{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5NK4DBUMKU6RWQQRUV255AC3EJ","short_pith_number":"pith:5NK4DBUM","canonical_record":{"source":{"id":"1401.3545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-15T11:10:35Z","cross_cats_sorted":[],"title_canon_sha256":"7226d28921ed6afd50219b728f3866189b17e190509632c942840b61448df18c","abstract_canon_sha256":"6c1a2e034fc96ad6d142aa2a08841c148730e1e37a962d15d67db04affdd2b53"},"schema_version":"1.0"},"canonical_sha256":"eb55c1868c553d1b4211a575de805b226acf76df5f1a6621b2e71f370ba1c5c3","source":{"kind":"arxiv","id":"1401.3545","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3545","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3545v1","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3545","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"5NK4DBUMKU6R","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5NK4DBUMKU6RWQQR","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5NK4DBUM","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5NK4DBUMKU6RWQQRUV255AC3EJ","target":"record","payload":{"canonical_record":{"source":{"id":"1401.3545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-15T11:10:35Z","cross_cats_sorted":[],"title_canon_sha256":"7226d28921ed6afd50219b728f3866189b17e190509632c942840b61448df18c","abstract_canon_sha256":"6c1a2e034fc96ad6d142aa2a08841c148730e1e37a962d15d67db04affdd2b53"},"schema_version":"1.0"},"canonical_sha256":"eb55c1868c553d1b4211a575de805b226acf76df5f1a6621b2e71f370ba1c5c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:33.182346Z","signature_b64":"4dCjsJKOi5AOsa4UIv6Tm2cQ30TLccpg8f+ROyTlZB9W81Te+f3Vu+b+ZYw+EHMZZ9R57QpyNTh1aiYmzjkrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb55c1868c553d1b4211a575de805b226acf76df5f1a6621b2e71f370ba1c5c3","last_reissued_at":"2026-05-18T02:18:33.181805Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:33.181805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.3545","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pJi9zD0lmpB7Zqw5sKPTrgNEC8CZiqJzcc3DxATMmzW4Iuh/5NAIGpk6JqCdV7Pt/3LWDS/nhk7sPZEm5ZJBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:11:35.040793Z"},"content_sha256":"aa7d919d7c59f5a27f874d1d9eab15a26f7ec618e1d9f743f33b95f5ef433efb","schema_version":"1.0","event_id":"sha256:aa7d919d7c59f5a27f874d1d9eab15a26f7ec618e1d9f743f33b95f5ef433efb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5NK4DBUMKU6RWQQRUV255AC3EJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On path-quasar Ramsey numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Binlong Li, Bo Ning","submitted_at":"2014-01-15T11:10:35Z","abstract_excerpt":"Let $G_1$ and $G_2$ be two given graphs. The Ramsey number $R(G_1,G_2)$ is the least integer $r$ such that for every graph $G$ on $r$ vertices, either $G$ contains a $G_1$ or $\\overline{G}$ contains a $G_2$. Parsons gave a recursive formula to determine the values of $R(P_n,K_{1,m})$, where $P_n$ is a path on $n$ vertices and $K_{1,m}$ is a star on $m+1$ vertices. In this note, we first give an explicit formula for the path-star Ramsey numbers. Secondly, we study the Ramsey numbers $R(P_n,K_1\\vee F_m)$, where $F_m$ is a linear forest on $m$ vertices. We determine the exact values of $R(P_n,K_1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3545","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCZQxQmUd0kuMwTsvrKv+KtmviZd8BAQmGIUQxcl2P2GWd19YSQUBLz99MwFFdPYzkEZs8cf+CyhPzb/GlEJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:11:35.041171Z"},"content_sha256":"ba25754828a1fac23e5c48c0f2df118d4ca96d8c822e88239c41bb99140e3d2b","schema_version":"1.0","event_id":"sha256:ba25754828a1fac23e5c48c0f2df118d4ca96d8c822e88239c41bb99140e3d2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NK4DBUMKU6RWQQRUV255AC3EJ/bundle.json","state_url":"https://pith.science/pith/5NK4DBUMKU6RWQQRUV255AC3EJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NK4DBUMKU6RWQQRUV255AC3EJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T15:11:35Z","links":{"resolver":"https://pith.science/pith/5NK4DBUMKU6RWQQRUV255AC3EJ","bundle":"https://pith.science/pith/5NK4DBUMKU6RWQQRUV255AC3EJ/bundle.json","state":"https://pith.science/pith/5NK4DBUMKU6RWQQRUV255AC3EJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NK4DBUMKU6RWQQRUV255AC3EJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5NK4DBUMKU6RWQQRUV255AC3EJ","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":"6c1a2e034fc96ad6d142aa2a08841c148730e1e37a962d15d67db04affdd2b53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-15T11:10:35Z","title_canon_sha256":"7226d28921ed6afd50219b728f3866189b17e190509632c942840b61448df18c"},"schema_version":"1.0","source":{"id":"1401.3545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3545","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3545v1","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3545","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"5NK4DBUMKU6R","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5NK4DBUMKU6RWQQR","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5NK4DBUM","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:ba25754828a1fac23e5c48c0f2df118d4ca96d8c822e88239c41bb99140e3d2b","target":"graph","created_at":"2026-05-18T02:18:33Z","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 $G_1$ and $G_2$ be two given graphs. The Ramsey number $R(G_1,G_2)$ is the least integer $r$ such that for every graph $G$ on $r$ vertices, either $G$ contains a $G_1$ or $\\overline{G}$ contains a $G_2$. Parsons gave a recursive formula to determine the values of $R(P_n,K_{1,m})$, where $P_n$ is a path on $n$ vertices and $K_{1,m}$ is a star on $m+1$ vertices. In this note, we first give an explicit formula for the path-star Ramsey numbers. Secondly, we study the Ramsey numbers $R(P_n,K_1\\vee F_m)$, where $F_m$ is a linear forest on $m$ vertices. We determine the exact values of $R(P_n,K_1","authors_text":"Binlong Li, Bo Ning","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-15T11:10:35Z","title":"On path-quasar Ramsey numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3545","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:aa7d919d7c59f5a27f874d1d9eab15a26f7ec618e1d9f743f33b95f5ef433efb","target":"record","created_at":"2026-05-18T02:18:33Z","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":"6c1a2e034fc96ad6d142aa2a08841c148730e1e37a962d15d67db04affdd2b53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-15T11:10:35Z","title_canon_sha256":"7226d28921ed6afd50219b728f3866189b17e190509632c942840b61448df18c"},"schema_version":"1.0","source":{"id":"1401.3545","kind":"arxiv","version":1}},"canonical_sha256":"eb55c1868c553d1b4211a575de805b226acf76df5f1a6621b2e71f370ba1c5c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb55c1868c553d1b4211a575de805b226acf76df5f1a6621b2e71f370ba1c5c3","first_computed_at":"2026-05-18T02:18:33.181805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:33.181805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4dCjsJKOi5AOsa4UIv6Tm2cQ30TLccpg8f+ROyTlZB9W81Te+f3Vu+b+ZYw+EHMZZ9R57QpyNTh1aiYmzjkrDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:33.182346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.3545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa7d919d7c59f5a27f874d1d9eab15a26f7ec618e1d9f743f33b95f5ef433efb","sha256:ba25754828a1fac23e5c48c0f2df118d4ca96d8c822e88239c41bb99140e3d2b"],"state_sha256":"cec3ab2262a4daef396147e306506176d5b23a31947b397c82b8a1d1b9217221"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FgrrBMZVz5PH3BnOQxBPu5Tq+ZD3BeIjxvqBM2VL3rVbQPh3owuGKHuOvYA9hPJXUpgFKV/i3XQ8ygCdRlH5AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:11:35.043251Z","bundle_sha256":"12fbbf6492b914ab3583b1d13beb06ea86ea49ada7bd07764faebf1ce3f7b433"}}