{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BJJYIUBWLBOLCJB7PYS5RODHJ6","short_pith_number":"pith:BJJYIUBW","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"},"canonical_sha256":"0a53845036585cb1243f7e25d8b8674f9635325b32103b2d94c033bc819d5abb","source":{"kind":"arxiv","id":"1412.1415","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1415","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1415v1","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1415","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"pith_short_12","alias_value":"BJJYIUBWLBOL","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BJJYIUBWLBOLCJB7","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BJJYIUBW","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BJJYIUBWLBOLCJB7PYS5RODHJ6","target":"record","payload":{"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"},"canonical_sha256":"0a53845036585cb1243f7e25d8b8674f9635325b32103b2d94c033bc819d5abb","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"},"source_kind":"arxiv","source_id":"1412.1415","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4leAxo2IEHjTmTGVGivaUb70sZFIL6cjOZSgEHjFRAr88fuuhdYQ/ArTDL1iwNUK6Em4oFvbQ13eH/RUBzUkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:05:24.298641Z"},"content_sha256":"2a738102e96d1a5828b69c13d848a3705c3b03cc214b81548a1f33dfbba683cf","schema_version":"1.0","event_id":"sha256:2a738102e96d1a5828b69c13d848a3705c3b03cc214b81548a1f33dfbba683cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BJJYIUBWLBOLCJB7PYS5RODHJ6","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6J+ryGBv2GFQ5FGwn4De68Wjh6rv96jV0B2Ruw3BKczg/hDLUSnSBNrnscWXIjhaQ8WCH/4JlBAZgaLDJzzODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:05:24.299019Z"},"content_sha256":"060c0bb1c35c91e532e5cbb43a2ca808cfe3e433a69ea4bb5911643e95c94e62","schema_version":"1.0","event_id":"sha256:060c0bb1c35c91e532e5cbb43a2ca808cfe3e433a69ea4bb5911643e95c94e62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6/bundle.json","state_url":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T14:05:24Z","links":{"resolver":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6","bundle":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6/bundle.json","state":"https://pith.science/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJJYIUBWLBOLCJB7PYS5RODHJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BJJYIUBWLBOLCJB7PYS5RODHJ6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"17bcdee403e3ab35a589a191743c0574daf8073aec2b20132bda72301824db47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-03T17:50:40Z","title_canon_sha256":"c0e0421c930668feb0c8fb00a1c1655ef0273fc70a644ac8887c8d0cf664f4ed"},"schema_version":"1.0","source":{"id":"1412.1415","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1415","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1415v1","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1415","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"pith_short_12","alias_value":"BJJYIUBWLBOL","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BJJYIUBWLBOLCJB7","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BJJYIUBW","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:060c0bb1c35c91e532e5cbb43a2ca808cfe3e433a69ea4bb5911643e95c94e62","target":"graph","created_at":"2026-05-18T02:32:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Alex Scott, Katherine Edwards, Maria Chudnovsky, Paul Seymour, Ringi Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-03T17:50:40Z","title":"Disjoint dijoins"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1415","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2a738102e96d1a5828b69c13d848a3705c3b03cc214b81548a1f33dfbba683cf","target":"record","created_at":"2026-05-18T02:32:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"17bcdee403e3ab35a589a191743c0574daf8073aec2b20132bda72301824db47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-03T17:50:40Z","title_canon_sha256":"c0e0421c930668feb0c8fb00a1c1655ef0273fc70a644ac8887c8d0cf664f4ed"},"schema_version":"1.0","source":{"id":"1412.1415","kind":"arxiv","version":1}},"canonical_sha256":"0a53845036585cb1243f7e25d8b8674f9635325b32103b2d94c033bc819d5abb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a53845036585cb1243f7e25d8b8674f9635325b32103b2d94c033bc819d5abb","first_computed_at":"2026-05-18T02:32:12.543158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:12.543158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"msK08Q+5eiFMDcM0LfHh4uL1pqiNQA7vtorDpayjT2GZM1MKiyezLJZ/TglPyb5uZv8Xdr9dC19ZAtC7aZrwBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:12.543633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1415","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a738102e96d1a5828b69c13d848a3705c3b03cc214b81548a1f33dfbba683cf","sha256:060c0bb1c35c91e532e5cbb43a2ca808cfe3e433a69ea4bb5911643e95c94e62"],"state_sha256":"f292dee5130c37d94d51a4cf74b3adf9523da1d2f07ea09d7d772d0463b34c51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pvk3ejHDQjgXgEgJXL0hK7qLsS1DANI9x0eT2u0RKqYYiUaWfAXfMdb56+dxtvEDvhrsowt2oppOV+OEE3BJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:05:24.302152Z","bundle_sha256":"8de2f2417733daff7e98b1b758f77bec645086b5c1b3b1c437b6c698a8d562bd"}}