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This result is best possible, and is one of the first results on vertex degree conditions for hypergraph tiling."},"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":"1309.2200","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-09T15:48:17Z","cross_cats_sorted":[],"title_canon_sha256":"49e17171ff420f8a4eef7b842b7344a89431d4ca9d928327adeeb98d44604307","abstract_canon_sha256":"3db06f6feb202a9bbb38175bd2908fe5bb22393acd54f3a5ded8751c259ee591"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:21.624896Z","signature_b64":"hnGnepIWvGLdmN6xd+ARbeaM+JY5XlNM1t54Z60J1TXq2HvZ9toJ58tLtd4xv/AVOIKLnUkc0eVFluzm5eMoBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04afc03d2dc0b33ce18dc3d015a872baaa78edb930821bb9f85dc23ece74675e","last_reissued_at":"2026-05-18T02:45:21.624338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:21.624338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimum vertex degree threshold for $C_4^3$-tiling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Han, Yi Zhao","submitted_at":"2013-09-09T15:48:17Z","abstract_excerpt":"We prove that the vertex degree threshold for tiling $\\C_4^3$ (the 3-uniform hypergraph with four vertices and two triples) in a 3-uniform hypergraph on $n\\in 4\\mathbb N$ vertices is $\\binom{n-1}2 - \\binom{\\frac34 n}2+\\frac38n+c$, where $c=1$ if $n\\in 8\\mathbb N$ and $c=-\\frac12$ otherwise. 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