{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PUMTIJVJYIE633XWQ7RWR55D2C","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":"b7bd9d279b932f5dfa1741a4b0213da97607f655c5f5a1afd773afc408d59519","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-12T19:24:05Z","title_canon_sha256":"24110fa4f0b5624345226790ddf4b2e535f98df0864e06152b0b4650f392eb0a"},"schema_version":"1.0","source":{"id":"1008.2193","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2193","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2193v4","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2193","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"PUMTIJVJYIE6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PUMTIJVJYIE633XW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PUMTIJVJ","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:9acd893ccb1ffe542a0be396818c67747d741886f25b1fe8f23c3288568403f8","target":"graph","created_at":"2026-05-18T00:39:18Z","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":"A famous conjecture of Lov\\'asz states that every connected vertex-transitive graph contains a Hamilton path. In this article we confirm the conjecture in the case that the graph is dense and sufficiently large. In fact, we show that such graphs contain a Hamilton cycle and moreover we provide a polynomial time algorithm for finding such a cycle.","authors_text":"Andr\\'as M\\'ath\\'e, Demetres Christofides, Jan Hladk\\'y","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-12T19:24:05Z","title":"Hamilton cycles in dense vertex-transitive graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2193","kind":"arxiv","version":4},"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:dd682d9c3ac6b93ebc323d7b0d0694c34284e836d4bcca2fb5599c5f118f614b","target":"record","created_at":"2026-05-18T00:39:18Z","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":"b7bd9d279b932f5dfa1741a4b0213da97607f655c5f5a1afd773afc408d59519","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-12T19:24:05Z","title_canon_sha256":"24110fa4f0b5624345226790ddf4b2e535f98df0864e06152b0b4650f392eb0a"},"schema_version":"1.0","source":{"id":"1008.2193","kind":"arxiv","version":4}},"canonical_sha256":"7d193426a9c209edeef687e368f7a3d086e2d3fa847d64d01b98aa7ff77ed046","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d193426a9c209edeef687e368f7a3d086e2d3fa847d64d01b98aa7ff77ed046","first_computed_at":"2026-05-18T00:39:18.815330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:18.815330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ORIyWkE82FredwjUGTsKUFYQeArQX3+ASdV7oel9/xZx+N6jgHF23NG7L4e/55B9wGRoY3vB/WB50qqgnolCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:18.815928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2193","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd682d9c3ac6b93ebc323d7b0d0694c34284e836d4bcca2fb5599c5f118f614b","sha256:9acd893ccb1ffe542a0be396818c67747d741886f25b1fe8f23c3288568403f8"],"state_sha256":"82b26403675ea0e0eb60c63daa2622e07268637f597bba6eadcd219b0bed71f3"}