{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:XFOS5JV3U3W37V4O6KCSDRY2JK","short_pith_number":"pith:XFOS5JV3","schema_version":"1.0","canonical_sha256":"b95d2ea6bba6edbfd78ef28521c71a4a8d4495de10bf1954e7d466f040a16d91","source":{"kind":"arxiv","id":"1009.5912","version":3},"attestation_state":"computed","paper":{"title":"Packing six T-joins in plane graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Kral, Ken-ichi Kawarabayashi, Zdenek Dvorak","submitted_at":"2010-09-29T15:25:19Z","abstract_excerpt":"Let G be a plane graph and T an even subset of its vertices. It has been conjectured that if all T-cuts of G have the same parity and the size of every T-cut is at least k, then G contains k edge-disjoint T-joins. The case k=3 is equivalent to the Four Color Theorem, and the cases k=4, which was conjectured by Seymour, and k=5 were proved by Guenin. We settle the next open case k=6."},"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":"1009.5912","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-29T15:25:19Z","cross_cats_sorted":[],"title_canon_sha256":"57043a4466fe5cc6a2d6b8431bc251df9380d860ae84e429412fe1e9e07224ed","abstract_canon_sha256":"81d989315c859bbfbcc35efdcc179c3b851276e90fbd0b439b8fcfc6d78eccc9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:27.421493Z","signature_b64":"D1zgHOXiK0UcjVk6Ac9qDHIEuC/psF0U9NOkhq1lZIL5mtWTK4daFpastV5omikCOqeM68CTasf+1KtF3+01Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b95d2ea6bba6edbfd78ef28521c71a4a8d4495de10bf1954e7d466f040a16d91","last_reissued_at":"2026-05-18T02:53:27.420749Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:27.420749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Packing six T-joins in plane graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Kral, Ken-ichi Kawarabayashi, Zdenek Dvorak","submitted_at":"2010-09-29T15:25:19Z","abstract_excerpt":"Let G be a plane graph and T an even subset of its vertices. It has been conjectured that if all T-cuts of G have the same parity and the size of every T-cut is at least k, then G contains k edge-disjoint T-joins. The case k=3 is equivalent to the Four Color Theorem, and the cases k=4, which was conjectured by Seymour, and k=5 were proved by Guenin. We settle the next open case k=6."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5912","kind":"arxiv","version":3},"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":"1009.5912","created_at":"2026-05-18T02:53:27.420879+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.5912v3","created_at":"2026-05-18T02:53:27.420879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5912","created_at":"2026-05-18T02:53:27.420879+00:00"},{"alias_kind":"pith_short_12","alias_value":"XFOS5JV3U3W3","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"XFOS5JV3U3W37V4O","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"XFOS5JV3","created_at":"2026-05-18T12:26:17.028572+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/XFOS5JV3U3W37V4O6KCSDRY2JK","json":"https://pith.science/pith/XFOS5JV3U3W37V4O6KCSDRY2JK.json","graph_json":"https://pith.science/api/pith-number/XFOS5JV3U3W37V4O6KCSDRY2JK/graph.json","events_json":"https://pith.science/api/pith-number/XFOS5JV3U3W37V4O6KCSDRY2JK/events.json","paper":"https://pith.science/paper/XFOS5JV3"},"agent_actions":{"view_html":"https://pith.science/pith/XFOS5JV3U3W37V4O6KCSDRY2JK","download_json":"https://pith.science/pith/XFOS5JV3U3W37V4O6KCSDRY2JK.json","view_paper":"https://pith.science/paper/XFOS5JV3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.5912&json=true","fetch_graph":"https://pith.science/api/pith-number/XFOS5JV3U3W37V4O6KCSDRY2JK/graph.json","fetch_events":"https://pith.science/api/pith-number/XFOS5JV3U3W37V4O6KCSDRY2JK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XFOS5JV3U3W37V4O6KCSDRY2JK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XFOS5JV3U3W37V4O6KCSDRY2JK/action/storage_attestation","attest_author":"https://pith.science/pith/XFOS5JV3U3W37V4O6KCSDRY2JK/action/author_attestation","sign_citation":"https://pith.science/pith/XFOS5JV3U3W37V4O6KCSDRY2JK/action/citation_signature","submit_replication":"https://pith.science/pith/XFOS5JV3U3W37V4O6KCSDRY2JK/action/replication_record"}},"created_at":"2026-05-18T02:53:27.420879+00:00","updated_at":"2026-05-18T02:53:27.420879+00:00"}