalent unordered Schur products. To exceed the symmetric Schur-product bound, we give a third"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11800","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.11800/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}