{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:57K27UPR6WIY7EHHVBKUGXD53L","short_pith_number":"pith:57K27UPR","schema_version":"1.0","canonical_sha256":"efd5afd1f1f5918f90e7a855435c7ddad095f7b7d64d8cb0896c7af7ac85dcfa","source":{"kind":"arxiv","id":"1310.3017","version":1},"attestation_state":"computed","paper":{"title":"Computation of the Ramsey Numbers $R(C_4,K_9)$ and $R(C_4,K_{10})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Alexander Lange, Ivan Livinsky, Stanis{\\l}aw Radziszowski","submitted_at":"2013-10-11T04:16:29Z","abstract_excerpt":"The Ramsey number $R(C_4,K_m)$ is the smallest $n$ such that any graph on $n$ vertices contains a cycle of length four or an independent set of order $m$. With the help of computer algorithms we obtain the exact values of the Ramsey numbers $R(C_4,K_9)=30$ and $R(C_4,K_{10})=36$. New bounds for the next two open cases are also presented."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.3017","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-11T04:16:29Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"a6eb23f40212150dddfdb977bea734f28dcb487252adf656aed01cc8d258b545","abstract_canon_sha256":"f0c9e1ec6e29466e871c1b490845d4e883cfee2e3609eed62701751c071072ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:45.242386Z","signature_b64":"8GpkRQZW1btVlOYGFCLArT1/xfetJkudrjEQw5SyHNnqZhT1pnT5TK3M4cG3Qb+0F+dEzeO16E87RIL3VVjmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efd5afd1f1f5918f90e7a855435c7ddad095f7b7d64d8cb0896c7af7ac85dcfa","last_reissued_at":"2026-05-18T03:10:45.241848Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:45.241848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computation of the Ramsey Numbers $R(C_4,K_9)$ and $R(C_4,K_{10})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Alexander Lange, Ivan Livinsky, Stanis{\\l}aw Radziszowski","submitted_at":"2013-10-11T04:16:29Z","abstract_excerpt":"The Ramsey number $R(C_4,K_m)$ is the smallest $n$ such that any graph on $n$ vertices contains a cycle of length four or an independent set of order $m$. With the help of computer algorithms we obtain the exact values of the Ramsey numbers $R(C_4,K_9)=30$ and $R(C_4,K_{10})=36$. New bounds for the next two open cases are also presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3017","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.3017","created_at":"2026-05-18T03:10:45.241930+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.3017v1","created_at":"2026-05-18T03:10:45.241930+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3017","created_at":"2026-05-18T03:10:45.241930+00:00"},{"alias_kind":"pith_short_12","alias_value":"57K27UPR6WIY","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"57K27UPR6WIY7EHH","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"57K27UPR","created_at":"2026-05-18T12:27:34.582898+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L","json":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L.json","graph_json":"https://pith.science/api/pith-number/57K27UPR6WIY7EHHVBKUGXD53L/graph.json","events_json":"https://pith.science/api/pith-number/57K27UPR6WIY7EHHVBKUGXD53L/events.json","paper":"https://pith.science/paper/57K27UPR"},"agent_actions":{"view_html":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L","download_json":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L.json","view_paper":"https://pith.science/paper/57K27UPR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.3017&json=true","fetch_graph":"https://pith.science/api/pith-number/57K27UPR6WIY7EHHVBKUGXD53L/graph.json","fetch_events":"https://pith.science/api/pith-number/57K27UPR6WIY7EHHVBKUGXD53L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L/action/storage_attestation","attest_author":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L/action/author_attestation","sign_citation":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L/action/citation_signature","submit_replication":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L/action/replication_record"}},"created_at":"2026-05-18T03:10:45.241930+00:00","updated_at":"2026-05-18T03:10:45.241930+00:00"}