{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z3JNA3E6X52GC4TARWBHEEJF4R","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":"0e120650eecc79665461dfaf658d31c6ad57b523cae2e571cfdb6de038bde3ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-04-26T11:44:19Z","title_canon_sha256":"2fec8a1a57a726caa88d45a37d38e49236245a7d0b672239a10e17a2541227a5"},"schema_version":"1.0","source":{"id":"1104.4892","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4892","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4892v2","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4892","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"Z3JNA3E6X52G","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z3JNA3E6X52GC4TA","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z3JNA3E6","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:cfb0aeff6eb56a012b82c3a17102f7996e57888fe7f17fa7b0c8e38aa7fcdf21","target":"graph","created_at":"2026-05-18T02:27:57Z","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 girth of a graph is the minimum weight of all simple cycles of the graph. We study the problem of determining the girth of an n-node unweighted undirected planar graph. The first non-trivial algorithm for the problem, given by Djidjev, runs in O(n^{5/4} log n) time. Chalermsook, Fakcharoenphol, and Nanongkai reduced the running time to O(n log^2 n). Weimann and Yuster further reduced the running time to O(n log n). In this paper, we solve the problem in O(n) time.","authors_text":"Hsien-Chih Chang, Hsueh-I Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-04-26T11:44:19Z","title":"Computing the Girth of a Planar Graph in Linear Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4892","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":"sha256:78cfd31f2b8bad8769631fbf1bf4c1f164b3d8268ebabf7894f4cc4d136ee17c","target":"record","created_at":"2026-05-18T02:27:57Z","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":"0e120650eecc79665461dfaf658d31c6ad57b523cae2e571cfdb6de038bde3ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-04-26T11:44:19Z","title_canon_sha256":"2fec8a1a57a726caa88d45a37d38e49236245a7d0b672239a10e17a2541227a5"},"schema_version":"1.0","source":{"id":"1104.4892","kind":"arxiv","version":2}},"canonical_sha256":"ced2d06c9ebf746172608d82721125e47702a4c469788ad124aadc1875d869a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ced2d06c9ebf746172608d82721125e47702a4c469788ad124aadc1875d869a0","first_computed_at":"2026-05-18T02:27:57.448496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:57.448496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fv09IcB+elhgW4HRMn1vfG68Astk/ZdjFot0sOGyCOGy0bhWyeknv70iW5mi0JAutB+N0uz4PoD46sE/YRNSDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:57.449126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4892","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78cfd31f2b8bad8769631fbf1bf4c1f164b3d8268ebabf7894f4cc4d136ee17c","sha256:cfb0aeff6eb56a012b82c3a17102f7996e57888fe7f17fa7b0c8e38aa7fcdf21"],"state_sha256":"22f59f79861a046610c839333b3bbf893f7bc5334082f0b36b989553b1191ded"}