{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TF3O6GI2A6OKF5BMBBBLFPA3E4","short_pith_number":"pith:TF3O6GI2","schema_version":"1.0","canonical_sha256":"9976ef191a079ca2f42c0842b2bc1b272157a762e21e0e039ace1808bd6a5ef2","source":{"kind":"arxiv","id":"1605.01942","version":1},"attestation_state":"computed","paper":{"title":"Edge-covers in d-interval hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ron Aharoni, Ron Holzman, Shira Zerbib","submitted_at":"2016-05-06T14:05:33Z","abstract_excerpt":"A d-interval hypergraph has d disjoint copies of the unit interval as its vertex set, and each edge is the union of d subintervals, one on each copy. Extending a classical result of Gallai on the case d = 1, Tardos and Kaiser used topological tools to bound the ratio between the transversal number and the matching number in such hypergraphs. We take a dual point of view, and bound the edge-covering number (namely the minimal number of edges covering the entire vertex set) in terms of a parameter expressing independence of systems of partitions of the d unit intervals. The main tool we use is a"},"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":"1605.01942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T14:05:33Z","cross_cats_sorted":[],"title_canon_sha256":"a3d81a49dbb7ee6ba9d188c55c4b7dbd331baee284f137a6468d49e3ad1af02b","abstract_canon_sha256":"071b893aec63aa24cfc5b6ac85f5737834e1c362d08ea1dccb2a148a42ebcb42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:30.866381Z","signature_b64":"s7drp4kLM3iclwLKJ4owf0BwYVoawHEYV2X2stUKKJ+3sSPVrIS7Ikw/5ON8nVnb+8qhjzuP5H5HXrReVBzRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9976ef191a079ca2f42c0842b2bc1b272157a762e21e0e039ace1808bd6a5ef2","last_reissued_at":"2026-05-18T01:15:30.865769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:30.865769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edge-covers in d-interval hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ron Aharoni, Ron Holzman, Shira Zerbib","submitted_at":"2016-05-06T14:05:33Z","abstract_excerpt":"A d-interval hypergraph has d disjoint copies of the unit interval as its vertex set, and each edge is the union of d subintervals, one on each copy. Extending a classical result of Gallai on the case d = 1, Tardos and Kaiser used topological tools to bound the ratio between the transversal number and the matching number in such hypergraphs. We take a dual point of view, and bound the edge-covering number (namely the minimal number of edges covering the entire vertex set) in terms of a parameter expressing independence of systems of partitions of the d unit intervals. The main tool we use is a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01942","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":"1605.01942","created_at":"2026-05-18T01:15:30.865861+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.01942v1","created_at":"2026-05-18T01:15:30.865861+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01942","created_at":"2026-05-18T01:15:30.865861+00:00"},{"alias_kind":"pith_short_12","alias_value":"TF3O6GI2A6OK","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"TF3O6GI2A6OKF5BM","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"TF3O6GI2","created_at":"2026-05-18T12:30:44.179134+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/TF3O6GI2A6OKF5BMBBBLFPA3E4","json":"https://pith.science/pith/TF3O6GI2A6OKF5BMBBBLFPA3E4.json","graph_json":"https://pith.science/api/pith-number/TF3O6GI2A6OKF5BMBBBLFPA3E4/graph.json","events_json":"https://pith.science/api/pith-number/TF3O6GI2A6OKF5BMBBBLFPA3E4/events.json","paper":"https://pith.science/paper/TF3O6GI2"},"agent_actions":{"view_html":"https://pith.science/pith/TF3O6GI2A6OKF5BMBBBLFPA3E4","download_json":"https://pith.science/pith/TF3O6GI2A6OKF5BMBBBLFPA3E4.json","view_paper":"https://pith.science/paper/TF3O6GI2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.01942&json=true","fetch_graph":"https://pith.science/api/pith-number/TF3O6GI2A6OKF5BMBBBLFPA3E4/graph.json","fetch_events":"https://pith.science/api/pith-number/TF3O6GI2A6OKF5BMBBBLFPA3E4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TF3O6GI2A6OKF5BMBBBLFPA3E4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TF3O6GI2A6OKF5BMBBBLFPA3E4/action/storage_attestation","attest_author":"https://pith.science/pith/TF3O6GI2A6OKF5BMBBBLFPA3E4/action/author_attestation","sign_citation":"https://pith.science/pith/TF3O6GI2A6OKF5BMBBBLFPA3E4/action/citation_signature","submit_replication":"https://pith.science/pith/TF3O6GI2A6OKF5BMBBBLFPA3E4/action/replication_record"}},"created_at":"2026-05-18T01:15:30.865861+00:00","updated_at":"2026-05-18T01:15:30.865861+00:00"}