{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BDI64X2D5RWZR32R7JIMORMNFH","short_pith_number":"pith:BDI64X2D","schema_version":"1.0","canonical_sha256":"08d1ee5f43ec6d98ef51fa50c7458d29cbed600d260f8dd16db4e57585b19194","source":{"kind":"arxiv","id":"2605.25727","version":1},"attestation_state":"computed","paper":{"title":"A Bruhat order for Latin squares and alternating sign hypermatrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angela Carnevale, Cian O'Brien","submitted_at":"2026-05-25T11:35:06Z","abstract_excerpt":"The Bruhat order on permutation matrices extends to alternating sign matrices via corner-sum matrices, where the order is given by entrywise domination. A classical result of Lascoux and Sch\\\"utzenberger states that alternating sign matrices form the Dedekind-MacNeille completion of the Bruhat order on permutations.\n  Brualdi and Dahl introduced alternating sign hypermatrices as a three-dimensional analogue of alternating sign matrices and used them to generalise Latin squares, which may be viewed as three-dimensional analogues of permutation matrices.\n  In this paper, in analogy with the two-"},"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":"2605.25727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-25T11:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"efc01a159b70b6066766af8872194ee8d4d46b47a28af6d3706df492200ee753","abstract_canon_sha256":"e33a2bdc5ce2ae41e414e76547f1a50063fbb87b4c2c40fb5715351d3ea5ca7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:52.325528Z","signature_b64":"1wmOrgHIXPb/TWPA9X5eAsH+VPCzmQXlyB37fSObRUhPaeCvvQKqrzFefXCKzylWRGLvbocaMWb+yuCE1d1pDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08d1ee5f43ec6d98ef51fa50c7458d29cbed600d260f8dd16db4e57585b19194","last_reissued_at":"2026-05-26T02:04:52.324846Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:52.324846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Bruhat order for Latin squares and alternating sign hypermatrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angela Carnevale, Cian O'Brien","submitted_at":"2026-05-25T11:35:06Z","abstract_excerpt":"The Bruhat order on permutation matrices extends to alternating sign matrices via corner-sum matrices, where the order is given by entrywise domination. A classical result of Lascoux and Sch\\\"utzenberger states that alternating sign matrices form the Dedekind-MacNeille completion of the Bruhat order on permutations.\n  Brualdi and Dahl introduced alternating sign hypermatrices as a three-dimensional analogue of alternating sign matrices and used them to generalise Latin squares, which may be viewed as three-dimensional analogues of permutation matrices.\n  In this paper, in analogy with the two-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25727","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/2605.25727/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":"2605.25727","created_at":"2026-05-26T02:04:52.324989+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.25727v1","created_at":"2026-05-26T02:04:52.324989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25727","created_at":"2026-05-26T02:04:52.324989+00:00"},{"alias_kind":"pith_short_12","alias_value":"BDI64X2D5RWZ","created_at":"2026-05-26T02:04:52.324989+00:00"},{"alias_kind":"pith_short_16","alias_value":"BDI64X2D5RWZR32R","created_at":"2026-05-26T02:04:52.324989+00:00"},{"alias_kind":"pith_short_8","alias_value":"BDI64X2D","created_at":"2026-05-26T02:04:52.324989+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/BDI64X2D5RWZR32R7JIMORMNFH","json":"https://pith.science/pith/BDI64X2D5RWZR32R7JIMORMNFH.json","graph_json":"https://pith.science/api/pith-number/BDI64X2D5RWZR32R7JIMORMNFH/graph.json","events_json":"https://pith.science/api/pith-number/BDI64X2D5RWZR32R7JIMORMNFH/events.json","paper":"https://pith.science/paper/BDI64X2D"},"agent_actions":{"view_html":"https://pith.science/pith/BDI64X2D5RWZR32R7JIMORMNFH","download_json":"https://pith.science/pith/BDI64X2D5RWZR32R7JIMORMNFH.json","view_paper":"https://pith.science/paper/BDI64X2D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.25727&json=true","fetch_graph":"https://pith.science/api/pith-number/BDI64X2D5RWZR32R7JIMORMNFH/graph.json","fetch_events":"https://pith.science/api/pith-number/BDI64X2D5RWZR32R7JIMORMNFH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BDI64X2D5RWZR32R7JIMORMNFH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BDI64X2D5RWZR32R7JIMORMNFH/action/storage_attestation","attest_author":"https://pith.science/pith/BDI64X2D5RWZR32R7JIMORMNFH/action/author_attestation","sign_citation":"https://pith.science/pith/BDI64X2D5RWZR32R7JIMORMNFH/action/citation_signature","submit_replication":"https://pith.science/pith/BDI64X2D5RWZR32R7JIMORMNFH/action/replication_record"}},"created_at":"2026-05-26T02:04:52.324989+00:00","updated_at":"2026-05-26T02:04:52.324989+00:00"}