{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:PFFZOWAFMTFQ2ZDC24ZYA4HCPW","short_pith_number":"pith:PFFZOWAF","schema_version":"1.0","canonical_sha256":"794b97580564cb0d6462d7338070e27d91d4bd9ff402e6bb7a67e703fa82f678","source":{"kind":"arxiv","id":"1904.03824","version":1},"attestation_state":"computed","paper":{"title":"Cohen Macaulay Hybrid Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Fazal Abbas, Imran Anwar, Safyan Ahmad","submitted_at":"2019-04-08T03:58:02Z","abstract_excerpt":"We introduce a new family of graphs, namely, hybrid graphs. There are infinitely many hybrid graphs associated to a single graph. We show that every hybrid graph associated to a given graph is Cohen Macaulay. Furthermore, we show that every CohenMacaulay chordal graph is a hybrid graph."},"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":"1904.03824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-04-08T03:58:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"91f13f22c3eab23ede567d155a483db7a183fb429e7b6841dc6faf31254a2f2d","abstract_canon_sha256":"3562860f96ea9692567d336dbbd638b1534f0aa754fd5dd6d66d90b8422d32ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:08.028238Z","signature_b64":"YTT124jD1p47vr9Axy5+G0GEx+7VnUH8sEMRze506uKoRLEoJREOnCq8bTgCoMQ5uDglPKb7glGPQijXHbqnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"794b97580564cb0d6462d7338070e27d91d4bd9ff402e6bb7a67e703fa82f678","last_reissued_at":"2026-05-17T23:49:08.027564Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:08.027564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohen Macaulay Hybrid Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Fazal Abbas, Imran Anwar, Safyan Ahmad","submitted_at":"2019-04-08T03:58:02Z","abstract_excerpt":"We introduce a new family of graphs, namely, hybrid graphs. There are infinitely many hybrid graphs associated to a single graph. We show that every hybrid graph associated to a given graph is Cohen Macaulay. Furthermore, we show that every CohenMacaulay chordal graph is a hybrid graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03824","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":"1904.03824","created_at":"2026-05-17T23:49:08.027683+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.03824v1","created_at":"2026-05-17T23:49:08.027683+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03824","created_at":"2026-05-17T23:49:08.027683+00:00"},{"alias_kind":"pith_short_12","alias_value":"PFFZOWAFMTFQ","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"PFFZOWAFMTFQ2ZDC","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"PFFZOWAF","created_at":"2026-05-18T12:33:24.271573+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/PFFZOWAFMTFQ2ZDC24ZYA4HCPW","json":"https://pith.science/pith/PFFZOWAFMTFQ2ZDC24ZYA4HCPW.json","graph_json":"https://pith.science/api/pith-number/PFFZOWAFMTFQ2ZDC24ZYA4HCPW/graph.json","events_json":"https://pith.science/api/pith-number/PFFZOWAFMTFQ2ZDC24ZYA4HCPW/events.json","paper":"https://pith.science/paper/PFFZOWAF"},"agent_actions":{"view_html":"https://pith.science/pith/PFFZOWAFMTFQ2ZDC24ZYA4HCPW","download_json":"https://pith.science/pith/PFFZOWAFMTFQ2ZDC24ZYA4HCPW.json","view_paper":"https://pith.science/paper/PFFZOWAF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.03824&json=true","fetch_graph":"https://pith.science/api/pith-number/PFFZOWAFMTFQ2ZDC24ZYA4HCPW/graph.json","fetch_events":"https://pith.science/api/pith-number/PFFZOWAFMTFQ2ZDC24ZYA4HCPW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PFFZOWAFMTFQ2ZDC24ZYA4HCPW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PFFZOWAFMTFQ2ZDC24ZYA4HCPW/action/storage_attestation","attest_author":"https://pith.science/pith/PFFZOWAFMTFQ2ZDC24ZYA4HCPW/action/author_attestation","sign_citation":"https://pith.science/pith/PFFZOWAFMTFQ2ZDC24ZYA4HCPW/action/citation_signature","submit_replication":"https://pith.science/pith/PFFZOWAFMTFQ2ZDC24ZYA4HCPW/action/replication_record"}},"created_at":"2026-05-17T23:49:08.027683+00:00","updated_at":"2026-05-17T23:49:08.027683+00:00"}