{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:K33KNQUN3LXI3CIR3MDUDV5XQC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f80ce1f4f7398e71e38ae3eb73ce377af33b9ec089c8cf70605266863571228e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-04T00:11:19Z","title_canon_sha256":"465fb802d6fca6b4f0e6c466dd7ad81b8ad53184172f99b61594f9d0afab164d"},"schema_version":"1.0","source":{"id":"1810.02009","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02009","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02009v3","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02009","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"pith_short_12","alias_value":"K33KNQUN3LXI","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K33KNQUN3LXI3CIR","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K33KNQUN","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:eafd283ca7d031f8649efc1506657b724c98f6c9433dcd5cf3fcfa3de5588060","target":"graph","created_at":"2026-05-17T23:52:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The Hamilton-Waterloo Problem HWP$(v;m,n;\\alpha,\\beta)$ asks for a 2-factorization of the complete graph $K_v$ or $K_v-I$, the complete graph with the edges of a 1-factor removed, into $\\alpha$ $C_m$-factors and $\\beta$ $C_n$-factors, where $3 \\leq m < n$. In the case that $m$ and $n$ are both even, the problem has been solved except possibly when $1 \\in \\{\\alpha,\\beta\\}$ or when $\\alpha$ and $\\beta$ are both odd, in which case necessarily $v \\equiv 2 \\pmod{4}$. In this paper, we develop a new construction that creates factorizations with larger cycles from existing factorizations under certai","authors_text":"A.C. Burgess, P. Danziger, T. Traetta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-04T00:11:19Z","title":"The Hamilton-Waterloo Problem with even cycle lengths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02009","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:860975b7c2a3499e01fa573e85225ac5d3c1ed3c864982793dad2bf4fce8fde7","target":"record","created_at":"2026-05-17T23:52:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f80ce1f4f7398e71e38ae3eb73ce377af33b9ec089c8cf70605266863571228e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-04T00:11:19Z","title_canon_sha256":"465fb802d6fca6b4f0e6c466dd7ad81b8ad53184172f99b61594f9d0afab164d"},"schema_version":"1.0","source":{"id":"1810.02009","kind":"arxiv","version":3}},"canonical_sha256":"56f6a6c28ddaee8d8911db0741d7b780bc050de53686a7422c070d34302fed8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56f6a6c28ddaee8d8911db0741d7b780bc050de53686a7422c070d34302fed8f","first_computed_at":"2026-05-17T23:52:52.040238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:52.040238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CmQlPYaXyBTCKPkzFUxYU/HCBFVUb3LrBwiKv/ltnNNyy2AIKdmxANhKl4blAMWfW/ZGJ5WQN8/ggn7r1JM6CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:52.040963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02009","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:860975b7c2a3499e01fa573e85225ac5d3c1ed3c864982793dad2bf4fce8fde7","sha256:eafd283ca7d031f8649efc1506657b724c98f6c9433dcd5cf3fcfa3de5588060"],"state_sha256":"ac24d301b39d6da2d8df42aacc8b03ed2e7de661b4dd9594920aad62b9d78a90"}