{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XD7ISN3ETGMUNQ57LLAY5ZT2GE","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":"b3f0ecef825096636d06aa0f005855252c93b5baf04c0509ea6e4e97609f2d3e","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-03T13:23:41Z","title_canon_sha256":"2b4d9ba613c9f5ad8f640e920895419896d24bf22406402439ddfc6a041505ec"},"schema_version":"1.0","source":{"id":"1301.0450","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0450","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0450v2","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0450","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"XD7ISN3ETGMU","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XD7ISN3ETGMUNQ57","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XD7ISN3E","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:967bbdb45153b52bfdae7af0e4c6ce331bbd9ce5642a29ab292f8ee16b3e6c18","target":"graph","created_at":"2026-05-18T02:58:13Z","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 $K_{n}^{c}$ denote a complete graph on $n$ vertices whose edges are colored in an arbitrary way. Let $\\Delta^{\\mathrm{mon}} (K_{n}^{c})$ denote the maximum number of edges of the same color incident with a vertex of $K_{n}^{c}$. A properly colored cycle (path) in $K_{n}^{c}$ is a cycle (path) in which adjacent edges have distinct colors. B. Bollob\\'{a}s and P. Erd\\\"{o}s (1976) proposed the following conjecture: if $\\Delta^{\\mathrm{mon}} (K_{n}^{c})<\\lfloor \\frac{n}{2} \\rfloor$, then $K_{n}^{c}$ contains a properly colored Hamiltonian cycle. Li, Wang and Zhou proved that if $\\Delta^{\\mathrm","authors_text":"Guanghui Wang, Guizhen Liu, Tao Wang","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-03T13:23:41Z","title":"Long properly colored cycles in edge colored complete graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0450","kind":"arxiv","version":2},"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:c2b1ab5d7076af65d5c5ef691dff5d1720d3820a667bccc1aadbeaaa5bbf5a22","target":"record","created_at":"2026-05-18T02:58:13Z","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":"b3f0ecef825096636d06aa0f005855252c93b5baf04c0509ea6e4e97609f2d3e","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-03T13:23:41Z","title_canon_sha256":"2b4d9ba613c9f5ad8f640e920895419896d24bf22406402439ddfc6a041505ec"},"schema_version":"1.0","source":{"id":"1301.0450","kind":"arxiv","version":2}},"canonical_sha256":"b8fe893764999946c3bf5ac18ee67a313025df77ed9f0a4143b1b3be81e170bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8fe893764999946c3bf5ac18ee67a313025df77ed9f0a4143b1b3be81e170bc","first_computed_at":"2026-05-18T02:58:13.194411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:13.194411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mj9pHjds3FM0mXCvU6o9qwfYQHSKd5lHxuhr9EO24ftzv1PwlLTq7qEHg1weudau9M2JYgoRL8rppE0SX7EcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:13.195164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0450","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2b1ab5d7076af65d5c5ef691dff5d1720d3820a667bccc1aadbeaaa5bbf5a22","sha256:967bbdb45153b52bfdae7af0e4c6ce331bbd9ce5642a29ab292f8ee16b3e6c18"],"state_sha256":"ff90d154c0b139c59c2719ed6ffd35c85a075b0675dfb9045bcf4fba4e95b51a"}