{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OR4AWECDJMZLWWBCJFLRXB44Y2","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":"3c5f37c45ebabc87cdd6a1e9ab92cd4d663bbff5d830fec04c14027072170d2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-03T08:15:39Z","title_canon_sha256":"1afe82791d012ddb44a251efae15ff0ca96d9896fc845de4537338a3652671ed"},"schema_version":"1.0","source":{"id":"1305.0636","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0636","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0636v5","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0636","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"OR4AWECDJMZL","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OR4AWECDJMZLWWBC","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OR4AWECD","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:b4b45c038c3ed86ff4b7d2befe3ddffa222a58251822dd7b447dcc4851974700","target":"graph","created_at":"2026-05-18T01:22:08Z","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 class of cographs is known to have unbounded linear clique-width. We prove that a hereditary class of cographs has bounded linear clique-width if and only if it does not contain all quasi-threshold graphs or their complements. The proof borrows ideas from the enumeration of permutation classes.","authors_text":"Nicholas Korpelainen, Robert Brignall, Vincent Vatter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-03T08:15:39Z","title":"Linear Clique-Width for Hereditary Classes of Cographs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0636","kind":"arxiv","version":5},"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:f8d7898e255ad7f3616495b4dc2386b5aab95722536f066aadff2dfa6edf38b2","target":"record","created_at":"2026-05-18T01:22:08Z","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":"3c5f37c45ebabc87cdd6a1e9ab92cd4d663bbff5d830fec04c14027072170d2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-03T08:15:39Z","title_canon_sha256":"1afe82791d012ddb44a251efae15ff0ca96d9896fc845de4537338a3652671ed"},"schema_version":"1.0","source":{"id":"1305.0636","kind":"arxiv","version":5}},"canonical_sha256":"74780b10434b32bb582249571b879cc6a0ea6f12c34c11a7524aa542e9c69cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74780b10434b32bb582249571b879cc6a0ea6f12c34c11a7524aa542e9c69cdf","first_computed_at":"2026-05-18T01:22:08.903377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:08.903377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ew5STFsFcXxYsS1LQ04mfjsxwXEG7VjS00VFcxy0ot+r36hZ6WHQU3KOdmHbSfi5j+QrtB6/7y/AcRjbii+rCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:08.904053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0636","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8d7898e255ad7f3616495b4dc2386b5aab95722536f066aadff2dfa6edf38b2","sha256:b4b45c038c3ed86ff4b7d2befe3ddffa222a58251822dd7b447dcc4851974700"],"state_sha256":"b34ac242598635802f28b762c3c0ccab5c943c7b57c94c96129a713ac8d64453"}