{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BJJYIUBWLBOLCJB7PYS5RODHJ6","short_pith_number":"pith:BJJYIUBW","schema_version":"1.0","canonical_sha256":"0a53845036585cb1243f7e25d8b8674f9635325b32103b2d94c033bc819d5abb","source":{"kind":"arxiv","id":"1412.1415","version":1},"attestation_state":"computed","paper":{"title":"Disjoint dijoins","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Katherine Edwards, Maria Chudnovsky, Paul Seymour, Ringi Kim","submitted_at":"2014-12-03T17:50:40Z","abstract_excerpt":"A dijoin in a digraph is a set of edges meeting every directed cut. D. R. Woodall conjectured in 1976 that if G is a digraph, and every directed cut of G has at least k edges, then there are k pairwise disjoint dijoins. This remains open, but a capacitated version is known to be false. In particular, A. Schrijver gave a digraph G and a subset S of its edge-set, such that every directed cut contains at least two edges in S, and yet there do not exist two disjoint dijoins included in S. In Schrijver's example, G is planar, and the subdigraph formed by the edges in S consists of three disjoint pa"},"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":"1412.1415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-03T17:50:40Z","cross_cats_sorted":[],"title_canon_sha256":"c0e0421c930668feb0c8fb00a1c1655ef0273fc70a644ac8887c8d0cf664f4ed","abstract_canon_sha256":"17bcdee403e3ab35a589a191743c0574daf8073aec2b20132bda72301824db47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:12.543633Z","signature_b64":"msK08Q+5eiFMDcM0LfHh4uL1pqiNQA7vtorDpayjT2GZM1MKiyezLJZ/TglPyb5uZv8Xdr9dC19ZAtC7aZrwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a53845036585cb1243f7e25d8b8674f9635325b32103b2d94c033bc819d5abb","last_reissued_at":"2026-05-18T02:32:12.543158Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:12.543158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Disjoint dijoins","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Katherine Edwards, Maria Chudnovsky, Paul Seymour, Ringi Kim","submitted_at":"2014-12-03T17:50:40Z","abstract_excerpt":"A dijoin in a digraph is a set of edges meeting every directed cut. D. R. Woodall conjectured in 1976 that if G is a digraph, and every directed cut of G has at least k edges, then there are k pairwise disjoint dijoins. This remains open, but a capacitated version is known to be false. In particular, A. Schrijver gave a digraph G and a subset S of its edge-set, such that every directed cut contains at least two edges in S, and yet there do not exist two disjoint dijoins included in S. In Schrijver's example, G is planar, and the subdigraph formed by the edges in S consists of three disjoint pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1415","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":"1412.1415","created_at":"2026-05-18T02:32:12.543228+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.1415v1","created_at":"2026-05-18T02:32:12.543228+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1415","created_at":"2026-05-18T02:32:12.543228+00:00"},{"alias_kind":"pith_short_12","alias_value":"BJJYIUBWLBOL","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BJJYIUBWLBOLCJB7","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BJJYIUBW","created_at":"2026-05-18T12:28:22.404517+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/BJJYIUBWLBOLCJB7PYS5RODHJ6","json":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6.json","graph_json":"https://pith.science/api/pith-number/BJJYIUBWLBOLCJB7PYS5RODHJ6/graph.json","events_json":"https://pith.science/api/pith-number/BJJYIUBWLBOLCJB7PYS5RODHJ6/events.json","paper":"https://pith.science/paper/BJJYIUBW"},"agent_actions":{"view_html":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6","download_json":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6.json","view_paper":"https://pith.science/paper/BJJYIUBW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.1415&json=true","fetch_graph":"https://pith.science/api/pith-number/BJJYIUBWLBOLCJB7PYS5RODHJ6/graph.json","fetch_events":"https://pith.science/api/pith-number/BJJYIUBWLBOLCJB7PYS5RODHJ6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6/action/storage_attestation","attest_author":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6/action/author_attestation","sign_citation":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6/action/citation_signature","submit_replication":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6/action/replication_record"}},"created_at":"2026-05-18T02:32:12.543228+00:00","updated_at":"2026-05-18T02:32:12.543228+00:00"}