{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:F55JXP5CPHFIYYGUYPHUQ2JGRK","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":"9cd0ce439942dc660c50f7decedde6e582327d5d3e1c0e5cf155c18e83f8ca18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-27T20:22:09Z","title_canon_sha256":"7f39735cf8853b606908a3f4793a2aef3dc5ce004c72098a6d368c60c93204ec"},"schema_version":"1.0","source":{"id":"1709.09725","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09725","created_at":"2026-05-18T00:34:06Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09725v1","created_at":"2026-05-18T00:34:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09725","created_at":"2026-05-18T00:34:06Z"},{"alias_kind":"pith_short_12","alias_value":"F55JXP5CPHFI","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F55JXP5CPHFIYYGU","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F55JXP5C","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:9c1549761d1141f50368b00110eb3958ef94a1b68d931f6196d4ae97a77ae71a","target":"graph","created_at":"2026-05-18T00:34:06Z","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":"Letters $x$ and $y$ alternate in a word $w$ if after deleting in $w$ all letters but the copies of $x$ and $y$ we either obtain a word $xyxy\\cdots$ (of even or odd length) or a word $yxyx\\cdots$ (of even or odd length). A graph $G=(V,E)$ is word-representable if and only if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $xy\\in E$. It is known that a graph is word-representable if and only if it admits a certain orientation called semi-transitive orientation.\n  Word-representable graphs generalize several important classes of graphs s","authors_text":"Hehui Wu, Jun Ma, Sergey Kitaev, Yangjing Long","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-27T20:22:09Z","title":"Word-representability of split graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09725","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":"sha256:6c803697c0abf88caa0bf613cffb9e491901ec95d436d1fc6f6c7576b2a8e7e9","target":"record","created_at":"2026-05-18T00:34:06Z","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":"9cd0ce439942dc660c50f7decedde6e582327d5d3e1c0e5cf155c18e83f8ca18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-27T20:22:09Z","title_canon_sha256":"7f39735cf8853b606908a3f4793a2aef3dc5ce004c72098a6d368c60c93204ec"},"schema_version":"1.0","source":{"id":"1709.09725","kind":"arxiv","version":1}},"canonical_sha256":"2f7a9bbfa279ca8c60d4c3cf4869268ab07afd9bef86aa7eb5fa7a0dea963904","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f7a9bbfa279ca8c60d4c3cf4869268ab07afd9bef86aa7eb5fa7a0dea963904","first_computed_at":"2026-05-18T00:34:06.936473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:06.936473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sP01P1PPTtWMplXVqpAzgcjabh77wgrmwP2fEPgm5H/tGojYYNacx6etFN65x/xdT5hJqNId6i7h7GD/z9N+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:06.937171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09725","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c803697c0abf88caa0bf613cffb9e491901ec95d436d1fc6f6c7576b2a8e7e9","sha256:9c1549761d1141f50368b00110eb3958ef94a1b68d931f6196d4ae97a77ae71a"],"state_sha256":"fa03fa1c0a5ce910c1807dfbc6900bc7daa6f8861525f8d28b83ae364691eba9"}