{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HFZWCYETJB6NK7KT4YGIIWWW7Y","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":"0d1cf4bc58ec011390a1fd9d41fa8769905a380ba77f378d5bb3e096e7746169","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-06-06T09:12:31Z","title_canon_sha256":"b197f135e6f301fa854209a02ce52b3d1a36796648808e6f914f4c27d9a59485"},"schema_version":"1.0","source":{"id":"1306.1345","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1345","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1345v2","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1345","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"pith_short_12","alias_value":"HFZWCYETJB6N","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HFZWCYETJB6NK7KT","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HFZWCYET","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:ce0bef4916b09d2b5a0fb82039576345a70d73de007839f3b64cc8c64d5728f9","target":"graph","created_at":"2026-05-18T02:48:10Z","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":"We prove that a connected graph has linear rank-width 1 if and only if it is a distance-hereditary graph and its split decomposition tree is a path. An immediate consequence is that one can decide in linear time whether a graph has linear rank-width at most 1, and give an obstruction if not. Other immediate consequences are several characterisations of graphs of linear rank-width 1. In particular a connected graph has linear rank-width 1 if and only if it is locally equivalent to a caterpillar if and only if it is a vertex-minor of a path [O-joung Kwon and Sang-il Oum, Graphs of small rank-wid","authors_text":"Binh-Minh Bui-Xuan, Mamadou Moustapha Kant\\'e, Vincent Limouzy","cross_cats":["cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-06-06T09:12:31Z","title":"A Note on Graphs of Linear Rank-Width 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1345","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":"sha256:8a59ba15790dd0fd6f6d11771363c2471156547e252069b70c30b04da5ef4c88","target":"record","created_at":"2026-05-18T02:48:10Z","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":"0d1cf4bc58ec011390a1fd9d41fa8769905a380ba77f378d5bb3e096e7746169","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-06-06T09:12:31Z","title_canon_sha256":"b197f135e6f301fa854209a02ce52b3d1a36796648808e6f914f4c27d9a59485"},"schema_version":"1.0","source":{"id":"1306.1345","kind":"arxiv","version":2}},"canonical_sha256":"3973616093487cd57d53e60c845ad6fe3b6d7578a2b389e8a218b63536a18a5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3973616093487cd57d53e60c845ad6fe3b6d7578a2b389e8a218b63536a18a5c","first_computed_at":"2026-05-18T02:48:10.003119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:10.003119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T5Pox6Uj0qpRm3Lx1j8c8KwKxW54cP2jdFfW2b21Kp8xhnNvaUrBj2MT7KwAe0IfJBNjVbsgPFe11LTcjSEkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:10.003576Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1345","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a59ba15790dd0fd6f6d11771363c2471156547e252069b70c30b04da5ef4c88","sha256:ce0bef4916b09d2b5a0fb82039576345a70d73de007839f3b64cc8c64d5728f9"],"state_sha256":"bfcf56e3e4694dd6581161be619c475ff2dc687e09e226890582c09215931c85"}