{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NN5RI5VPLMFRNKXFUPSD5NIZK3","short_pith_number":"pith:NN5RI5VP","schema_version":"1.0","canonical_sha256":"6b7b1476af5b0b16aae5a3e43eb51956fe15781c66f354f96476972a4a1600d9","source":{"kind":"arxiv","id":"1710.04752","version":1},"attestation_state":"computed","paper":{"title":"Vertex degree sums for perfect matchings in 3-uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mei Lu, Yi Zhang, Yi Zhao","submitted_at":"2017-10-13T00:00:19Z","abstract_excerpt":"We determine the minimum degree sum of two adjacent vertices that ensures a perfect matching in a 3-graph without isolated vertex. More precisely, suppose that $H$ is a 3-uniform hypergraph whose order $n$ is sufficiently large and divisible by $3$. If $H$ contains no isolated vertex and $deg(u)+ deg(v) > \\frac{2}{3}n^2-\\frac{8}{3}n+2$ for any two vertices $u$ and $v$ that are contained in some edge of $H$, then $H$ contains a perfect matching. This bound is tight."},"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":"1710.04752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-13T00:00:19Z","cross_cats_sorted":[],"title_canon_sha256":"b6fc34a4848028516d1ec19f14b6ac75a417982fac4eb921883c6bba07e57bab","abstract_canon_sha256":"d96c3a86143762fe853b3da83e64ac7676aaac4e107218723839e6d0f4a98768"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:56.825956Z","signature_b64":"hU9XGmSsDpmeyM7smNrMD94UpXq7kwNqiVLuPR456ptgdlgm8ClWJEhkz+hk6QdKxUKqDKqF7GyKYT6mm5BYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b7b1476af5b0b16aae5a3e43eb51956fe15781c66f354f96476972a4a1600d9","last_reissued_at":"2026-05-18T00:32:56.825269Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:56.825269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vertex degree sums for perfect matchings in 3-uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mei Lu, Yi Zhang, Yi Zhao","submitted_at":"2017-10-13T00:00:19Z","abstract_excerpt":"We determine the minimum degree sum of two adjacent vertices that ensures a perfect matching in a 3-graph without isolated vertex. More precisely, suppose that $H$ is a 3-uniform hypergraph whose order $n$ is sufficiently large and divisible by $3$. If $H$ contains no isolated vertex and $deg(u)+ deg(v) > \\frac{2}{3}n^2-\\frac{8}{3}n+2$ for any two vertices $u$ and $v$ that are contained in some edge of $H$, then $H$ contains a perfect matching. This bound is tight."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04752","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":"1710.04752","created_at":"2026-05-18T00:32:56.825384+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.04752v1","created_at":"2026-05-18T00:32:56.825384+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04752","created_at":"2026-05-18T00:32:56.825384+00:00"},{"alias_kind":"pith_short_12","alias_value":"NN5RI5VPLMFR","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"NN5RI5VPLMFRNKXF","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"NN5RI5VP","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.24878","citing_title":"An Improved Lower Bound for the Erd\\H{o}s-Lov\\'asz Cover Number Problem","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NN5RI5VPLMFRNKXFUPSD5NIZK3","json":"https://pith.science/pith/NN5RI5VPLMFRNKXFUPSD5NIZK3.json","graph_json":"https://pith.science/api/pith-number/NN5RI5VPLMFRNKXFUPSD5NIZK3/graph.json","events_json":"https://pith.science/api/pith-number/NN5RI5VPLMFRNKXFUPSD5NIZK3/events.json","paper":"https://pith.science/paper/NN5RI5VP"},"agent_actions":{"view_html":"https://pith.science/pith/NN5RI5VPLMFRNKXFUPSD5NIZK3","download_json":"https://pith.science/pith/NN5RI5VPLMFRNKXFUPSD5NIZK3.json","view_paper":"https://pith.science/paper/NN5RI5VP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.04752&json=true","fetch_graph":"https://pith.science/api/pith-number/NN5RI5VPLMFRNKXFUPSD5NIZK3/graph.json","fetch_events":"https://pith.science/api/pith-number/NN5RI5VPLMFRNKXFUPSD5NIZK3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NN5RI5VPLMFRNKXFUPSD5NIZK3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NN5RI5VPLMFRNKXFUPSD5NIZK3/action/storage_attestation","attest_author":"https://pith.science/pith/NN5RI5VPLMFRNKXFUPSD5NIZK3/action/author_attestation","sign_citation":"https://pith.science/pith/NN5RI5VPLMFRNKXFUPSD5NIZK3/action/citation_signature","submit_replication":"https://pith.science/pith/NN5RI5VPLMFRNKXFUPSD5NIZK3/action/replication_record"}},"created_at":"2026-05-18T00:32:56.825384+00:00","updated_at":"2026-05-18T00:32:56.825384+00:00"}