{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WFMB3PWWE4EEWFD27WICHJ3JOR","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":"26227fd30373403165555d5b8192a4223070f388003559ad795015c9ad82f213","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-20T00:27:32Z","title_canon_sha256":"cfe18104292fbfb6d610a8122464c9d39b641562e9fe7d9aaec51c38203a67d0"},"schema_version":"1.0","source":{"id":"2310.13204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.13204","created_at":"2026-07-05T07:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"2310.13204v1","created_at":"2026-07-05T07:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.13204","created_at":"2026-07-05T07:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"WFMB3PWWE4EE","created_at":"2026-07-05T07:02:58Z"},{"alias_kind":"pith_short_16","alias_value":"WFMB3PWWE4EEWFD2","created_at":"2026-07-05T07:02:58Z"},{"alias_kind":"pith_short_8","alias_value":"WFMB3PWW","created_at":"2026-07-05T07:02:58Z"}],"graph_snapshots":[{"event_id":"sha256:666a8432fd7278cf5c5353d2550b77469e00d06422d4e5ad3c614bead08bc95e","target":"graph","created_at":"2026-07-05T07:02:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.13204/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given two graphs $G_1$ and $G_2$, the Ramsey number $r(G_1,G_2)$ refers to the smallest positive integer $N$ such that any graph $G$ with $N$ vertices contains $G_1$ as a subgraph, or the complement of $G$ contains $G_2$ as a subgraph. A connected graph $H$ is said to be $p$-good if $r(K_p,H)=(p-1)(|H|-1)+1$. A generalized fan, denoted as $K_1+nH$, is formed by the disjoint union of $n$ copies of $H$ along with an additional vertex that is connected to each vertex of $nH$. Recently Chung and Lin proved that $K_1+nH$ is $p$-good for $n\\ge cp\\ell/|H|$, where $c\\approx 52.456$ and $\\ell=r(K_{p},H","authors_text":"Yanbo Zhang, Yaojun Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-20T00:27:32Z","title":"Ramsey goodness of fans"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.13204","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":"sha256:31fe21a62153e220b803a438a842cfdfe749edd06c83fb7181480f8868e75ae4","target":"record","created_at":"2026-07-05T07:02:58Z","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":"26227fd30373403165555d5b8192a4223070f388003559ad795015c9ad82f213","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-20T00:27:32Z","title_canon_sha256":"cfe18104292fbfb6d610a8122464c9d39b641562e9fe7d9aaec51c38203a67d0"},"schema_version":"1.0","source":{"id":"2310.13204","kind":"arxiv","version":1}},"canonical_sha256":"b1581dbed627084b147afd9023a769747c45e0fd0a2cea494b1f2bbaddef51f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1581dbed627084b147afd9023a769747c45e0fd0a2cea494b1f2bbaddef51f2","first_computed_at":"2026-07-05T07:02:58.891437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:02:58.891437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6AYXPfJNCMXkALNOO3t27606lWWM0rIkmMcGja624VdmLXrO/laIJfJzj2txFO+RL5Xk9+lXAXKpqKoNacPhBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:02:58.891937Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.13204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31fe21a62153e220b803a438a842cfdfe749edd06c83fb7181480f8868e75ae4","sha256:666a8432fd7278cf5c5353d2550b77469e00d06422d4e5ad3c614bead08bc95e"],"state_sha256":"dab9cbdabc84a9a36c4dbba18f257f520a060f3a31932e503a606291e801aa49"}