{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4QNBDNGY6FXBMWUSHNHDY5XRMA","short_pith_number":"pith:4QNBDNGY","schema_version":"1.0","canonical_sha256":"e41a11b4d8f16e165a923b4e3c76f160037e06a03c2b261d9b545ff34004fcad","source":{"kind":"arxiv","id":"1406.3397","version":4},"attestation_state":"computed","paper":{"title":"On the dimension of posets with cover graphs of treewidth $2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gwena\\\"el Joret, Piotr Micek, Ruidong Wang, Veit Wiechert, William T. Trotter","submitted_at":"2014-06-13T01:03:56Z","abstract_excerpt":"In 1977, Trotter and Moore proved that a poset has dimension at most $3$ whenever its cover graph is a forest, or equivalently, has treewidth at most $1$. On the other hand, a well-known construction of Kelly shows that there are posets of arbitrarily large dimension whose cover graphs have treewidth $3$. In this paper we focus on the boundary case of treewidth $2$. It was recently shown that the dimension is bounded if the cover graph is outerplanar (Felsner, Trotter, and Wiechert) or if it has pathwidth $2$ (Bir\\'o, Keller, and Young). This can be interpreted as evidence that the dimension s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.3397","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-13T01:03:56Z","cross_cats_sorted":[],"title_canon_sha256":"b6515ab1ad5a8ba534e6fdd4a32cc6becaf9408ebd64cb2d276351630a2ecc93","abstract_canon_sha256":"b1f78fa4a665dcc9929189dd18dc8699f31648f77766fb7da996884254574dd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:39.045957Z","signature_b64":"iTwFpp0Megmx8bkdmd9kXe0Jid99vXkW1gWDa5Ablwvf5LpzI/tSPE4opAmY3EEszZL7DN49f3DFHv3POtKeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e41a11b4d8f16e165a923b4e3c76f160037e06a03c2b261d9b545ff34004fcad","last_reissued_at":"2026-05-18T01:15:39.045202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:39.045202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the dimension of posets with cover graphs of treewidth $2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gwena\\\"el Joret, Piotr Micek, Ruidong Wang, Veit Wiechert, William T. Trotter","submitted_at":"2014-06-13T01:03:56Z","abstract_excerpt":"In 1977, Trotter and Moore proved that a poset has dimension at most $3$ whenever its cover graph is a forest, or equivalently, has treewidth at most $1$. On the other hand, a well-known construction of Kelly shows that there are posets of arbitrarily large dimension whose cover graphs have treewidth $3$. In this paper we focus on the boundary case of treewidth $2$. It was recently shown that the dimension is bounded if the cover graph is outerplanar (Felsner, Trotter, and Wiechert) or if it has pathwidth $2$ (Bir\\'o, Keller, and Young). This can be interpreted as evidence that the dimension s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3397","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1406.3397","created_at":"2026-05-18T01:15:39.045341+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.3397v4","created_at":"2026-05-18T01:15:39.045341+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3397","created_at":"2026-05-18T01:15:39.045341+00:00"},{"alias_kind":"pith_short_12","alias_value":"4QNBDNGY6FXB","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4QNBDNGY6FXBMWUS","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4QNBDNGY","created_at":"2026-05-18T12:28:14.216126+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4QNBDNGY6FXBMWUSHNHDY5XRMA","json":"https://pith.science/pith/4QNBDNGY6FXBMWUSHNHDY5XRMA.json","graph_json":"https://pith.science/api/pith-number/4QNBDNGY6FXBMWUSHNHDY5XRMA/graph.json","events_json":"https://pith.science/api/pith-number/4QNBDNGY6FXBMWUSHNHDY5XRMA/events.json","paper":"https://pith.science/paper/4QNBDNGY"},"agent_actions":{"view_html":"https://pith.science/pith/4QNBDNGY6FXBMWUSHNHDY5XRMA","download_json":"https://pith.science/pith/4QNBDNGY6FXBMWUSHNHDY5XRMA.json","view_paper":"https://pith.science/paper/4QNBDNGY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.3397&json=true","fetch_graph":"https://pith.science/api/pith-number/4QNBDNGY6FXBMWUSHNHDY5XRMA/graph.json","fetch_events":"https://pith.science/api/pith-number/4QNBDNGY6FXBMWUSHNHDY5XRMA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4QNBDNGY6FXBMWUSHNHDY5XRMA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4QNBDNGY6FXBMWUSHNHDY5XRMA/action/storage_attestation","attest_author":"https://pith.science/pith/4QNBDNGY6FXBMWUSHNHDY5XRMA/action/author_attestation","sign_citation":"https://pith.science/pith/4QNBDNGY6FXBMWUSHNHDY5XRMA/action/citation_signature","submit_replication":"https://pith.science/pith/4QNBDNGY6FXBMWUSHNHDY5XRMA/action/replication_record"}},"created_at":"2026-05-18T01:15:39.045341+00:00","updated_at":"2026-05-18T01:15:39.045341+00:00"}