{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4JEY5CHHPGABYQVX2F5GLJGMDD","short_pith_number":"pith:4JEY5CHH","schema_version":"1.0","canonical_sha256":"e2498e88e779801c42b7d17a65a4cc18f7c73ba3954309939825e7ad8ef34070","source":{"kind":"arxiv","id":"1506.05677","version":1},"attestation_state":"computed","paper":{"title":"Blocking optimal arborescences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Attila Bern\\'ath, Gyula Pap","submitted_at":"2015-06-18T13:51:29Z","abstract_excerpt":"The problem of covering minimum cost common bases of two matroids is NP-complete, even if the two matroids coincide, and the costs are all equal to 1. In this paper we show that the following special case is solvable in polynomial time: given a digraph $D=(V,A)$ with a designated root node $r\\in V$ and arc-costs $c:A\\to \\mathbb{R}$, find a minimum cardinality subset $H$ of the arc set $A$ such that $H$ intersects every minimum $c$-cost $r$-arborescence. By an $r$-arborescence we mean a spanning arborescence of root $r$. The algorithm we give solves a weighted version as well, in which a nonneg"},"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":"1506.05677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-18T13:51:29Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"25278567b5bf7bea11fde05103558ba7f00ee4f553d2b87ebbd0a31ea72855bb","abstract_canon_sha256":"4ab68429e23b2b3df4d4cfd50879d252a9275b227eeb23a854749136c6c4ed7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:10.037242Z","signature_b64":"0ibY7KizAcLO+mNrwy7JNNvFrBBgtRp916G1RBY6yqcVUJ8Yl5VVjWrJS+yU+ozXS+uH7cXfoJy2ZELziEmBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2498e88e779801c42b7d17a65a4cc18f7c73ba3954309939825e7ad8ef34070","last_reissued_at":"2026-05-18T01:44:10.036603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:10.036603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blocking optimal arborescences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Attila Bern\\'ath, Gyula Pap","submitted_at":"2015-06-18T13:51:29Z","abstract_excerpt":"The problem of covering minimum cost common bases of two matroids is NP-complete, even if the two matroids coincide, and the costs are all equal to 1. In this paper we show that the following special case is solvable in polynomial time: given a digraph $D=(V,A)$ with a designated root node $r\\in V$ and arc-costs $c:A\\to \\mathbb{R}$, find a minimum cardinality subset $H$ of the arc set $A$ such that $H$ intersects every minimum $c$-cost $r$-arborescence. By an $r$-arborescence we mean a spanning arborescence of root $r$. The algorithm we give solves a weighted version as well, in which a nonneg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05677","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":"1506.05677","created_at":"2026-05-18T01:44:10.036697+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.05677v1","created_at":"2026-05-18T01:44:10.036697+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05677","created_at":"2026-05-18T01:44:10.036697+00:00"},{"alias_kind":"pith_short_12","alias_value":"4JEY5CHHPGAB","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4JEY5CHHPGABYQVX","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4JEY5CHH","created_at":"2026-05-18T12:29:05.191682+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/4JEY5CHHPGABYQVX2F5GLJGMDD","json":"https://pith.science/pith/4JEY5CHHPGABYQVX2F5GLJGMDD.json","graph_json":"https://pith.science/api/pith-number/4JEY5CHHPGABYQVX2F5GLJGMDD/graph.json","events_json":"https://pith.science/api/pith-number/4JEY5CHHPGABYQVX2F5GLJGMDD/events.json","paper":"https://pith.science/paper/4JEY5CHH"},"agent_actions":{"view_html":"https://pith.science/pith/4JEY5CHHPGABYQVX2F5GLJGMDD","download_json":"https://pith.science/pith/4JEY5CHHPGABYQVX2F5GLJGMDD.json","view_paper":"https://pith.science/paper/4JEY5CHH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.05677&json=true","fetch_graph":"https://pith.science/api/pith-number/4JEY5CHHPGABYQVX2F5GLJGMDD/graph.json","fetch_events":"https://pith.science/api/pith-number/4JEY5CHHPGABYQVX2F5GLJGMDD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4JEY5CHHPGABYQVX2F5GLJGMDD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4JEY5CHHPGABYQVX2F5GLJGMDD/action/storage_attestation","attest_author":"https://pith.science/pith/4JEY5CHHPGABYQVX2F5GLJGMDD/action/author_attestation","sign_citation":"https://pith.science/pith/4JEY5CHHPGABYQVX2F5GLJGMDD/action/citation_signature","submit_replication":"https://pith.science/pith/4JEY5CHHPGABYQVX2F5GLJGMDD/action/replication_record"}},"created_at":"2026-05-18T01:44:10.036697+00:00","updated_at":"2026-05-18T01:44:10.036697+00:00"}