{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JEWUEO2KUNPAJCOEQU4AIRRDV4","short_pith_number":"pith:JEWUEO2K","schema_version":"1.0","canonical_sha256":"492d423b4aa35e0489c48538044623af3f7455211424fb67f598f30b8a31ae18","source":{"kind":"arxiv","id":"1202.5718","version":1},"attestation_state":"computed","paper":{"title":"Chordal Graphs are Fully Orientable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Hsin-Hao Lai, Ko-Wei Lih","submitted_at":"2012-02-26T02:58:23Z","abstract_excerpt":"Suppose that D is an acyclic orientation of a graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let m and M denote the minimum and the maximum of the number of dependent arcs over all acyclic orientations of G. We call G fully orientable if G has an acyclic orientation with exactly d dependent arcs for every d satisfying m <= d <= M. A graph G is called chordal if every cycle in G of length at least four has a chord. We show that all chordal graphs are fully orientable."},"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":"1202.5718","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-26T02:58:23Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"a3857b91cbf1dd1a6f7a1f02e94c652ad7c1842f477e5e212d1c60563df7bbb8","abstract_canon_sha256":"63fd1a0c11ca84d200a585aaf82c3bc9f278b12296743e7147dc50483d6fd174"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:24.905142Z","signature_b64":"432obc3ypBovYk6vXfVpIi0d/kO88CIoAD9xLgWTdj0d8590w98Fe2x3JeSlMj0443NxV/m/JmLGTUe7Iz1YCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"492d423b4aa35e0489c48538044623af3f7455211424fb67f598f30b8a31ae18","last_reissued_at":"2026-05-18T04:01:24.904335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:24.904335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chordal Graphs are Fully Orientable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Hsin-Hao Lai, Ko-Wei Lih","submitted_at":"2012-02-26T02:58:23Z","abstract_excerpt":"Suppose that D is an acyclic orientation of a graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let m and M denote the minimum and the maximum of the number of dependent arcs over all acyclic orientations of G. We call G fully orientable if G has an acyclic orientation with exactly d dependent arcs for every d satisfying m <= d <= M. A graph G is called chordal if every cycle in G of length at least four has a chord. We show that all chordal graphs are fully orientable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5718","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":"1202.5718","created_at":"2026-05-18T04:01:24.904485+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.5718v1","created_at":"2026-05-18T04:01:24.904485+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5718","created_at":"2026-05-18T04:01:24.904485+00:00"},{"alias_kind":"pith_short_12","alias_value":"JEWUEO2KUNPA","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JEWUEO2KUNPAJCOE","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JEWUEO2K","created_at":"2026-05-18T12:27:11.947152+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/JEWUEO2KUNPAJCOEQU4AIRRDV4","json":"https://pith.science/pith/JEWUEO2KUNPAJCOEQU4AIRRDV4.json","graph_json":"https://pith.science/api/pith-number/JEWUEO2KUNPAJCOEQU4AIRRDV4/graph.json","events_json":"https://pith.science/api/pith-number/JEWUEO2KUNPAJCOEQU4AIRRDV4/events.json","paper":"https://pith.science/paper/JEWUEO2K"},"agent_actions":{"view_html":"https://pith.science/pith/JEWUEO2KUNPAJCOEQU4AIRRDV4","download_json":"https://pith.science/pith/JEWUEO2KUNPAJCOEQU4AIRRDV4.json","view_paper":"https://pith.science/paper/JEWUEO2K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.5718&json=true","fetch_graph":"https://pith.science/api/pith-number/JEWUEO2KUNPAJCOEQU4AIRRDV4/graph.json","fetch_events":"https://pith.science/api/pith-number/JEWUEO2KUNPAJCOEQU4AIRRDV4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JEWUEO2KUNPAJCOEQU4AIRRDV4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JEWUEO2KUNPAJCOEQU4AIRRDV4/action/storage_attestation","attest_author":"https://pith.science/pith/JEWUEO2KUNPAJCOEQU4AIRRDV4/action/author_attestation","sign_citation":"https://pith.science/pith/JEWUEO2KUNPAJCOEQU4AIRRDV4/action/citation_signature","submit_replication":"https://pith.science/pith/JEWUEO2KUNPAJCOEQU4AIRRDV4/action/replication_record"}},"created_at":"2026-05-18T04:01:24.904485+00:00","updated_at":"2026-05-18T04:01:24.904485+00:00"}