{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:H6QVT3IDMZBPW6OJOVES7TSRB6","short_pith_number":"pith:H6QVT3ID","schema_version":"1.0","canonical_sha256":"3fa159ed036642fb79c975492fce510fb99d01b1d2d1dcc7b3b72f939b7bd784","source":{"kind":"arxiv","id":"2606.25884","version":1},"attestation_state":"computed","paper":{"title":"Generalising Latin square orthogonality and Frobenius-K\\\"onig with alternating sign matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alena Ernst, Cian O'Brien, Jens Zumbr\\\"agel, John Sheekey, Stefano Lia","submitted_at":"2026-06-24T14:26:22Z","abstract_excerpt":"The theory of Latin squares has a long history. While the objects themselves appeared earlier, the study of their general mathematical theory dates back to Euler in the 18th century. Latin squares can be interpreted as 3-dimensional permutation hypermatrices, and alternating sign matrices often arise as a natural generalisation of permutation matrices. In 2018, Brualdi and Dahl introduced a generalisation of classical Latin squares using alternating sign hypermatrices. Inspired by their definition, we develop the theory of Italian squares, a related generalisation of Latin squares, together wi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.25884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-24T14:26:22Z","cross_cats_sorted":[],"title_canon_sha256":"c94e57e1fa5ee618f8eac524b09e55502d619c7430b355ce98be27c63c4092e2","abstract_canon_sha256":"08d3080431864267a425a33a3ce4f7fc13be883082d506ea304054f271fed2a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:42.240624Z","signature_b64":"stnj1J9EQsenWcMTS8fZOJTt3tUDd2FfXwo0IiAjfV4FaKISBHcLyOSWLb7rD8YBbyLj/yR+Zdi7GWPJrVzYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fa159ed036642fb79c975492fce510fb99d01b1d2d1dcc7b3b72f939b7bd784","last_reissued_at":"2026-06-25T01:18:42.240264Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:42.240264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalising Latin square orthogonality and Frobenius-K\\\"onig with alternating sign matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alena Ernst, Cian O'Brien, Jens Zumbr\\\"agel, John Sheekey, Stefano Lia","submitted_at":"2026-06-24T14:26:22Z","abstract_excerpt":"The theory of Latin squares has a long history. While the objects themselves appeared earlier, the study of their general mathematical theory dates back to Euler in the 18th century. Latin squares can be interpreted as 3-dimensional permutation hypermatrices, and alternating sign matrices often arise as a natural generalisation of permutation matrices. In 2018, Brualdi and Dahl introduced a generalisation of classical Latin squares using alternating sign hypermatrices. Inspired by their definition, we develop the theory of Italian squares, a related generalisation of Latin squares, together wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25884","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/2606.25884/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.25884","created_at":"2026-06-25T01:18:42.240323+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.25884v1","created_at":"2026-06-25T01:18:42.240323+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25884","created_at":"2026-06-25T01:18:42.240323+00:00"},{"alias_kind":"pith_short_12","alias_value":"H6QVT3IDMZBP","created_at":"2026-06-25T01:18:42.240323+00:00"},{"alias_kind":"pith_short_16","alias_value":"H6QVT3IDMZBPW6OJ","created_at":"2026-06-25T01:18:42.240323+00:00"},{"alias_kind":"pith_short_8","alias_value":"H6QVT3ID","created_at":"2026-06-25T01:18:42.240323+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/H6QVT3IDMZBPW6OJOVES7TSRB6","json":"https://pith.science/pith/H6QVT3IDMZBPW6OJOVES7TSRB6.json","graph_json":"https://pith.science/api/pith-number/H6QVT3IDMZBPW6OJOVES7TSRB6/graph.json","events_json":"https://pith.science/api/pith-number/H6QVT3IDMZBPW6OJOVES7TSRB6/events.json","paper":"https://pith.science/paper/H6QVT3ID"},"agent_actions":{"view_html":"https://pith.science/pith/H6QVT3IDMZBPW6OJOVES7TSRB6","download_json":"https://pith.science/pith/H6QVT3IDMZBPW6OJOVES7TSRB6.json","view_paper":"https://pith.science/paper/H6QVT3ID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.25884&json=true","fetch_graph":"https://pith.science/api/pith-number/H6QVT3IDMZBPW6OJOVES7TSRB6/graph.json","fetch_events":"https://pith.science/api/pith-number/H6QVT3IDMZBPW6OJOVES7TSRB6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H6QVT3IDMZBPW6OJOVES7TSRB6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H6QVT3IDMZBPW6OJOVES7TSRB6/action/storage_attestation","attest_author":"https://pith.science/pith/H6QVT3IDMZBPW6OJOVES7TSRB6/action/author_attestation","sign_citation":"https://pith.science/pith/H6QVT3IDMZBPW6OJOVES7TSRB6/action/citation_signature","submit_replication":"https://pith.science/pith/H6QVT3IDMZBPW6OJOVES7TSRB6/action/replication_record"}},"created_at":"2026-06-25T01:18:42.240323+00:00","updated_at":"2026-06-25T01:18:42.240323+00:00"}