{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AJCA2UIVZT5ZLDAW2EGC2EZFNQ","short_pith_number":"pith:AJCA2UIV","schema_version":"1.0","canonical_sha256":"02440d5115ccfb958c16d10c2d13256c2b7ee1031c059aea3292a51f2750f944","source":{"kind":"arxiv","id":"1808.02319","version":1},"attestation_state":"computed","paper":{"title":"Codegree threshold for tiling $k$-graphs with two edges sharing exactly $\\ell$ vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lei Yu, Xinmin Hou","submitted_at":"2018-08-07T12:16:54Z","abstract_excerpt":"Given integer $k$ and a $k$-graph $F$, let $t_{k-1}(n,F)$ be the minimum integer $t$ such that every $k$-graph $H$ on $n$ vertices with codegree at least $t$ contains an $F$-factor. For integers $k\\geq3$ and $0\\leq\\ell\\leq k-1$, let $\\mathcal{Y}_{k,\\ell}$ be a $k$-graph with two edges that shares exactly $\\ell$ vertices. Han and Zhao (JCTA, 2015) asked the following question: For all $k\\ge 3$, $0\\le \\ell\\le k-1$ and sufficiently large $n$ divisible by $2k-\\ell$, determine the exact value of $t_{k-1}(n,\\mathcal{Y}_{k,\\ell})$. In this paper, we show that $t_{k-1}(n,\\mathcal{Y}_{k,\\ell})=\\frac{n}"},"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":"1808.02319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-07T12:16:54Z","cross_cats_sorted":[],"title_canon_sha256":"4b03a9a38b044d8611c18bef00450bcda727eb015d5eb0bccd5b61360b0eaf56","abstract_canon_sha256":"e92de04992962a144b204e4269f145628a2c0637b1fd35edb2e7bb06d288ff23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:46.900565Z","signature_b64":"60rbO45lpxB9hfF2msRFKOJgGa3rXui1iDpwNbZaUj5vrnXGz7lDM6S0FK9LBdZ0/2W9XSpTxwn+VmSEmPkSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02440d5115ccfb958c16d10c2d13256c2b7ee1031c059aea3292a51f2750f944","last_reissued_at":"2026-05-18T00:08:46.899953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:46.899953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Codegree threshold for tiling $k$-graphs with two edges sharing exactly $\\ell$ vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lei Yu, Xinmin Hou","submitted_at":"2018-08-07T12:16:54Z","abstract_excerpt":"Given integer $k$ and a $k$-graph $F$, let $t_{k-1}(n,F)$ be the minimum integer $t$ such that every $k$-graph $H$ on $n$ vertices with codegree at least $t$ contains an $F$-factor. For integers $k\\geq3$ and $0\\leq\\ell\\leq k-1$, let $\\mathcal{Y}_{k,\\ell}$ be a $k$-graph with two edges that shares exactly $\\ell$ vertices. Han and Zhao (JCTA, 2015) asked the following question: For all $k\\ge 3$, $0\\le \\ell\\le k-1$ and sufficiently large $n$ divisible by $2k-\\ell$, determine the exact value of $t_{k-1}(n,\\mathcal{Y}_{k,\\ell})$. In this paper, we show that $t_{k-1}(n,\\mathcal{Y}_{k,\\ell})=\\frac{n}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02319","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":"1808.02319","created_at":"2026-05-18T00:08:46.900036+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.02319v1","created_at":"2026-05-18T00:08:46.900036+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02319","created_at":"2026-05-18T00:08:46.900036+00:00"},{"alias_kind":"pith_short_12","alias_value":"AJCA2UIVZT5Z","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AJCA2UIVZT5ZLDAW","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AJCA2UIV","created_at":"2026-05-18T12:32:13.499390+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/AJCA2UIVZT5ZLDAW2EGC2EZFNQ","json":"https://pith.science/pith/AJCA2UIVZT5ZLDAW2EGC2EZFNQ.json","graph_json":"https://pith.science/api/pith-number/AJCA2UIVZT5ZLDAW2EGC2EZFNQ/graph.json","events_json":"https://pith.science/api/pith-number/AJCA2UIVZT5ZLDAW2EGC2EZFNQ/events.json","paper":"https://pith.science/paper/AJCA2UIV"},"agent_actions":{"view_html":"https://pith.science/pith/AJCA2UIVZT5ZLDAW2EGC2EZFNQ","download_json":"https://pith.science/pith/AJCA2UIVZT5ZLDAW2EGC2EZFNQ.json","view_paper":"https://pith.science/paper/AJCA2UIV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.02319&json=true","fetch_graph":"https://pith.science/api/pith-number/AJCA2UIVZT5ZLDAW2EGC2EZFNQ/graph.json","fetch_events":"https://pith.science/api/pith-number/AJCA2UIVZT5ZLDAW2EGC2EZFNQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AJCA2UIVZT5ZLDAW2EGC2EZFNQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AJCA2UIVZT5ZLDAW2EGC2EZFNQ/action/storage_attestation","attest_author":"https://pith.science/pith/AJCA2UIVZT5ZLDAW2EGC2EZFNQ/action/author_attestation","sign_citation":"https://pith.science/pith/AJCA2UIVZT5ZLDAW2EGC2EZFNQ/action/citation_signature","submit_replication":"https://pith.science/pith/AJCA2UIVZT5ZLDAW2EGC2EZFNQ/action/replication_record"}},"created_at":"2026-05-18T00:08:46.900036+00:00","updated_at":"2026-05-18T00:08:46.900036+00:00"}