{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QCIF3AB7O224PUZWTFC3ZDEQCB","short_pith_number":"pith:QCIF3AB7","schema_version":"1.0","canonical_sha256":"80905d803f76b5c7d3369945bc8c90107c977d09244b61e46943e259d26f3b22","source":{"kind":"arxiv","id":"1512.07177","version":2},"attestation_state":"computed","paper":{"title":"Perfect Matchings in Hypergraphs and the Erd\\H{o}s matching conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Han","submitted_at":"2015-12-22T17:51:45Z","abstract_excerpt":"We prove a new upper bound for the minimum $d$-degree threshold for perfect matchings in $k$-uniform hypergraphs when $d<k/2$. As a consequence, this determines exact values of the threshold when $0.42k \\le d < k/2$ or when $(k,d)=(12,5)$ or $(17,7)$. Our approach is to give an upper bound on the Erd\\H{o}s Matching Conjecture and convert the result to the minimum $d$-degree setting by an approach of K\\\"uhn, Osthus and Townsend. To obtain exact thresholds, we also apply a result of Treglown and Zhao."},"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":"1512.07177","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-22T17:51:45Z","cross_cats_sorted":[],"title_canon_sha256":"27c689e139d7f6ac3a667765f35c55bf360e54715ce917a87c52ab91d5cdd04e","abstract_canon_sha256":"195f401b5f5abbe863b17248b2cd5ec09923c1b999a14a8cd5f83e73841dc4d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:06.426684Z","signature_b64":"Qoqq5JGntc62E20GYGUTecCPt/onyuXYE3nWe+AI12bSC4qePROClQ3qRxPtDjmeZO94C217SHV1WqAt48FADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80905d803f76b5c7d3369945bc8c90107c977d09244b61e46943e259d26f3b22","last_reissued_at":"2026-05-18T01:15:06.426139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:06.426139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perfect Matchings in Hypergraphs and the Erd\\H{o}s matching conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Han","submitted_at":"2015-12-22T17:51:45Z","abstract_excerpt":"We prove a new upper bound for the minimum $d$-degree threshold for perfect matchings in $k$-uniform hypergraphs when $d<k/2$. As a consequence, this determines exact values of the threshold when $0.42k \\le d < k/2$ or when $(k,d)=(12,5)$ or $(17,7)$. Our approach is to give an upper bound on the Erd\\H{o}s Matching Conjecture and convert the result to the minimum $d$-degree setting by an approach of K\\\"uhn, Osthus and Townsend. To obtain exact thresholds, we also apply a result of Treglown and Zhao."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07177","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":"1512.07177","created_at":"2026-05-18T01:15:06.426213+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.07177v2","created_at":"2026-05-18T01:15:06.426213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07177","created_at":"2026-05-18T01:15:06.426213+00:00"},{"alias_kind":"pith_short_12","alias_value":"QCIF3AB7O224","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"QCIF3AB7O224PUZW","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"QCIF3AB7","created_at":"2026-05-18T12:29:37.295048+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/QCIF3AB7O224PUZWTFC3ZDEQCB","json":"https://pith.science/pith/QCIF3AB7O224PUZWTFC3ZDEQCB.json","graph_json":"https://pith.science/api/pith-number/QCIF3AB7O224PUZWTFC3ZDEQCB/graph.json","events_json":"https://pith.science/api/pith-number/QCIF3AB7O224PUZWTFC3ZDEQCB/events.json","paper":"https://pith.science/paper/QCIF3AB7"},"agent_actions":{"view_html":"https://pith.science/pith/QCIF3AB7O224PUZWTFC3ZDEQCB","download_json":"https://pith.science/pith/QCIF3AB7O224PUZWTFC3ZDEQCB.json","view_paper":"https://pith.science/paper/QCIF3AB7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.07177&json=true","fetch_graph":"https://pith.science/api/pith-number/QCIF3AB7O224PUZWTFC3ZDEQCB/graph.json","fetch_events":"https://pith.science/api/pith-number/QCIF3AB7O224PUZWTFC3ZDEQCB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QCIF3AB7O224PUZWTFC3ZDEQCB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QCIF3AB7O224PUZWTFC3ZDEQCB/action/storage_attestation","attest_author":"https://pith.science/pith/QCIF3AB7O224PUZWTFC3ZDEQCB/action/author_attestation","sign_citation":"https://pith.science/pith/QCIF3AB7O224PUZWTFC3ZDEQCB/action/citation_signature","submit_replication":"https://pith.science/pith/QCIF3AB7O224PUZWTFC3ZDEQCB/action/replication_record"}},"created_at":"2026-05-18T01:15:06.426213+00:00","updated_at":"2026-05-18T01:15:06.426213+00:00"}