{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:RUR3AZTPAHT7YMXVFP6XPMSD2M","short_pith_number":"pith:RUR3AZTP","schema_version":"1.0","canonical_sha256":"8d23b0666f01e7fc32f52bfd77b243d33b1ec1d883858d60210bd41e85f05214","source":{"kind":"arxiv","id":"1401.4159","version":2},"attestation_state":"computed","paper":{"title":"Proof of the $1$-factorization and Hamilton Decomposition Conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Allan Lo, Andrew Treglown, B\\'ela Csaba, Daniela K\\\"uhn, Deryk Osthus","submitted_at":"2014-01-16T20:44:15Z","abstract_excerpt":"In this paper we prove the following results (via a unified approach) for all sufficiently large $n$:\n  (i) [$1$-factorization conjecture] Suppose that $n$ is even and $D\\geq 2\\lceil n/4\\rceil -1$. Then every $D$-regular graph $G$ on $n$ vertices has a decomposition into perfect matchings. Equivalently, $\\chi'(G)=D$.\n  (ii) [Hamilton decomposition conjecture] Suppose that $D \\ge \\lfloor n/2 \\rfloor $. Then every $D$-regular graph $G$ on $n$ vertices has a decomposition into Hamilton cycles and at most one perfect matching.\n  (iii) [Optimal packings of Hamilton cycles] Suppose that $G$ is a gra"},"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":"1401.4159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-16T20:44:15Z","cross_cats_sorted":[],"title_canon_sha256":"b47b6742d8690b3da06554eada1fd260605a410ed2a4684a1cf5ca55059568fe","abstract_canon_sha256":"a4ebb0310004fc6d288e763d28fc9fa0a71649f5967f2e3e3402de2b07cce9d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:38.227697Z","signature_b64":"ynUd6WIKvOg9mn44IBxnBeJZXSoLPNaTKU/164NC86OusqmW3pBEPy0bFLOiqMohos32VAZUsGGDS59vurhjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d23b0666f01e7fc32f52bfd77b243d33b1ec1d883858d60210bd41e85f05214","last_reissued_at":"2026-05-18T02:39:38.227267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:38.227267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of the $1$-factorization and Hamilton Decomposition Conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Allan Lo, Andrew Treglown, B\\'ela Csaba, Daniela K\\\"uhn, Deryk Osthus","submitted_at":"2014-01-16T20:44:15Z","abstract_excerpt":"In this paper we prove the following results (via a unified approach) for all sufficiently large $n$:\n  (i) [$1$-factorization conjecture] Suppose that $n$ is even and $D\\geq 2\\lceil n/4\\rceil -1$. Then every $D$-regular graph $G$ on $n$ vertices has a decomposition into perfect matchings. Equivalently, $\\chi'(G)=D$.\n  (ii) [Hamilton decomposition conjecture] Suppose that $D \\ge \\lfloor n/2 \\rfloor $. Then every $D$-regular graph $G$ on $n$ vertices has a decomposition into Hamilton cycles and at most one perfect matching.\n  (iii) [Optimal packings of Hamilton cycles] Suppose that $G$ is a gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4159","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":"1401.4159","created_at":"2026-05-18T02:39:38.227332+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.4159v2","created_at":"2026-05-18T02:39:38.227332+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4159","created_at":"2026-05-18T02:39:38.227332+00:00"},{"alias_kind":"pith_short_12","alias_value":"RUR3AZTPAHT7","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RUR3AZTPAHT7YMXV","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RUR3AZTP","created_at":"2026-05-18T12:28:46.137349+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/RUR3AZTPAHT7YMXVFP6XPMSD2M","json":"https://pith.science/pith/RUR3AZTPAHT7YMXVFP6XPMSD2M.json","graph_json":"https://pith.science/api/pith-number/RUR3AZTPAHT7YMXVFP6XPMSD2M/graph.json","events_json":"https://pith.science/api/pith-number/RUR3AZTPAHT7YMXVFP6XPMSD2M/events.json","paper":"https://pith.science/paper/RUR3AZTP"},"agent_actions":{"view_html":"https://pith.science/pith/RUR3AZTPAHT7YMXVFP6XPMSD2M","download_json":"https://pith.science/pith/RUR3AZTPAHT7YMXVFP6XPMSD2M.json","view_paper":"https://pith.science/paper/RUR3AZTP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.4159&json=true","fetch_graph":"https://pith.science/api/pith-number/RUR3AZTPAHT7YMXVFP6XPMSD2M/graph.json","fetch_events":"https://pith.science/api/pith-number/RUR3AZTPAHT7YMXVFP6XPMSD2M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RUR3AZTPAHT7YMXVFP6XPMSD2M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RUR3AZTPAHT7YMXVFP6XPMSD2M/action/storage_attestation","attest_author":"https://pith.science/pith/RUR3AZTPAHT7YMXVFP6XPMSD2M/action/author_attestation","sign_citation":"https://pith.science/pith/RUR3AZTPAHT7YMXVFP6XPMSD2M/action/citation_signature","submit_replication":"https://pith.science/pith/RUR3AZTPAHT7YMXVFP6XPMSD2M/action/replication_record"}},"created_at":"2026-05-18T02:39:38.227332+00:00","updated_at":"2026-05-18T02:39:38.227332+00:00"}