{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZDAR7IVLNKANWA4IUMAWRCIVTH","short_pith_number":"pith:ZDAR7IVL","canonical_record":{"source":{"id":"1305.1366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-07T00:47:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cd77d48adb558e4c17d9c0e70bd737f82088dff2d199126f0cdd6173251123a4","abstract_canon_sha256":"648ac38ae83519f13c12b2edbeb2ea655ebb581bab14677a2e36bd6d6da3ca3e"},"schema_version":"1.0"},"canonical_sha256":"c8c11fa2ab6a80db0388a30168891599decff2193fd6271455904be111a6dda7","source":{"kind":"arxiv","id":"1305.1366","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1366","created_at":"2026-05-18T03:14:19Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1366v2","created_at":"2026-05-18T03:14:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1366","created_at":"2026-05-18T03:14:19Z"},{"alias_kind":"pith_short_12","alias_value":"ZDAR7IVLNKAN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZDAR7IVLNKANWA4I","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZDAR7IVL","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZDAR7IVLNKANWA4IUMAWRCIVTH","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-07T00:47:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cd77d48adb558e4c17d9c0e70bd737f82088dff2d199126f0cdd6173251123a4","abstract_canon_sha256":"648ac38ae83519f13c12b2edbeb2ea655ebb581bab14677a2e36bd6d6da3ca3e"},"schema_version":"1.0"},"canonical_sha256":"c8c11fa2ab6a80db0388a30168891599decff2193fd6271455904be111a6dda7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:19.506060Z","signature_b64":"y1InYEloJaD9SBbDoun7tyAexNgjXWOAk8BoNgNykvl6t9f8G1ceoHQrWbX/8IVHjZJ1c79mSXPn85IZJZAOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8c11fa2ab6a80db0388a30168891599decff2193fd6271455904be111a6dda7","last_reissued_at":"2026-05-18T03:14:19.504781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:19.504781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1366","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9E5TNtHu4HDbAVW2OdlT9S23MgWCOJEtrnzVQL4Dt5aomDJEqgBGztvx5YklO75nok6/atd1vxwoHWXsY1kXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:47:13.583378Z"},"content_sha256":"100f5242882b169adc27906cb32dc49d916522adf7c003d9c957f0846839ffc4","schema_version":"1.0","event_id":"sha256:100f5242882b169adc27906cb32dc49d916522adf7c003d9c957f0846839ffc4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZDAR7IVLNKANWA4IUMAWRCIVTH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Domination Number of Generalized Petersen Graphs with a Faulty Vertex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Jun-Lin Guo, Kuo-Hua Wu, Ton Kloks, Yue-Li Wang","submitted_at":"2013-05-07T00:47:55Z","abstract_excerpt":"In this paper, we investigate the domination number of generalized Petersen graphs P(n, 2) when there is a faulty vertex. Denote by $\\gamma(P(n,2))$ the domination number of P(n,2) and $\\gamma(P_f(n,2))$ the domination number of P(n,2) with a faulty vertex $u_f$. We show that $\\gamma(P_f(n,2))=\\gamma(P(n,2))-1$ when $n=5k+1$ or $5k+2$ and $\\gamma(P_f(n,2))=\\gamma(P(n,2))$ for the other cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1366","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kyZKXsal4ACXx1pTyrGugqssGRaOakl0FL6y1S5j8xvIW4yK7i2sgGWX9HqtvCS40GOxCv+9F2yEbNvNeYh/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:47:13.583756Z"},"content_sha256":"7211da12bb131c5e2274de46aa42f0429d6e91d7d1fea39d8f46dab680c10ec5","schema_version":"1.0","event_id":"sha256:7211da12bb131c5e2274de46aa42f0429d6e91d7d1fea39d8f46dab680c10ec5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH/bundle.json","state_url":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH/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":"2026-06-12T09:47:13Z","links":{"resolver":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH","bundle":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH/bundle.json","state":"https://pith.science/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZDAR7IVLNKANWA4IUMAWRCIVTH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZDAR7IVLNKANWA4IUMAWRCIVTH","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":"648ac38ae83519f13c12b2edbeb2ea655ebb581bab14677a2e36bd6d6da3ca3e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-07T00:47:55Z","title_canon_sha256":"cd77d48adb558e4c17d9c0e70bd737f82088dff2d199126f0cdd6173251123a4"},"schema_version":"1.0","source":{"id":"1305.1366","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1366","created_at":"2026-05-18T03:14:19Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1366v2","created_at":"2026-05-18T03:14:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1366","created_at":"2026-05-18T03:14:19Z"},{"alias_kind":"pith_short_12","alias_value":"ZDAR7IVLNKAN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZDAR7IVLNKANWA4I","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZDAR7IVL","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:7211da12bb131c5e2274de46aa42f0429d6e91d7d1fea39d8f46dab680c10ec5","target":"graph","created_at":"2026-05-18T03:14:19Z","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":"In this paper, we investigate the domination number of generalized Petersen graphs P(n, 2) when there is a faulty vertex. Denote by $\\gamma(P(n,2))$ the domination number of P(n,2) and $\\gamma(P_f(n,2))$ the domination number of P(n,2) with a faulty vertex $u_f$. We show that $\\gamma(P_f(n,2))=\\gamma(P(n,2))-1$ when $n=5k+1$ or $5k+2$ and $\\gamma(P_f(n,2))=\\gamma(P(n,2))$ for the other cases.","authors_text":"Jun-Lin Guo, Kuo-Hua Wu, Ton Kloks, Yue-Li Wang","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-07T00:47:55Z","title":"The Domination Number of Generalized Petersen Graphs with a Faulty Vertex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1366","kind":"arxiv","version":2},"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":"sha256:100f5242882b169adc27906cb32dc49d916522adf7c003d9c957f0846839ffc4","target":"record","created_at":"2026-05-18T03:14:19Z","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":"648ac38ae83519f13c12b2edbeb2ea655ebb581bab14677a2e36bd6d6da3ca3e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-07T00:47:55Z","title_canon_sha256":"cd77d48adb558e4c17d9c0e70bd737f82088dff2d199126f0cdd6173251123a4"},"schema_version":"1.0","source":{"id":"1305.1366","kind":"arxiv","version":2}},"canonical_sha256":"c8c11fa2ab6a80db0388a30168891599decff2193fd6271455904be111a6dda7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8c11fa2ab6a80db0388a30168891599decff2193fd6271455904be111a6dda7","first_computed_at":"2026-05-18T03:14:19.504781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:19.504781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y1InYEloJaD9SBbDoun7tyAexNgjXWOAk8BoNgNykvl6t9f8G1ceoHQrWbX/8IVHjZJ1c79mSXPn85IZJZAOAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:19.506060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1366","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:100f5242882b169adc27906cb32dc49d916522adf7c003d9c957f0846839ffc4","sha256:7211da12bb131c5e2274de46aa42f0429d6e91d7d1fea39d8f46dab680c10ec5"],"state_sha256":"b50d20eff3918230c87d6a15201a6229b911904838aa7bfb8bd309155a788dbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WMphf44mkIiO2aTKM0kRHHeZM3BdbItn7rzC4lwjG0lhvmm8eSPK+KDfpczsEnnWGzo3JkTNvl3rh+RFYZ5aDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:47:13.585629Z","bundle_sha256":"955526b4768fdeaa42b5af32aac8a175d8cbce55b903d286eeff052e6a758cc5"}}