{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:63YPZRJNZ5OM2DED3LU35RDUI6","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":"55b3eb033650a70a00d12dd6871eb041ddb5dd9227ba7716f503d760fa27a9ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-06T18:19:34Z","title_canon_sha256":"9a3b26594921b169dfd7e13e553b23b10165daf9852bf901e32250fc456fdcea"},"schema_version":"1.0","source":{"id":"1310.1610","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1610","created_at":"2026-05-18T03:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1610v1","created_at":"2026-05-18T03:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1610","created_at":"2026-05-18T03:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"63YPZRJNZ5OM","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"63YPZRJNZ5OM2DED","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"63YPZRJN","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:ef3a6f79a8c79c0eca71e904f8d0dd5738f30f7176bfb17030e3b803cbeb0e19","target":"graph","created_at":"2026-05-18T03:11:11Z","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 give tight upper bounds on the total domination number, the weakly connected domination number and the connected domination number of a graph in terms of order and Euler characteristic. We also present upper bounds for the restrained bondage number, the total restrained bondage number and the restricted edge connectivity of graphs in terms of the orientable/nonorientable genus and maximum degree.","authors_text":"Vladimir Samodivkin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-06T18:19:34Z","title":"Upper bounds for domination related parameters in graphs on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1610","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":"sha256:3be3afaba91f48d9711595755c9e3b092f2e2b868029665aa94fce1415bcd1c9","target":"record","created_at":"2026-05-18T03:11:11Z","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":"55b3eb033650a70a00d12dd6871eb041ddb5dd9227ba7716f503d760fa27a9ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-06T18:19:34Z","title_canon_sha256":"9a3b26594921b169dfd7e13e553b23b10165daf9852bf901e32250fc456fdcea"},"schema_version":"1.0","source":{"id":"1310.1610","kind":"arxiv","version":1}},"canonical_sha256":"f6f0fcc52dcf5ccd0c83dae9bec47447a4255f0a2a61454cd68beddc3b5c5545","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6f0fcc52dcf5ccd0c83dae9bec47447a4255f0a2a61454cd68beddc3b5c5545","first_computed_at":"2026-05-18T03:11:11.310891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:11.310891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/LkWYevOhq8+W+dgpUlURTLT+yFVdDKzA8wQGbx5m7o0UwSCQM09Q6670abaC6BJysEGqax8Ygw04t/gyjYTAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:11.311773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1610","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3be3afaba91f48d9711595755c9e3b092f2e2b868029665aa94fce1415bcd1c9","sha256:ef3a6f79a8c79c0eca71e904f8d0dd5738f30f7176bfb17030e3b803cbeb0e19"],"state_sha256":"e924669c9bce8a6ae914d43b697f2829789acc69daee7ec26c16217c8d6d34aa"}