{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OOWCJ3W7J4MYORT6UKCE6ME76T","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":"1dd3e7c82214e8868b97292dbd2fc4d800bb14adf6194f6aaba450840882bcb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-22T19:08:36Z","title_canon_sha256":"735d9a7d947d9801054fb6030ed133ddd5da749585de58b863c38a0a5c1d2a56"},"schema_version":"1.0","source":{"id":"1505.06181","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06181","created_at":"2026-05-18T00:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06181v2","created_at":"2026-05-18T00:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06181","created_at":"2026-05-18T00:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"OOWCJ3W7J4MY","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OOWCJ3W7J4MYORT6","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OOWCJ3W7","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:9b6522d7396ab6b70d2a6a03ab2629ef418f7c62633c5d00b179473eb3c3805f","target":"graph","created_at":"2026-05-18T00:40:17Z","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 $n$-vertex graph with $n\\ge 3$. A classic result of Dirac from 1952 asserts that $G$ is hamiltonian if $\\delta(G)\\ge n/2$. Dirac's theorem is one of the most influential results in the study of hamiltonicity and by now there are many related known results\\,(see, e.g., J. A. Bondy, Basic Graph Theory: Paths and Circuits, Chapter 1 in: {\\it Handbook of Combinatorics Vol.1}). A {\\it Halin graph} is a planar graph consisting of two edge-disjoint subgraphs: a spanning tree of at least 4 vertices and with no vertex of degree 2, and a cycle induced on the set of the leaves of the spanni","authors_text":"Guantao Chen, Songling Shan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-22T19:08:36Z","title":"Dirac's Condition for Spanning Halin Subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06181","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":"sha256:1be05e76f5e87e45843efe7cbf5957d37808abd35df8c2f5377eb847eaadc7c8","target":"record","created_at":"2026-05-18T00:40:17Z","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":"1dd3e7c82214e8868b97292dbd2fc4d800bb14adf6194f6aaba450840882bcb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-22T19:08:36Z","title_canon_sha256":"735d9a7d947d9801054fb6030ed133ddd5da749585de58b863c38a0a5c1d2a56"},"schema_version":"1.0","source":{"id":"1505.06181","kind":"arxiv","version":2}},"canonical_sha256":"73ac24eedf4f1987467ea2844f309ff4edbe4bd93d517fe659aca23a0c86bdca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73ac24eedf4f1987467ea2844f309ff4edbe4bd93d517fe659aca23a0c86bdca","first_computed_at":"2026-05-18T00:40:17.607404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:17.607404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4JFYi/o/R4aftfiTCyfM/OLLazEaAk0nXm+SfHqibEx/K740G4RVkjL6n93t9A9GmselHVq68so7SEH3ImKbCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:17.608055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06181","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1be05e76f5e87e45843efe7cbf5957d37808abd35df8c2f5377eb847eaadc7c8","sha256:9b6522d7396ab6b70d2a6a03ab2629ef418f7c62633c5d00b179473eb3c3805f"],"state_sha256":"0183b4fba99f90cca7bb8ed45794426243d4a8e49b625286c2f6a1050a175885"}