{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:EGKT6FZLNCR4PCTZQIEP3XPEUM","short_pith_number":"pith:EGKT6FZL","schema_version":"1.0","canonical_sha256":"21953f172b68a3c78a798208fddde4a30f9dc1879dadd9a06494d89d4233b70c","source":{"kind":"arxiv","id":"1108.1757","version":2},"attestation_state":"computed","paper":{"title":"A Geometric Theory for Hypergraph Matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter Keevash, Richard Mycroft","submitted_at":"2011-08-08T17:19:53Z","abstract_excerpt":"We develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two distinct types: 'space barriers' from convex geometry, and 'divisibility barriers' from arithmetic lattice-based constructions. To formulate precise results, we introduce the setting of simplicial complexes with minimum degree sequences, which is a generalisation of the usual minimum degree condition. We determine the essentially best possible minimum degree sequence for finding an almost perfect match"},"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":"1108.1757","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-08T17:19:53Z","cross_cats_sorted":[],"title_canon_sha256":"781cb4728db831b83adcc49d8dc12d964e283235c2d95513bff23ce0523713ae","abstract_canon_sha256":"e5ec1ccd9622ec2c20ce3852473c0e0909a96571c4dd6485d9c48cb2f29454f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:17.182914Z","signature_b64":"oGa5mWX2CLI5pqZkSLSDmKO/lSYY7pFTboImSpBE61jJeftBB3EKnIf4UwOYv/rnpQGdd26JS6Xb4AEjAafKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21953f172b68a3c78a798208fddde4a30f9dc1879dadd9a06494d89d4233b70c","last_reissued_at":"2026-05-18T01:33:17.182331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:17.182331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Geometric Theory for Hypergraph Matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter Keevash, Richard Mycroft","submitted_at":"2011-08-08T17:19:53Z","abstract_excerpt":"We develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two distinct types: 'space barriers' from convex geometry, and 'divisibility barriers' from arithmetic lattice-based constructions. To formulate precise results, we introduce the setting of simplicial complexes with minimum degree sequences, which is a generalisation of the usual minimum degree condition. We determine the essentially best possible minimum degree sequence for finding an almost perfect match"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1757","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":"1108.1757","created_at":"2026-05-18T01:33:17.182427+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.1757v2","created_at":"2026-05-18T01:33:17.182427+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1757","created_at":"2026-05-18T01:33:17.182427+00:00"},{"alias_kind":"pith_short_12","alias_value":"EGKT6FZLNCR4","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"EGKT6FZLNCR4PCTZ","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"EGKT6FZL","created_at":"2026-05-18T12:26:28.662955+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/EGKT6FZLNCR4PCTZQIEP3XPEUM","json":"https://pith.science/pith/EGKT6FZLNCR4PCTZQIEP3XPEUM.json","graph_json":"https://pith.science/api/pith-number/EGKT6FZLNCR4PCTZQIEP3XPEUM/graph.json","events_json":"https://pith.science/api/pith-number/EGKT6FZLNCR4PCTZQIEP3XPEUM/events.json","paper":"https://pith.science/paper/EGKT6FZL"},"agent_actions":{"view_html":"https://pith.science/pith/EGKT6FZLNCR4PCTZQIEP3XPEUM","download_json":"https://pith.science/pith/EGKT6FZLNCR4PCTZQIEP3XPEUM.json","view_paper":"https://pith.science/paper/EGKT6FZL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.1757&json=true","fetch_graph":"https://pith.science/api/pith-number/EGKT6FZLNCR4PCTZQIEP3XPEUM/graph.json","fetch_events":"https://pith.science/api/pith-number/EGKT6FZLNCR4PCTZQIEP3XPEUM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EGKT6FZLNCR4PCTZQIEP3XPEUM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EGKT6FZLNCR4PCTZQIEP3XPEUM/action/storage_attestation","attest_author":"https://pith.science/pith/EGKT6FZLNCR4PCTZQIEP3XPEUM/action/author_attestation","sign_citation":"https://pith.science/pith/EGKT6FZLNCR4PCTZQIEP3XPEUM/action/citation_signature","submit_replication":"https://pith.science/pith/EGKT6FZLNCR4PCTZQIEP3XPEUM/action/replication_record"}},"created_at":"2026-05-18T01:33:17.182427+00:00","updated_at":"2026-05-18T01:33:17.182427+00:00"}