{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SEQRI32UBWPA4SYD3SU4ELNXQN","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":"94a949ab5ec4a99215feaf9d717460450f5ca30b1418faff5795316433adb61a","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-03-27T12:09:50Z","title_canon_sha256":"e60bb0a9863ee440957305a05bf2bc2dacdb2609b4d775b1283bb8aee1b66b6a"},"schema_version":"1.0","source":{"id":"1703.09023","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09023","created_at":"2026-05-18T00:47:54Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09023v1","created_at":"2026-05-18T00:47:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09023","created_at":"2026-05-18T00:47:54Z"},{"alias_kind":"pith_short_12","alias_value":"SEQRI32UBWPA","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SEQRI32UBWPA4SYD","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SEQRI32U","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:453252e19bf6afc3b7e29c9f3d9ea49d976f6fe550b7d42948d99ee1f8dd671c","target":"graph","created_at":"2026-05-18T00:47:54Z","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":"The minimum dominating set (MDS) problem is a fundamental subject of theoretical computer science, and has found vast applications in different areas, including sensor networks, protein interaction networks, and structural controllability. However, the determination of the size of a MDS and the number of all MDSs in a general network is NP-hard, and it thus makes sense to seek particular graphs for which the MDS problem can be solved analytically. In this paper, we study the MDS problem in the pseudofractal scale-free web and the Sierpi\\'nski graph, which have the same number of vertices and e","authors_text":"Huan Li, Liren Shan, Zhongzhi Zhang","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-03-27T12:09:50Z","title":"Domination number and minimum dominating sets in pseudofractal scale-free web and Sierpi\\'nski graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09023","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":"sha256:7c4fe2cfabfaa8a7c6a7089280df50aec2eeb435297b880444388c7236b4aaf7","target":"record","created_at":"2026-05-18T00:47:54Z","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":"94a949ab5ec4a99215feaf9d717460450f5ca30b1418faff5795316433adb61a","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-03-27T12:09:50Z","title_canon_sha256":"e60bb0a9863ee440957305a05bf2bc2dacdb2609b4d775b1283bb8aee1b66b6a"},"schema_version":"1.0","source":{"id":"1703.09023","kind":"arxiv","version":1}},"canonical_sha256":"9121146f540d9e0e4b03dca9c22db78375592b3143f5d408971c3bb634fd198e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9121146f540d9e0e4b03dca9c22db78375592b3143f5d408971c3bb634fd198e","first_computed_at":"2026-05-18T00:47:54.532458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:54.532458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I+nnOz30vLmvFGc219pu1FdjWs2E5bBpEg+TEnskqmeHwsLnsyXUoEkmOeeLMLU/3mNw+F/I4RJjlfNS101bAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:54.533116Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.09023","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c4fe2cfabfaa8a7c6a7089280df50aec2eeb435297b880444388c7236b4aaf7","sha256:453252e19bf6afc3b7e29c9f3d9ea49d976f6fe550b7d42948d99ee1f8dd671c"],"state_sha256":"77e070c6cc59f8c272a24ea013f0b7768d08edcb29f4f1b4026b085384684b82"}