{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CMWIVQWM7KSB5RGXSCUBVE4MB2","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":"6ed97be9c808f4b7c949c31ad5cb30cc819c29861525fd46ca6f07936109f27e","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T18:48:29Z","title_canon_sha256":"8f21f5536b0852bef29686e1363e74ef5b355cd6fbb60acf85849d04ff6cc450"},"schema_version":"1.0","source":{"id":"1301.5271","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5271","created_at":"2026-05-18T00:55:17Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5271v3","created_at":"2026-05-18T00:55:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5271","created_at":"2026-05-18T00:55:17Z"},{"alias_kind":"pith_short_12","alias_value":"CMWIVQWM7KSB","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CMWIVQWM7KSB5RGX","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CMWIVQWM","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:3ce3a2858a97897709f437dcdfb6c172355a04b137bf4fc87b01df0897e19ff0","target":"graph","created_at":"2026-05-18T00:55:17Z","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":"Over the last 30 years, researchers have investigated connections between dimension for posets and planarity for graphs. Here we extend this line of research to the structural graph theory parameter tree-width by proving that the dimension of a finite poset is bounded in terms of its height and the tree-width of its cover graph.","authors_text":"Bartosz Walczak, Gwena\\\"el Joret, Kevin G. Milans, Piotr Micek, Ruidong Wang, William T. Trotter","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T18:48:29Z","title":"Tree-width and dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5271","kind":"arxiv","version":3},"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":"sha256:57b9f0313431c44a9090c151c61f9caada36fdf365e175342c7f7d4abd19146e","target":"record","created_at":"2026-05-18T00:55:17Z","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":"6ed97be9c808f4b7c949c31ad5cb30cc819c29861525fd46ca6f07936109f27e","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T18:48:29Z","title_canon_sha256":"8f21f5536b0852bef29686e1363e74ef5b355cd6fbb60acf85849d04ff6cc450"},"schema_version":"1.0","source":{"id":"1301.5271","kind":"arxiv","version":3}},"canonical_sha256":"132c8ac2ccfaa41ec4d790a81a938c0e898815169829cdd614987f0a85246aa8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"132c8ac2ccfaa41ec4d790a81a938c0e898815169829cdd614987f0a85246aa8","first_computed_at":"2026-05-18T00:55:17.969895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:17.969895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"crl/JLjxJZ67PM12HGV5I4F1BJEPVBpdvcnxEMg4iNrNDsroqYk7xtUMPkU67IxGS01LW16GzrJvpF5JNXl4Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:17.970495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5271","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57b9f0313431c44a9090c151c61f9caada36fdf365e175342c7f7d4abd19146e","sha256:3ce3a2858a97897709f437dcdfb6c172355a04b137bf4fc87b01df0897e19ff0"],"state_sha256":"ec0bb3bbf3a55a769554045066fc080a4dc255a35a5cb41d7737021cdf0f07d5"}