{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RYLCP4CLYO43LZAYCTA6KVTZSX","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":"3b258c2e4a572e8a30e3a97cf72a2d764b0d68efce7d621be9aa6820c024bc02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-18T15:15:50Z","title_canon_sha256":"c6023e03cfd97a01d6329a5ace2c8dc5174725fa79307f806d135c8206f82bca"},"schema_version":"1.0","source":{"id":"1201.3818","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3818","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3818v1","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3818","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"RYLCP4CLYO43","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RYLCP4CLYO43LZAY","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RYLCP4CL","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:cb76d6c57d10ef3eef2b1cec4ad8a5abeb8733c253dbd7dfe4f092d0e3e9dbae","target":"graph","created_at":"2026-05-18T04:04:17Z","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":"Let $G$ be an edge-colored graph. A heterochromatic cycle of $G$ is one in which every two edges have different colors. For a vertex $v\\in V(G)$, let $CN(v)$ denote the set of colors which are assigned to the edges incident to $v$. In this note we prove that $G$ contains a heterochromatic cycle of length 4 if $G$ has $n\\geq 60$ vertices and $|CN(u)\\cup CN(v)|\\geq n-1$ for every pair of vertices $u$ and $v$ of $G$. This extends a result of Broersma et al. on the existence of heterochromatic cycles of length 3 or 4.","authors_text":"Bo Ning, Shenggui Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-18T15:15:50Z","title":"A note on heterochromatic cycles of length 4 in edge-colored graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3818","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":"sha256:37b9d3cd2da64edbd75c7ca5ef324a3f8b30c6b8bb91444728d4ab22bb6f3b75","target":"record","created_at":"2026-05-18T04:04:17Z","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":"3b258c2e4a572e8a30e3a97cf72a2d764b0d68efce7d621be9aa6820c024bc02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-18T15:15:50Z","title_canon_sha256":"c6023e03cfd97a01d6329a5ace2c8dc5174725fa79307f806d135c8206f82bca"},"schema_version":"1.0","source":{"id":"1201.3818","kind":"arxiv","version":1}},"canonical_sha256":"8e1627f04bc3b9b5e41814c1e5567995c886ced31f56efdd36d1dd5d5b705f69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e1627f04bc3b9b5e41814c1e5567995c886ced31f56efdd36d1dd5d5b705f69","first_computed_at":"2026-05-18T04:04:17.914201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:17.914201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"93y89IO4zBoHB13NVe0bS1eJTgaBeIFKvUy9a5HLi3KrKG5ZT7b/F2G7QO84rTqgnSJVCk0NeAzVXGe9VrWoAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:17.914919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3818","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37b9d3cd2da64edbd75c7ca5ef324a3f8b30c6b8bb91444728d4ab22bb6f3b75","sha256:cb76d6c57d10ef3eef2b1cec4ad8a5abeb8733c253dbd7dfe4f092d0e3e9dbae"],"state_sha256":"002daf247bdc1e2da3f317abc5ac414a6cca10a57021f76cd5e504e8e7f67910"}