{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:T6CLG6XWCMLPZIKYKLT2BPCFI2","short_pith_number":"pith:T6CLG6XW","schema_version":"1.0","canonical_sha256":"9f84b37af61316fca15852e7a0bc4546a0d00605a675119b73957f04834afe00","source":{"kind":"arxiv","id":"2310.15909","version":2},"attestation_state":"computed","paper":{"title":"Towards a high-dimensional Dirac's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hyunwoo Lee","submitted_at":"2023-10-24T15:15:13Z","abstract_excerpt":"Dirac's theorem determines the sharp minimum degree threshold for graphs to contain perfect matchings and Hamiltonian cycles. There have been various attempts to generalize this theorem to hypergraphs with larger uniformity by considering hypergraph matchings and Hamiltonian cycles. In this paper, we consider another natural generalization of perfect matchings, Steiner triple systems. As a Steiner triple system can be viewed as a partition of pairs of vertices, it is a natural high-dimensional analogue of a perfect matching in graphs. We prove that for sufficiently large integer $n$ with $n \\e"},"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":"2310.15909","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-24T15:15:13Z","cross_cats_sorted":[],"title_canon_sha256":"9ed1c9d473e49a445df5f35d71bd20611b09ed03ddf9995f6e0a83028deaf2b4","abstract_canon_sha256":"e4077f7b9228f80ca47faa0105947ed1b4defadd5083b507c5cd00266a7fc9a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:39:15.713427Z","signature_b64":"FuS+poul7oGnhXP1bt9enh6/g/fycv/5JwQq3d2A4ey3+KKa69xtH1w7eeml1Ez2Rv48UbXLaiBzqawdO0FCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f84b37af61316fca15852e7a0bc4546a0d00605a675119b73957f04834afe00","last_reissued_at":"2026-07-05T10:39:15.712962Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:39:15.712962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards a high-dimensional Dirac's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hyunwoo Lee","submitted_at":"2023-10-24T15:15:13Z","abstract_excerpt":"Dirac's theorem determines the sharp minimum degree threshold for graphs to contain perfect matchings and Hamiltonian cycles. There have been various attempts to generalize this theorem to hypergraphs with larger uniformity by considering hypergraph matchings and Hamiltonian cycles. In this paper, we consider another natural generalization of perfect matchings, Steiner triple systems. As a Steiner triple system can be viewed as a partition of pairs of vertices, it is a natural high-dimensional analogue of a perfect matching in graphs. We prove that for sufficiently large integer $n$ with $n \\e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.15909","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.15909/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2310.15909","created_at":"2026-07-05T10:39:15.713019+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.15909v2","created_at":"2026-07-05T10:39:15.713019+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.15909","created_at":"2026-07-05T10:39:15.713019+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6CLG6XWCMLP","created_at":"2026-07-05T10:39:15.713019+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6CLG6XWCMLPZIKY","created_at":"2026-07-05T10:39:15.713019+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6CLG6XW","created_at":"2026-07-05T10:39:15.713019+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.17996","citing_title":"Ramsey--Dirac theory for bounded degree hypertrees","ref_index":40,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T6CLG6XWCMLPZIKYKLT2BPCFI2","json":"https://pith.science/pith/T6CLG6XWCMLPZIKYKLT2BPCFI2.json","graph_json":"https://pith.science/api/pith-number/T6CLG6XWCMLPZIKYKLT2BPCFI2/graph.json","events_json":"https://pith.science/api/pith-number/T6CLG6XWCMLPZIKYKLT2BPCFI2/events.json","paper":"https://pith.science/paper/T6CLG6XW"},"agent_actions":{"view_html":"https://pith.science/pith/T6CLG6XWCMLPZIKYKLT2BPCFI2","download_json":"https://pith.science/pith/T6CLG6XWCMLPZIKYKLT2BPCFI2.json","view_paper":"https://pith.science/paper/T6CLG6XW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.15909&json=true","fetch_graph":"https://pith.science/api/pith-number/T6CLG6XWCMLPZIKYKLT2BPCFI2/graph.json","fetch_events":"https://pith.science/api/pith-number/T6CLG6XWCMLPZIKYKLT2BPCFI2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6CLG6XWCMLPZIKYKLT2BPCFI2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6CLG6XWCMLPZIKYKLT2BPCFI2/action/storage_attestation","attest_author":"https://pith.science/pith/T6CLG6XWCMLPZIKYKLT2BPCFI2/action/author_attestation","sign_citation":"https://pith.science/pith/T6CLG6XWCMLPZIKYKLT2BPCFI2/action/citation_signature","submit_replication":"https://pith.science/pith/T6CLG6XWCMLPZIKYKLT2BPCFI2/action/replication_record"}},"created_at":"2026-07-05T10:39:15.713019+00:00","updated_at":"2026-07-05T10:39:15.713019+00:00"}