{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UMOXZXZTMXORCWVUKVCQIJAMWQ","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":"1baa44313b127a796ab6c3093664d41e0b6fff0a81985e39824b2c4aa1c42d36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-15T13:36:10Z","title_canon_sha256":"f0e3ada3321bb85eded4869d6470e98fa852b6821cef7cba3dcf0807a3317441"},"schema_version":"1.0","source":{"id":"1703.05149","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05149","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05149v1","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05149","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"UMOXZXZTMXOR","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UMOXZXZTMXORCWVU","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UMOXZXZT","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:d25ec20f9c925d8e2f5f151bdb24cc8a1ba0e704b728780593622ca19cc16724","target":"graph","created_at":"2026-05-18T00:48:38Z","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":"Two graphs $G_1$ and $G_2$ on $n$ vertices are said to \\textit{pack} if there exist injective mappings of their vertex sets into $[n]$ such that the images of their edge sets are disjoint. A longstanding conjecture due to Bollob\\'as and Eldridge and, independently, Catlin, asserts that, if $(\\Delta(G_1)+1) (\\Delta(G_2)+1) \\le n+1$, then $G_1$ and $G_2$ pack. We consider the validity of this assertion under the additional assumptions that neither $G_1$ nor $G_2$ contain a $4$-, $6$- or $8$-cycle, and that $\\Delta(G_1)$ or $\\Delta(G_2)$ is large enough ($\\ge 940060$).","authors_text":"Ross J. Kang, Wouter Cames van Batenburg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-15T13:36:10Z","title":"The Bollob\\'as-Eldridge-Catlin conjecture for even girth at least $10$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05149","kind":"arxiv","version":1},"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":"sha256:9516085026ab78a546169416dda68a278e892759ce94ea17b68f9f07f2c358a2","target":"record","created_at":"2026-05-18T00:48:38Z","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":"1baa44313b127a796ab6c3093664d41e0b6fff0a81985e39824b2c4aa1c42d36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-15T13:36:10Z","title_canon_sha256":"f0e3ada3321bb85eded4869d6470e98fa852b6821cef7cba3dcf0807a3317441"},"schema_version":"1.0","source":{"id":"1703.05149","kind":"arxiv","version":1}},"canonical_sha256":"a31d7cdf3365dd115ab4554504240cb41bc8c0055a377e1770ac788446a2f4e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a31d7cdf3365dd115ab4554504240cb41bc8c0055a377e1770ac788446a2f4e7","first_computed_at":"2026-05-18T00:48:38.249033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:38.249033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rcInKOsErw8fr3N5xtrL/ySf4NLovU1hf8cqNhAZwnnoa8oOKWdCC1T7MXkIuRyfdIJfH2KPhf7JDZkWneXiAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:38.249558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05149","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9516085026ab78a546169416dda68a278e892759ce94ea17b68f9f07f2c358a2","sha256:d25ec20f9c925d8e2f5f151bdb24cc8a1ba0e704b728780593622ca19cc16724"],"state_sha256":"1d1afccceaa073c86f0c7d2bc2e387af4dbf160e7687e032823d1994d23a841a"}