{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:H7VYRVQCITJ554ED2NBZJX3F4Z","short_pith_number":"pith:H7VYRVQC","schema_version":"1.0","canonical_sha256":"3feb88d60244d3def083d34394df65e66ab2829be59643016fa93a5e582a6e4f","source":{"kind":"arxiv","id":"1701.05639","version":2},"attestation_state":"computed","paper":{"title":"Orthogonal Tree Decompositions of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David R. Wood, Gwena\\\"el Joret, Pat Morin, Sergey Norin, Vida Dujmovi\\'c","submitted_at":"2017-01-19T23:09:46Z","abstract_excerpt":"This paper studies graphs that have two tree decompositions with the property that every bag from the first decomposition has a bounded-size intersection with every bag from the second decomposition. We show that every graph in each of the following classes has a tree decomposition and a linear-sized path decomposition with bounded intersections: (1) every proper minor-closed class, (2) string graphs with a linear number of crossings in a fixed surface, (3) graphs with linear crossing number in a fixed surface. Here `linear size' means that the total size of the bags in the path decomposition "},"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":"1701.05639","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-19T23:09:46Z","cross_cats_sorted":[],"title_canon_sha256":"cea0d21f64822ef4766172ce91270556f2d284d7b52773b2d45c0ff682a3922f","abstract_canon_sha256":"89fa4bf38b467ea56aec3bce54df2fd3edbc08c78f1572f7a5738c3c7e896fab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:42.353820Z","signature_b64":"U5NzfSf7FZ2JfkVfEsDM/IegGUeWTXY/LJsWPxi++UL/eEBHkpxKJlPwf2ezcM1HH5K+Mzk4xQ7xihFxbzIeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3feb88d60244d3def083d34394df65e66ab2829be59643016fa93a5e582a6e4f","last_reissued_at":"2026-05-18T00:15:42.353296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:42.353296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orthogonal Tree Decompositions of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David R. Wood, Gwena\\\"el Joret, Pat Morin, Sergey Norin, Vida Dujmovi\\'c","submitted_at":"2017-01-19T23:09:46Z","abstract_excerpt":"This paper studies graphs that have two tree decompositions with the property that every bag from the first decomposition has a bounded-size intersection with every bag from the second decomposition. We show that every graph in each of the following classes has a tree decomposition and a linear-sized path decomposition with bounded intersections: (1) every proper minor-closed class, (2) string graphs with a linear number of crossings in a fixed surface, (3) graphs with linear crossing number in a fixed surface. Here `linear size' means that the total size of the bags in the path decomposition "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05639","kind":"arxiv","version":2},"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":"1701.05639","created_at":"2026-05-18T00:15:42.353393+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.05639v2","created_at":"2026-05-18T00:15:42.353393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05639","created_at":"2026-05-18T00:15:42.353393+00:00"},{"alias_kind":"pith_short_12","alias_value":"H7VYRVQCITJ5","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"H7VYRVQCITJ554ED","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"H7VYRVQC","created_at":"2026-05-18T12:31:18.294218+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/H7VYRVQCITJ554ED2NBZJX3F4Z","json":"https://pith.science/pith/H7VYRVQCITJ554ED2NBZJX3F4Z.json","graph_json":"https://pith.science/api/pith-number/H7VYRVQCITJ554ED2NBZJX3F4Z/graph.json","events_json":"https://pith.science/api/pith-number/H7VYRVQCITJ554ED2NBZJX3F4Z/events.json","paper":"https://pith.science/paper/H7VYRVQC"},"agent_actions":{"view_html":"https://pith.science/pith/H7VYRVQCITJ554ED2NBZJX3F4Z","download_json":"https://pith.science/pith/H7VYRVQCITJ554ED2NBZJX3F4Z.json","view_paper":"https://pith.science/paper/H7VYRVQC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.05639&json=true","fetch_graph":"https://pith.science/api/pith-number/H7VYRVQCITJ554ED2NBZJX3F4Z/graph.json","fetch_events":"https://pith.science/api/pith-number/H7VYRVQCITJ554ED2NBZJX3F4Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H7VYRVQCITJ554ED2NBZJX3F4Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H7VYRVQCITJ554ED2NBZJX3F4Z/action/storage_attestation","attest_author":"https://pith.science/pith/H7VYRVQCITJ554ED2NBZJX3F4Z/action/author_attestation","sign_citation":"https://pith.science/pith/H7VYRVQCITJ554ED2NBZJX3F4Z/action/citation_signature","submit_replication":"https://pith.science/pith/H7VYRVQCITJ554ED2NBZJX3F4Z/action/replication_record"}},"created_at":"2026-05-18T00:15:42.353393+00:00","updated_at":"2026-05-18T00:15:42.353393+00:00"}