{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FHUSBZYIM3RFC3IFWDAJYHSAKJ","short_pith_number":"pith:FHUSBZYI","canonical_record":{"source":{"id":"1205.0343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-05-02T07:35:44Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"55b5553b45d5fff5100f15607dd5afe7a9e6a173030cdd0512953ccd43c88a9b","abstract_canon_sha256":"58485968a806fe91874635ea38487ee3078747c55920af646a4c852faab3a525"},"schema_version":"1.0"},"canonical_sha256":"29e920e70866e2516d05b0c09c1e405258fc513962c21c231b7286bd6515360d","source":{"kind":"arxiv","id":"1205.0343","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0343","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0343v1","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0343","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"FHUSBZYIM3RF","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FHUSBZYIM3RFC3IF","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FHUSBZYI","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FHUSBZYIM3RFC3IFWDAJYHSAKJ","target":"record","payload":{"canonical_record":{"source":{"id":"1205.0343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-05-02T07:35:44Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"55b5553b45d5fff5100f15607dd5afe7a9e6a173030cdd0512953ccd43c88a9b","abstract_canon_sha256":"58485968a806fe91874635ea38487ee3078747c55920af646a4c852faab3a525"},"schema_version":"1.0"},"canonical_sha256":"29e920e70866e2516d05b0c09c1e405258fc513962c21c231b7286bd6515360d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:34.737336Z","signature_b64":"bReMkUKR7y6NmzdJG/9y3I270YvfqBxosrYrX7xsfVlq02qgwX5eLGfO+xYIx0TSOdJ2xRFRQqCR2dCt7m7CCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29e920e70866e2516d05b0c09c1e405258fc513962c21c231b7286bd6515360d","last_reissued_at":"2026-05-18T03:56:34.736924Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:34.736924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.0343","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":"2026-05-18T03:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S4dh+QDaK8QAmoJpbjqS13za9BiAybZtPE4PdqDqx5KwHuPOa+3s5n7bRcEoogaJrQcbUgchFtkoG7ll1544Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T10:44:09.634011Z"},"content_sha256":"55aa93af9687e83c9838aa8df0429bbd3c7cf55845c42d81bc1ed6b81aa9ba12","schema_version":"1.0","event_id":"sha256:55aa93af9687e83c9838aa8df0429bbd3c7cf55845c42d81bc1ed6b81aa9ba12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FHUSBZYIM3RFC3IFWDAJYHSAKJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Signed and Minus Domination in Complete Multipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Hongyu Liang","submitted_at":"2012-05-02T07:35:44Z","abstract_excerpt":"In this paper we determine the exact values of the signed domination number, signed total domination number, and minus domination number of complete multipartite graphs, which substantially generalizes some previous results obtained for special subclasses of complete multipartite graphs such as cliques and complete bipartite graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0343","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":"2026-05-18T03:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"94iNRi3aLajiEbt2onqSncp84CwAlLnrGbbBm8OS+jHpKUlvUvRqA28NmTPrvdSUypl9sGV3d+frv734WQYqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T10:44:09.634353Z"},"content_sha256":"845c338d85f5b2be1e2b8bff0adf9cd773d357b71b8e1aab9be31dbe15c18120","schema_version":"1.0","event_id":"sha256:845c338d85f5b2be1e2b8bff0adf9cd773d357b71b8e1aab9be31dbe15c18120"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHUSBZYIM3RFC3IFWDAJYHSAKJ/bundle.json","state_url":"https://pith.science/pith/FHUSBZYIM3RFC3IFWDAJYHSAKJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHUSBZYIM3RFC3IFWDAJYHSAKJ/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":"2026-06-29T10:44:09Z","links":{"resolver":"https://pith.science/pith/FHUSBZYIM3RFC3IFWDAJYHSAKJ","bundle":"https://pith.science/pith/FHUSBZYIM3RFC3IFWDAJYHSAKJ/bundle.json","state":"https://pith.science/pith/FHUSBZYIM3RFC3IFWDAJYHSAKJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHUSBZYIM3RFC3IFWDAJYHSAKJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FHUSBZYIM3RFC3IFWDAJYHSAKJ","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":"58485968a806fe91874635ea38487ee3078747c55920af646a4c852faab3a525","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-05-02T07:35:44Z","title_canon_sha256":"55b5553b45d5fff5100f15607dd5afe7a9e6a173030cdd0512953ccd43c88a9b"},"schema_version":"1.0","source":{"id":"1205.0343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0343","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0343v1","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0343","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"FHUSBZYIM3RF","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FHUSBZYIM3RFC3IF","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FHUSBZYI","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:845c338d85f5b2be1e2b8bff0adf9cd773d357b71b8e1aab9be31dbe15c18120","target":"graph","created_at":"2026-05-18T03:56:34Z","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":"In this paper we determine the exact values of the signed domination number, signed total domination number, and minus domination number of complete multipartite graphs, which substantially generalizes some previous results obtained for special subclasses of complete multipartite graphs such as cliques and complete bipartite graphs.","authors_text":"Hongyu Liang","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-05-02T07:35:44Z","title":"Signed and Minus Domination in Complete Multipartite Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0343","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":"sha256:55aa93af9687e83c9838aa8df0429bbd3c7cf55845c42d81bc1ed6b81aa9ba12","target":"record","created_at":"2026-05-18T03:56:34Z","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":"58485968a806fe91874635ea38487ee3078747c55920af646a4c852faab3a525","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-05-02T07:35:44Z","title_canon_sha256":"55b5553b45d5fff5100f15607dd5afe7a9e6a173030cdd0512953ccd43c88a9b"},"schema_version":"1.0","source":{"id":"1205.0343","kind":"arxiv","version":1}},"canonical_sha256":"29e920e70866e2516d05b0c09c1e405258fc513962c21c231b7286bd6515360d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29e920e70866e2516d05b0c09c1e405258fc513962c21c231b7286bd6515360d","first_computed_at":"2026-05-18T03:56:34.736924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:34.736924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bReMkUKR7y6NmzdJG/9y3I270YvfqBxosrYrX7xsfVlq02qgwX5eLGfO+xYIx0TSOdJ2xRFRQqCR2dCt7m7CCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:34.737336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55aa93af9687e83c9838aa8df0429bbd3c7cf55845c42d81bc1ed6b81aa9ba12","sha256:845c338d85f5b2be1e2b8bff0adf9cd773d357b71b8e1aab9be31dbe15c18120"],"state_sha256":"02d44c18cd164b10d645dbb92964e44c7dd43e5a463a9122f5294ef35f1ad563"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SudOxmdzvBILWdWB5ZnJ9qq7OWHKpr82iOzZ9K10v2m9IlvWHjay5eu6Ko8EeHNa/E69TwdDkPJZc5CTAU2wBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T10:44:09.636162Z","bundle_sha256":"7e35730738c81746593436e4d01cbbd48f6bfa800b33242932d5591c056d26b9"}}