{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EFCZB5N65BL6TR6DJGU54MFOTM","short_pith_number":"pith:EFCZB5N6","schema_version":"1.0","canonical_sha256":"214590f5bee857e9c7c349a9de30ae9b2c53c61071adc90268c3e3b2fdc5ae9a","source":{"kind":"arxiv","id":"1807.01119","version":1},"attestation_state":"computed","paper":{"title":"A short derivation of the structure theorem for graphs with excluded topological minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Wei{\\ss}auer, Joshua Erde","submitted_at":"2018-07-03T12:31:58Z","abstract_excerpt":"As a major step in their proof of Wagner's conjecture, Robertson and Seymour showed that every graph not containing a fixed graph $H$ as a minor has a tree-decomposition in which each torso is almost embeddable in a surface of bounded genus. Recently, Grohe and Marx proved a similar result for graphs not containing $H$ as a topological minor. They showed that every graph which does not contain $H$ as a topological minor has a tree-decomposition in which every torso is either almost embeddable in a surface of bounded genus, or has a bounded number of vertices of high degree. We give a short pro"},"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":"1807.01119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-03T12:31:58Z","cross_cats_sorted":[],"title_canon_sha256":"e8d8bd495c627e85213ee1300c41b6de212d4ffa01aa91d4eb7444e80d4cbd2f","abstract_canon_sha256":"ac281df91b2b6aab77a3aedcf9b6ec1df7e94f94ea1b77cc0732ff5200c1cf94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:45.266907Z","signature_b64":"i6jU7Ib1PwrFGcMOezhhm9B+0ANj78QUSbJMsbGwUZ+VyEyhohUxlwMQ6IQ67v5Bo4Fm5SZZDVwksX74/MM7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"214590f5bee857e9c7c349a9de30ae9b2c53c61071adc90268c3e3b2fdc5ae9a","last_reissued_at":"2026-05-18T00:11:45.266242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:45.266242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A short derivation of the structure theorem for graphs with excluded topological minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Wei{\\ss}auer, Joshua Erde","submitted_at":"2018-07-03T12:31:58Z","abstract_excerpt":"As a major step in their proof of Wagner's conjecture, Robertson and Seymour showed that every graph not containing a fixed graph $H$ as a minor has a tree-decomposition in which each torso is almost embeddable in a surface of bounded genus. Recently, Grohe and Marx proved a similar result for graphs not containing $H$ as a topological minor. They showed that every graph which does not contain $H$ as a topological minor has a tree-decomposition in which every torso is either almost embeddable in a surface of bounded genus, or has a bounded number of vertices of high degree. We give a short pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01119","kind":"arxiv","version":1},"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":"1807.01119","created_at":"2026-05-18T00:11:45.266373+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.01119v1","created_at":"2026-05-18T00:11:45.266373+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01119","created_at":"2026-05-18T00:11:45.266373+00:00"},{"alias_kind":"pith_short_12","alias_value":"EFCZB5N65BL6","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EFCZB5N65BL6TR6D","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EFCZB5N6","created_at":"2026-05-18T12:32:22.470017+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/EFCZB5N65BL6TR6DJGU54MFOTM","json":"https://pith.science/pith/EFCZB5N65BL6TR6DJGU54MFOTM.json","graph_json":"https://pith.science/api/pith-number/EFCZB5N65BL6TR6DJGU54MFOTM/graph.json","events_json":"https://pith.science/api/pith-number/EFCZB5N65BL6TR6DJGU54MFOTM/events.json","paper":"https://pith.science/paper/EFCZB5N6"},"agent_actions":{"view_html":"https://pith.science/pith/EFCZB5N65BL6TR6DJGU54MFOTM","download_json":"https://pith.science/pith/EFCZB5N65BL6TR6DJGU54MFOTM.json","view_paper":"https://pith.science/paper/EFCZB5N6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.01119&json=true","fetch_graph":"https://pith.science/api/pith-number/EFCZB5N65BL6TR6DJGU54MFOTM/graph.json","fetch_events":"https://pith.science/api/pith-number/EFCZB5N65BL6TR6DJGU54MFOTM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EFCZB5N65BL6TR6DJGU54MFOTM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EFCZB5N65BL6TR6DJGU54MFOTM/action/storage_attestation","attest_author":"https://pith.science/pith/EFCZB5N65BL6TR6DJGU54MFOTM/action/author_attestation","sign_citation":"https://pith.science/pith/EFCZB5N65BL6TR6DJGU54MFOTM/action/citation_signature","submit_replication":"https://pith.science/pith/EFCZB5N65BL6TR6DJGU54MFOTM/action/replication_record"}},"created_at":"2026-05-18T00:11:45.266373+00:00","updated_at":"2026-05-18T00:11:45.266373+00:00"}