{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XZ5YATA6RAMD6UUVT7QWEFJ66K","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8f68180f46b7b15eb3b0326d9f4256728d25ba9a9bedc28baa273a6ec50524bc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-15T02:24:37Z","title_canon_sha256":"932fdb583257758266c583161ef3f9d169a7860c1dba995e697d857d131b3faf"},"schema_version":"1.0","source":{"id":"2605.15540","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15540","created_at":"2026-05-20T00:01:04Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15540v1","created_at":"2026-05-20T00:01:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15540","created_at":"2026-05-20T00:01:04Z"},{"alias_kind":"pith_short_12","alias_value":"XZ5YATA6RAMD","created_at":"2026-05-20T00:01:04Z"},{"alias_kind":"pith_short_16","alias_value":"XZ5YATA6RAMD6UUV","created_at":"2026-05-20T00:01:04Z"},{"alias_kind":"pith_short_8","alias_value":"XZ5YATA6","created_at":"2026-05-20T00:01:04Z"}],"graph_snapshots":[{"event_id":"sha256:750f742ab3c09c7e7ab413d4042e4f9570d32e6e37cca163f0194f2f885dea7e","target":"graph","created_at":"2026-05-20T00:01:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We give two explicit quantum Latin squares of order 6, one with cardinality 13 and one with cardinality 17."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Two explicit quantum Latin squares of order 6 are constructed with cardinalities 13 and 17 using direct-sum decompositions and Hadamard pairs."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Explicit constructions yield quantum Latin squares of order 6 with cardinalities 13 and 17."}],"snapshot_sha256":"25440b728879ba4a41bb5824e8e7ec7f09b4530c97da2925ab7087fda23a23be"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"2605a7092763ec2cf0235bbacb0ff58957f6566eb5f85c86e7b1280bbca7c8c9"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"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"}],"endpoint":"/pith/2605.15540/integrity.json","findings":[],"snapshot_sha256":"2d92d8a0bccd3023d3d11a176f0708b97edb274bae3c69e6ce70b9af398dfd1c","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give two explicit quantum Latin squares of order $6$, one with cardinality $13$ and one with cardinality $17$. 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.","authors_text":"Zhipeng Xu","cross_cats":[],"headline":"Explicit constructions yield quantum Latin squares of order 6 with cardinalities 13 and 17.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-15T02:24:37Z","title":"Two Quantum Latin Squares of Order 6 with Cardinalities 13 and 17"},"references":{"count":15,"internal_anchors":5,"resolved_work":15,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"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","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"J. Dénes and A. D. Keedwell,Latin Squares and Their Applications, Akadémiai Kiadó, Budapest, 1974","work_id":"d4ed641a-6f0d-4818-b2bd-600d4f2fd855","year":1974},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"C. J. Colbourn and J. H. Dinitz, editors,Handbook of Combinatorial Designs, second edition, Chapman & Hall/CRC, Boca Raton, 2007","work_id":"95455d27-4ad2-447f-803d-a6fb06e6a63d","year":2007},{"cited_arxiv_id":"","doi":"10.4153/cjm-1960-016-5","is_internal_anchor":false,"ref_index":4,"title":"R. C. Bose, S. S. Shrikhande, and E. T. Parker,Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler’s conjecture, Canadian Journal of Mathematics12, 189–20","work_id":"06141997-6cd2-4f39-a508-aa7d50af38b7","year":1960},{"cited_arxiv_id":"quant-ph/0003070","doi":"10.1088/0305-","is_internal_anchor":true,"ref_index":5,"title":"All Teleportation and Dense Coding Schemes","work_id":"8e7438cb-9b85-4268-af89-20891c102aa2","year":2001}],"snapshot_sha256":"e06891f67925db251651e6178c5917ec5b3d0d944c0dbe6c2719876ffec2094f"},"source":{"id":"2605.15540","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T14:26:13.258768Z","id":"554012ea-fdd9-49b8-b70f-fdf80587bd52","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"Explicit constructions yield quantum Latin squares of order 6 with cardinalities 13 and 17.","strongest_claim":"We give two explicit quantum Latin squares of order 6, one with cardinality 13 and one with cardinality 17.","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."}},"verdict_id":"554012ea-fdd9-49b8-b70f-fdf80587bd52"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:98aa83802d2bc8d0137d9cf2929b6add64a80e9f2e46b1ed5c3d85d866a30a42","target":"record","created_at":"2026-05-20T00:01:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8f68180f46b7b15eb3b0326d9f4256728d25ba9a9bedc28baa273a6ec50524bc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-15T02:24:37Z","title_canon_sha256":"932fdb583257758266c583161ef3f9d169a7860c1dba995e697d857d131b3faf"},"schema_version":"1.0","source":{"id":"2605.15540","kind":"arxiv","version":1}},"canonical_sha256":"be7b804c1e88183f52959fe162153ef29fef66d5804a015c87d7aeda2171824e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be7b804c1e88183f52959fe162153ef29fef66d5804a015c87d7aeda2171824e","first_computed_at":"2026-05-20T00:01:04.300424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:04.300424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xeQcTXxemsuk51ZxL7S+heUoXZ6Ke/1HlpGKki05HymViXgp2U0i4NCJ5s0uOPSqg4ZogodXSCA9YlWzHFO1Dg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:04.301250Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15540","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98aa83802d2bc8d0137d9cf2929b6add64a80e9f2e46b1ed5c3d85d866a30a42","sha256:750f742ab3c09c7e7ab413d4042e4f9570d32e6e37cca163f0194f2f885dea7e"],"state_sha256":"8929bf0f7802e5f2a997ae5d7290c445991433ceadaa99b2b558e8dffcc400b1"}