{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YI2JUVZ7CS6O2UIT62BJQDZCEV","short_pith_number":"pith:YI2JUVZ7","schema_version":"1.0","canonical_sha256":"c2349a573f14bced5113f682980f22254c6312b17a54fa13dbe77f30ca7f7e90","source":{"kind":"arxiv","id":"1701.05961","version":1},"attestation_state":"computed","paper":{"title":"Approximations of the domination number of a graph","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chris Hartman, Glenn G. Chappell, John Gimbel","submitted_at":"2017-01-21T01:28:05Z","abstract_excerpt":"Given a graph G, the domination number gamma(G) of G is the minimum order of a set S of vertices such that each vertex not in S is adjacent to some vertex in S. Equivalently, label the vertices from {0, 1} so that the sum over each closed neighborhood is at least one; the minimum value of the sum of all labels, with this restriction, is the domination number. The fractional domination number gamma_f(G) is defined in the same way, except that the vertex labels are chosen from [0, 1]. Given an ordering of the vertex set of G, let gamma_g(G) be the approximation of the domination number by the st"},"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":"1701.05961","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2017-01-21T01:28:05Z","cross_cats_sorted":[],"title_canon_sha256":"1fffcd4268c657462326432ffed87f195a713c338c9dd13008ee24202f68739a","abstract_canon_sha256":"9f0ab3afef596c1ad913d0038fcdb6e49a996dab5b1db960baaa3d263b9ffa1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:19.747751Z","signature_b64":"Zq6MsoYS1Toi93JAOamaPRYCxm6OM82k+xZysNc79QQnW3UCYxvgGSYUfD8Q6a08V3cQUfelMrHuqYeXp42jAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2349a573f14bced5113f682980f22254c6312b17a54fa13dbe77f30ca7f7e90","last_reissued_at":"2026-05-18T00:52:19.747094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:19.747094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximations of the domination number of a graph","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chris Hartman, Glenn G. Chappell, John Gimbel","submitted_at":"2017-01-21T01:28:05Z","abstract_excerpt":"Given a graph G, the domination number gamma(G) of G is the minimum order of a set S of vertices such that each vertex not in S is adjacent to some vertex in S. Equivalently, label the vertices from {0, 1} so that the sum over each closed neighborhood is at least one; the minimum value of the sum of all labels, with this restriction, is the domination number. The fractional domination number gamma_f(G) is defined in the same way, except that the vertex labels are chosen from [0, 1]. Given an ordering of the vertex set of G, let gamma_g(G) be the approximation of the domination number by the st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05961","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":"1701.05961","created_at":"2026-05-18T00:52:19.747187+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.05961v1","created_at":"2026-05-18T00:52:19.747187+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05961","created_at":"2026-05-18T00:52:19.747187+00:00"},{"alias_kind":"pith_short_12","alias_value":"YI2JUVZ7CS6O","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YI2JUVZ7CS6O2UIT","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YI2JUVZ7","created_at":"2026-05-18T12:31:56.362134+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/YI2JUVZ7CS6O2UIT62BJQDZCEV","json":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV.json","graph_json":"https://pith.science/api/pith-number/YI2JUVZ7CS6O2UIT62BJQDZCEV/graph.json","events_json":"https://pith.science/api/pith-number/YI2JUVZ7CS6O2UIT62BJQDZCEV/events.json","paper":"https://pith.science/paper/YI2JUVZ7"},"agent_actions":{"view_html":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV","download_json":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV.json","view_paper":"https://pith.science/paper/YI2JUVZ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.05961&json=true","fetch_graph":"https://pith.science/api/pith-number/YI2JUVZ7CS6O2UIT62BJQDZCEV/graph.json","fetch_events":"https://pith.science/api/pith-number/YI2JUVZ7CS6O2UIT62BJQDZCEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV/action/storage_attestation","attest_author":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV/action/author_attestation","sign_citation":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV/action/citation_signature","submit_replication":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV/action/replication_record"}},"created_at":"2026-05-18T00:52:19.747187+00:00","updated_at":"2026-05-18T00:52:19.747187+00:00"}