{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TF3O6GI2A6OKF5BMBBBLFPA3E4","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":"071b893aec63aa24cfc5b6ac85f5737834e1c362d08ea1dccb2a148a42ebcb42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T14:05:33Z","title_canon_sha256":"a3d81a49dbb7ee6ba9d188c55c4b7dbd331baee284f137a6468d49e3ad1af02b"},"schema_version":"1.0","source":{"id":"1605.01942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01942","created_at":"2026-05-18T01:15:30Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01942v1","created_at":"2026-05-18T01:15:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01942","created_at":"2026-05-18T01:15:30Z"},{"alias_kind":"pith_short_12","alias_value":"TF3O6GI2A6OK","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TF3O6GI2A6OKF5BM","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TF3O6GI2","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:bdde066989eb036f21adc5bf9ad23fa9e679d5221e35c3bf89fd717547bc4fa4","target":"graph","created_at":"2026-05-18T01:15:30Z","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 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","authors_text":"Ron Aharoni, Ron Holzman, Shira Zerbib","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T14:05:33Z","title":"Edge-covers in d-interval hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01942","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":"sha256:1c7104b2f18774d36a5c323f76982e7917cd5ca54c872c9ad7683c46afbe6a68","target":"record","created_at":"2026-05-18T01:15:30Z","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":"071b893aec63aa24cfc5b6ac85f5737834e1c362d08ea1dccb2a148a42ebcb42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T14:05:33Z","title_canon_sha256":"a3d81a49dbb7ee6ba9d188c55c4b7dbd331baee284f137a6468d49e3ad1af02b"},"schema_version":"1.0","source":{"id":"1605.01942","kind":"arxiv","version":1}},"canonical_sha256":"9976ef191a079ca2f42c0842b2bc1b272157a762e21e0e039ace1808bd6a5ef2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9976ef191a079ca2f42c0842b2bc1b272157a762e21e0e039ace1808bd6a5ef2","first_computed_at":"2026-05-18T01:15:30.865769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:30.865769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s7drp4kLM3iclwLKJ4owf0BwYVoawHEYV2X2stUKKJ+3sSPVrIS7Ikw/5ON8nVnb+8qhjzuP5H5HXrReVBzRAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:30.866381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c7104b2f18774d36a5c323f76982e7917cd5ca54c872c9ad7683c46afbe6a68","sha256:bdde066989eb036f21adc5bf9ad23fa9e679d5221e35c3bf89fd717547bc4fa4"],"state_sha256":"65820feab3e8710a8a73b2f175b3e753505748447133c11513930bab21897215"}