{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:63LXER7SVXVZYMR4E2HKTE5QTQ","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":"16bf8a56d98a3df2056c15a67b9054a31e3b52ed97a3f660bfbcdf55399d0f4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-27T19:34:05Z","title_canon_sha256":"4162c473a6ee493b0f8cd6db033cbbdbfc8ad86c8a4ca09b5fa9b672f1515716"},"schema_version":"1.0","source":{"id":"1903.11663","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11663","created_at":"2026-05-17T23:50:02Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11663v1","created_at":"2026-05-17T23:50:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11663","created_at":"2026-05-17T23:50:02Z"},{"alias_kind":"pith_short_12","alias_value":"63LXER7SVXVZ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"63LXER7SVXVZYMR4","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"63LXER7S","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:db84de7872d22bb66839dcae1aa8627203e2d4c0c3c5599de454467fc7265380","target":"graph","created_at":"2026-05-17T23:50:02Z","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":"Among the well-known sufficient degree conditions for the Hamiltonicity of a finite graph, the condition of Asratian and Khachatrian is the weakest and thus gives the strongest result. Diestel conjectured that it should extend to locally finite infinite graphs~$G$, in that the same condition implies that the Freudenthal compactification of $G$ contains a circle through all its vertices and ends. We prove Diestel's conjecture for claw-free graphs.","authors_text":"Karl Heuer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-27T19:34:05Z","title":"A sufficient local degree condition for Hamiltonicity in locally finite claw-free graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11663","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":"sha256:12240bb74cff08604be69acdb3c654f37f627a854aaf801e7e9b63f0f8e11783","target":"record","created_at":"2026-05-17T23:50:02Z","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":"16bf8a56d98a3df2056c15a67b9054a31e3b52ed97a3f660bfbcdf55399d0f4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-27T19:34:05Z","title_canon_sha256":"4162c473a6ee493b0f8cd6db033cbbdbfc8ad86c8a4ca09b5fa9b672f1515716"},"schema_version":"1.0","source":{"id":"1903.11663","kind":"arxiv","version":1}},"canonical_sha256":"f6d77247f2adeb9c323c268ea993b09c27cba0cbe499c86843c5f8d781f416b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6d77247f2adeb9c323c268ea993b09c27cba0cbe499c86843c5f8d781f416b7","first_computed_at":"2026-05-17T23:50:02.085965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:02.085965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"02UcxqHnxSDrd9I6APn2bktrisaMtiWr4rwUsUSflJ6jzSYm1ZmyFjLb5CCIPIJFh/BcpRsNQQN8GINUoioDBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:02.086398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.11663","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12240bb74cff08604be69acdb3c654f37f627a854aaf801e7e9b63f0f8e11783","sha256:db84de7872d22bb66839dcae1aa8627203e2d4c0c3c5599de454467fc7265380"],"state_sha256":"e5bb501f7a448b2077415b3de61312e04f383d6d4cca7914038615b0d762b945"}