{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YI2JUVZ7CS6O2UIT62BJQDZCEV","short_pith_number":"pith:YI2JUVZ7","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"},"canonical_sha256":"c2349a573f14bced5113f682980f22254c6312b17a54fa13dbe77f30ca7f7e90","source":{"kind":"arxiv","id":"1701.05961","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05961","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05961v1","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05961","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"YI2JUVZ7CS6O","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YI2JUVZ7CS6O2UIT","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YI2JUVZ7","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YI2JUVZ7CS6O2UIT62BJQDZCEV","target":"record","payload":{"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"},"canonical_sha256":"c2349a573f14bced5113f682980f22254c6312b17a54fa13dbe77f30ca7f7e90","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"},"source_kind":"arxiv","source_id":"1701.05961","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V2SXGd9U/XFEGoyhJiUXWqGlLk4aRUF67Wt2qWlGwpqO10b16SslM3EAA6gSUE0+9VHA1JPv2aVFlJmSunuvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:22:52.789377Z"},"content_sha256":"ccdb0e80b8f17512709e0a55a065c172f91105c7158f6319c14fce8f7af1b50d","schema_version":"1.0","event_id":"sha256:ccdb0e80b8f17512709e0a55a065c172f91105c7158f6319c14fce8f7af1b50d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YI2JUVZ7CS6O2UIT62BJQDZCEV","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VERFzQOLuoVFWq8cCHWjhMQE1uU8qkUYoTBXZkQYFtceGg2TDFUveINVegKPg4dJYb7J+sOTuqjgrqo/dHVmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:22:52.789716Z"},"content_sha256":"5845fd9e86beb83ae69c5b9548b3d52e15e720d67cf54613aa2fcf89dc43acc2","schema_version":"1.0","event_id":"sha256:5845fd9e86beb83ae69c5b9548b3d52e15e720d67cf54613aa2fcf89dc43acc2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV/bundle.json","state_url":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T17:22:52Z","links":{"resolver":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV","bundle":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV/bundle.json","state":"https://pith.science/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YI2JUVZ7CS6O2UIT62BJQDZCEV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YI2JUVZ7CS6O2UIT62BJQDZCEV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9f0ab3afef596c1ad913d0038fcdb6e49a996dab5b1db960baaa3d263b9ffa1b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2017-01-21T01:28:05Z","title_canon_sha256":"1fffcd4268c657462326432ffed87f195a713c338c9dd13008ee24202f68739a"},"schema_version":"1.0","source":{"id":"1701.05961","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05961","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05961v1","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05961","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"YI2JUVZ7CS6O","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YI2JUVZ7CS6O2UIT","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YI2JUVZ7","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:5845fd9e86beb83ae69c5b9548b3d52e15e720d67cf54613aa2fcf89dc43acc2","target":"graph","created_at":"2026-05-18T00:52:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Chris Hartman, Glenn G. Chappell, John Gimbel","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2017-01-21T01:28:05Z","title":"Approximations of the domination number of a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05961","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ccdb0e80b8f17512709e0a55a065c172f91105c7158f6319c14fce8f7af1b50d","target":"record","created_at":"2026-05-18T00:52:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9f0ab3afef596c1ad913d0038fcdb6e49a996dab5b1db960baaa3d263b9ffa1b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2017-01-21T01:28:05Z","title_canon_sha256":"1fffcd4268c657462326432ffed87f195a713c338c9dd13008ee24202f68739a"},"schema_version":"1.0","source":{"id":"1701.05961","kind":"arxiv","version":1}},"canonical_sha256":"c2349a573f14bced5113f682980f22254c6312b17a54fa13dbe77f30ca7f7e90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2349a573f14bced5113f682980f22254c6312b17a54fa13dbe77f30ca7f7e90","first_computed_at":"2026-05-18T00:52:19.747094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:19.747094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zq6MsoYS1Toi93JAOamaPRYCxm6OM82k+xZysNc79QQnW3UCYxvgGSYUfD8Q6a08V3cQUfelMrHuqYeXp42jAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:19.747751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05961","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccdb0e80b8f17512709e0a55a065c172f91105c7158f6319c14fce8f7af1b50d","sha256:5845fd9e86beb83ae69c5b9548b3d52e15e720d67cf54613aa2fcf89dc43acc2"],"state_sha256":"e6fbac4ee4b658a47b803b8d04ae0289bfa96cf95ebdcbfb20b0c8f1e9c110d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e9qdJul5zmbIzrX0nhU+irwTb79mrepnK6TbiR/P+vI5HEAgqAnF6YP2JDxR2LmWM1QQRPlyHzLPAE/JG4P6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T17:22:52.791838Z","bundle_sha256":"d7bda01fa016b956d6ac95c30a510c04aee1ea9b4f02ebd6e75965be0c1b4504"}}