{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7PXZWHD2V7U7AABBK3LUNKNGSN","short_pith_number":"pith:7PXZWHD2","schema_version":"1.0","canonical_sha256":"fbef9b1c7aafe9f0002156d746a9a6936d5fa9f0d6daa66c40c09e9a4c6ff46f","source":{"kind":"arxiv","id":"1301.0374","version":2},"attestation_state":"computed","paper":{"title":"The triangle-free graphs with rank 6","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Long Wang, Yi Wang, Yi-Zheng Fan","submitted_at":"2013-01-03T04:15:19Z","abstract_excerpt":"The rank of a graph G is defined to be the rank of its adjacency matrix A(G). In this paper we characterize all connected triangle-free graphs with rank 6."},"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":"1301.0374","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-03T04:15:19Z","cross_cats_sorted":[],"title_canon_sha256":"455bdb681e7f8c63e38ad0fdf95582bd99c23fedee3af6501c3bb771b9903c04","abstract_canon_sha256":"2e2f12fdbd27c7293092ec1885a8b9cc74f6f02ce3bafa0573d7b7a1b7bd0b6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:37.504486Z","signature_b64":"1DQaEneP16khVnxhMsZla6vVdQLCAJVtMeuooKffcFnjEdxHJBwetrd0AIdwdHfUmOK6/DFo7ccSc5R1ye9VAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbef9b1c7aafe9f0002156d746a9a6936d5fa9f0d6daa66c40c09e9a4c6ff46f","last_reissued_at":"2026-05-18T02:42:37.503858Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:37.503858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The triangle-free graphs with rank 6","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Long Wang, Yi Wang, Yi-Zheng Fan","submitted_at":"2013-01-03T04:15:19Z","abstract_excerpt":"The rank of a graph G is defined to be the rank of its adjacency matrix A(G). In this paper we characterize all connected triangle-free graphs with rank 6."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0374","kind":"arxiv","version":2},"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":"1301.0374","created_at":"2026-05-18T02:42:37.503944+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.0374v2","created_at":"2026-05-18T02:42:37.503944+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0374","created_at":"2026-05-18T02:42:37.503944+00:00"},{"alias_kind":"pith_short_12","alias_value":"7PXZWHD2V7U7","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7PXZWHD2V7U7AABB","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7PXZWHD2","created_at":"2026-05-18T12:27:36.564083+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/7PXZWHD2V7U7AABBK3LUNKNGSN","json":"https://pith.science/pith/7PXZWHD2V7U7AABBK3LUNKNGSN.json","graph_json":"https://pith.science/api/pith-number/7PXZWHD2V7U7AABBK3LUNKNGSN/graph.json","events_json":"https://pith.science/api/pith-number/7PXZWHD2V7U7AABBK3LUNKNGSN/events.json","paper":"https://pith.science/paper/7PXZWHD2"},"agent_actions":{"view_html":"https://pith.science/pith/7PXZWHD2V7U7AABBK3LUNKNGSN","download_json":"https://pith.science/pith/7PXZWHD2V7U7AABBK3LUNKNGSN.json","view_paper":"https://pith.science/paper/7PXZWHD2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.0374&json=true","fetch_graph":"https://pith.science/api/pith-number/7PXZWHD2V7U7AABBK3LUNKNGSN/graph.json","fetch_events":"https://pith.science/api/pith-number/7PXZWHD2V7U7AABBK3LUNKNGSN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7PXZWHD2V7U7AABBK3LUNKNGSN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7PXZWHD2V7U7AABBK3LUNKNGSN/action/storage_attestation","attest_author":"https://pith.science/pith/7PXZWHD2V7U7AABBK3LUNKNGSN/action/author_attestation","sign_citation":"https://pith.science/pith/7PXZWHD2V7U7AABBK3LUNKNGSN/action/citation_signature","submit_replication":"https://pith.science/pith/7PXZWHD2V7U7AABBK3LUNKNGSN/action/replication_record"}},"created_at":"2026-05-18T02:42:37.503944+00:00","updated_at":"2026-05-18T02:42:37.503944+00:00"}