{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VWHZMK45ALAZ2BNOGQELBJEOWL","short_pith_number":"pith:VWHZMK45","schema_version":"1.0","canonical_sha256":"ad8f962b9d02c19d05ae3408b0a48eb2c8a28dad46674b7d35e1e38aeaade0d4","source":{"kind":"arxiv","id":"1412.3067","version":2},"attestation_state":"computed","paper":{"title":"Covers in Partitioned Intersecting Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C.J. Argue, Ron Aharoni","submitted_at":"2014-12-09T19:38:12Z","abstract_excerpt":"Given an integer $r$ and a vector $\\vec{a}=(a_1, \\ldots ,a_p)$ of positive numbers with $\\sum_{i \\le p} a_i=r$, an $r$-uniform hypergraph $H$ is said to be $\\vec{a}$-partitioned if $V(H)=\\bigcup_{i \\le p}V_i$, where the sets $V_i$ are disjoint, and $|e \\cap V_i|=a_i$ for all $e \\in H,~~i \\le p$. A $\\vec{1}$-partitioned hypergraph is said to be $r$-partite. Let $t(\\vec{a})$ be the maximum, over all intersecting $\\vec{a}$-partitioned hypergraphs $H$, of the minimal size of a cover of $H$. A famous conjecture of Ryser is that $t(\\vec{1})\\le r-1$. Tuza conjectured that if $r>2$ then $t(\\vec{a})=r$"},"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":"1412.3067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-09T19:38:12Z","cross_cats_sorted":[],"title_canon_sha256":"6bc718270ad36cec857ad097a6c7cfcaee8f20eae9e02914dfaa94339bad6677","abstract_canon_sha256":"93724c95ad97833937826f8b0ac44f71b34f1a5e60eb7250b7a094bd1259e5fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:15.144278Z","signature_b64":"+CjS4S7sM4KAkmprkI+DXnBjhBsJo6zM57PtoyBl3TqBNomDfC7w5zepN5YGAq6GjR2hO55FHYvFhqA14fw1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad8f962b9d02c19d05ae3408b0a48eb2c8a28dad46674b7d35e1e38aeaade0d4","last_reissued_at":"2026-05-18T02:30:15.143859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:15.143859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Covers in Partitioned Intersecting Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C.J. Argue, Ron Aharoni","submitted_at":"2014-12-09T19:38:12Z","abstract_excerpt":"Given an integer $r$ and a vector $\\vec{a}=(a_1, \\ldots ,a_p)$ of positive numbers with $\\sum_{i \\le p} a_i=r$, an $r$-uniform hypergraph $H$ is said to be $\\vec{a}$-partitioned if $V(H)=\\bigcup_{i \\le p}V_i$, where the sets $V_i$ are disjoint, and $|e \\cap V_i|=a_i$ for all $e \\in H,~~i \\le p$. A $\\vec{1}$-partitioned hypergraph is said to be $r$-partite. Let $t(\\vec{a})$ be the maximum, over all intersecting $\\vec{a}$-partitioned hypergraphs $H$, of the minimal size of a cover of $H$. A famous conjecture of Ryser is that $t(\\vec{1})\\le r-1$. Tuza conjectured that if $r>2$ then $t(\\vec{a})=r$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3067","kind":"arxiv","version":2},"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":"1412.3067","created_at":"2026-05-18T02:30:15.143925+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.3067v2","created_at":"2026-05-18T02:30:15.143925+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3067","created_at":"2026-05-18T02:30:15.143925+00:00"},{"alias_kind":"pith_short_12","alias_value":"VWHZMK45ALAZ","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"VWHZMK45ALAZ2BNO","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"VWHZMK45","created_at":"2026-05-18T12:28:54.890064+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/VWHZMK45ALAZ2BNOGQELBJEOWL","json":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL.json","graph_json":"https://pith.science/api/pith-number/VWHZMK45ALAZ2BNOGQELBJEOWL/graph.json","events_json":"https://pith.science/api/pith-number/VWHZMK45ALAZ2BNOGQELBJEOWL/events.json","paper":"https://pith.science/paper/VWHZMK45"},"agent_actions":{"view_html":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL","download_json":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL.json","view_paper":"https://pith.science/paper/VWHZMK45","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.3067&json=true","fetch_graph":"https://pith.science/api/pith-number/VWHZMK45ALAZ2BNOGQELBJEOWL/graph.json","fetch_events":"https://pith.science/api/pith-number/VWHZMK45ALAZ2BNOGQELBJEOWL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL/action/storage_attestation","attest_author":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL/action/author_attestation","sign_citation":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL/action/citation_signature","submit_replication":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL/action/replication_record"}},"created_at":"2026-05-18T02:30:15.143925+00:00","updated_at":"2026-05-18T02:30:15.143925+00:00"}