{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4GUVCTBRWVSH6CZYXFTLKUW7MF","short_pith_number":"pith:4GUVCTBR","schema_version":"1.0","canonical_sha256":"e1a9514c31b5647f0b38b966b552df61501338de989564198a5904d4f9c211ed","source":{"kind":"arxiv","id":"1402.2469","version":1},"attestation_state":"computed","paper":{"title":"The edge ideals of complete multipartite hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Dariush Kiani, Sara Saeedi Madani","submitted_at":"2014-02-11T12:18:36Z","abstract_excerpt":"We classify all complete uniform multipartite hypergraphs with respect to some algebraic properties, such as being (almost) complete intersection, Gorenstein, level, $l$-Cohen-Macaulay, $l$-Buchsbaum, unmixed, and satisfying Serre's condition $S_r$, via some combinatorial terms. Also, we prove that for a complete $s$-uniform $t$-partite hypergraph $H$, vertex decomposability, shellability, sequentially $S_r$ and sequentially Cohen-Macaulay properties coincide with the condition that $H$ has $t-1$ sides consisting of a single vertex. Moreover, we show that the latter condition occurs if and onl"},"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":"1402.2469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-11T12:18:36Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"2c5e37e755d49ae0dd73790173a527e7d29ca5a8aba627f3c206a9bba43564dd","abstract_canon_sha256":"23cf657ada037083d981cc12feb25351ff7a0089944dae07afa2f319fe0e5961"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:08.250870Z","signature_b64":"ly98g7So/BrixJ6d5jsRHAnklfgKVdU38zGR0X6Zp+DOBO64A7y5gq5Gx2ghnJQ75s1SiW9rzxMq0YMLMPRhAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1a9514c31b5647f0b38b966b552df61501338de989564198a5904d4f9c211ed","last_reissued_at":"2026-05-18T02:59:08.250313Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:08.250313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The edge ideals of complete multipartite hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Dariush Kiani, Sara Saeedi Madani","submitted_at":"2014-02-11T12:18:36Z","abstract_excerpt":"We classify all complete uniform multipartite hypergraphs with respect to some algebraic properties, such as being (almost) complete intersection, Gorenstein, level, $l$-Cohen-Macaulay, $l$-Buchsbaum, unmixed, and satisfying Serre's condition $S_r$, via some combinatorial terms. Also, we prove that for a complete $s$-uniform $t$-partite hypergraph $H$, vertex decomposability, shellability, sequentially $S_r$ and sequentially Cohen-Macaulay properties coincide with the condition that $H$ has $t-1$ sides consisting of a single vertex. Moreover, we show that the latter condition occurs if and onl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2469","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":""},"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":"1402.2469","created_at":"2026-05-18T02:59:08.250399+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.2469v1","created_at":"2026-05-18T02:59:08.250399+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2469","created_at":"2026-05-18T02:59:08.250399+00:00"},{"alias_kind":"pith_short_12","alias_value":"4GUVCTBRWVSH","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4GUVCTBRWVSH6CZY","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4GUVCTBR","created_at":"2026-05-18T12:28:14.216126+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/4GUVCTBRWVSH6CZYXFTLKUW7MF","json":"https://pith.science/pith/4GUVCTBRWVSH6CZYXFTLKUW7MF.json","graph_json":"https://pith.science/api/pith-number/4GUVCTBRWVSH6CZYXFTLKUW7MF/graph.json","events_json":"https://pith.science/api/pith-number/4GUVCTBRWVSH6CZYXFTLKUW7MF/events.json","paper":"https://pith.science/paper/4GUVCTBR"},"agent_actions":{"view_html":"https://pith.science/pith/4GUVCTBRWVSH6CZYXFTLKUW7MF","download_json":"https://pith.science/pith/4GUVCTBRWVSH6CZYXFTLKUW7MF.json","view_paper":"https://pith.science/paper/4GUVCTBR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.2469&json=true","fetch_graph":"https://pith.science/api/pith-number/4GUVCTBRWVSH6CZYXFTLKUW7MF/graph.json","fetch_events":"https://pith.science/api/pith-number/4GUVCTBRWVSH6CZYXFTLKUW7MF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4GUVCTBRWVSH6CZYXFTLKUW7MF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4GUVCTBRWVSH6CZYXFTLKUW7MF/action/storage_attestation","attest_author":"https://pith.science/pith/4GUVCTBRWVSH6CZYXFTLKUW7MF/action/author_attestation","sign_citation":"https://pith.science/pith/4GUVCTBRWVSH6CZYXFTLKUW7MF/action/citation_signature","submit_replication":"https://pith.science/pith/4GUVCTBRWVSH6CZYXFTLKUW7MF/action/replication_record"}},"created_at":"2026-05-18T02:59:08.250399+00:00","updated_at":"2026-05-18T02:59:08.250399+00:00"}