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The first construction is based on an orthogonal direct-sum decomposition $\\mathbb{C}^6 = \\mathbb{C}^4 \\oplus \\mathbb{C}^2$. 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Throughout, vectors differing only by a global phase are counted as identical. The first construction is based on an orthogonal direct-sum decomposition $\\mathbb{C}^6 = \\mathbb{C}^4 \\oplus \\mathbb{C}^2$. The second construction is based on two-dimensional Hadamard pairs supported on coordinate planes."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We give two explicit quantum Latin squares of order 6, one with cardinality 13 and one with cardinality 17.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The constructions described, based on the orthogonal direct-sum decomposition of C^6 and the two-dimensional Hadamard pairs on coordinate planes, satisfy all the required properties of a quantum Latin square.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Two explicit quantum Latin squares of order 6 are constructed with cardinalities 13 and 17 using direct-sum decompositions and Hadamard pairs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Explicit constructions yield quantum Latin squares of order 6 with cardinalities 13 and 17.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"25440b728879ba4a41bb5824e8e7ec7f09b4530c97da2925ab7087fda23a23be"},"source":{"id":"2605.15540","kind":"arxiv","version":1},"verdict":{"id":"554012ea-fdd9-49b8-b70f-fdf80587bd52","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T14:26:13.258768Z","strongest_claim":"We give two explicit quantum Latin squares of order 6, one with cardinality 13 and one with cardinality 17.","one_line_summary":"Two explicit quantum Latin squares of order 6 are constructed with cardinalities 13 and 17 using direct-sum decompositions and Hadamard pairs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The constructions described, based on the orthogonal direct-sum decomposition of C^6 and the two-dimensional Hadamard pairs on coordinate planes, satisfy all the required properties of a quantum Latin square.","pith_extraction_headline":"Explicit constructions yield quantum Latin squares of order 6 with cardinalities 13 and 17."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15540/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T14:37:25.500815Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T14:31:17.435706Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T14:22:01.186189Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T14:21:54.027603Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"shingle_duplication","ran_at":"2026-05-19T13:49:41.827455Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T13:49:41.365078Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.612995Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"2d92d8a0bccd3023d3d11a176f0708b97edb274bae3c69e6ce70b9af398dfd1c"},"references":{"count":15,"sample":[{"doi":"","year":null,"title":"Euler,Recherches sur une nouvelle espèce de quarrés magiques, Verhandelingen uit- gegeven door het Zeeuwsch Genootschap der Wetenschappen te Vlissingen9, 85–239, 1782","work_id":"8cc49226-f0d5-4f6b-8c31-9e9b07690201","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1974,"title":"J. 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