{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:57K27UPR6WIY7EHHVBKUGXD53L","short_pith_number":"pith:57K27UPR","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"},"canonical_sha256":"efd5afd1f1f5918f90e7a855435c7ddad095f7b7d64d8cb0896c7af7ac85dcfa","source":{"kind":"arxiv","id":"1310.3017","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3017","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3017v1","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3017","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"pith_short_12","alias_value":"57K27UPR6WIY","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"57K27UPR6WIY7EHH","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"57K27UPR","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:57K27UPR6WIY7EHHVBKUGXD53L","target":"record","payload":{"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"},"canonical_sha256":"efd5afd1f1f5918f90e7a855435c7ddad095f7b7d64d8cb0896c7af7ac85dcfa","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"},"source_kind":"arxiv","source_id":"1310.3017","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":"2026-05-18T03:10:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sug55sl2kKX/Up8FE/wQKmb4il+53LGNFnIvmf4egH/q2c+7YEfJyflGUq0mMDZYYX/IYOeI+NOpOFJn+KJIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:53:04.289341Z"},"content_sha256":"b084fcf8326e9dc7f86bf7a9220861047f732c3194c4ac2d25cadcf1b9e479e4","schema_version":"1.0","event_id":"sha256:b084fcf8326e9dc7f86bf7a9220861047f732c3194c4ac2d25cadcf1b9e479e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:57K27UPR6WIY7EHHVBKUGXD53L","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:10:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zOYN+MniP25Z/VuqnrgbnN7GMRq68Ou2WjW25QySkuuMaW+Ftx/V6mcj2qMZGIj/MixmbJ2zXSCldYtBaLy0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:53:04.289949Z"},"content_sha256":"3b7efb7c2c543e17de43f851314735466a5bc26aba7522bd43b2e3e0d7c907a8","schema_version":"1.0","event_id":"sha256:3b7efb7c2c543e17de43f851314735466a5bc26aba7522bd43b2e3e0d7c907a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L/bundle.json","state_url":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57K27UPR6WIY7EHHVBKUGXD53L/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":"2026-06-09T06:53:04Z","links":{"resolver":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L","bundle":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L/bundle.json","state":"https://pith.science/pith/57K27UPR6WIY7EHHVBKUGXD53L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57K27UPR6WIY7EHHVBKUGXD53L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:57K27UPR6WIY7EHHVBKUGXD53L","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":"f0c9e1ec6e29466e871c1b490845d4e883cfee2e3609eed62701751c071072ea","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-11T04:16:29Z","title_canon_sha256":"a6eb23f40212150dddfdb977bea734f28dcb487252adf656aed01cc8d258b545"},"schema_version":"1.0","source":{"id":"1310.3017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3017","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3017v1","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3017","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"pith_short_12","alias_value":"57K27UPR6WIY","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"57K27UPR6WIY7EHH","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"57K27UPR","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:3b7efb7c2c543e17de43f851314735466a5bc26aba7522bd43b2e3e0d7c907a8","target":"graph","created_at":"2026-05-18T03:10:45Z","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":"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.","authors_text":"Alexander Lange, Ivan Livinsky, Stanis{\\l}aw Radziszowski","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-11T04:16:29Z","title":"Computation of the Ramsey Numbers $R(C_4,K_9)$ and $R(C_4,K_{10})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3017","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:b084fcf8326e9dc7f86bf7a9220861047f732c3194c4ac2d25cadcf1b9e479e4","target":"record","created_at":"2026-05-18T03:10:45Z","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":"f0c9e1ec6e29466e871c1b490845d4e883cfee2e3609eed62701751c071072ea","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-11T04:16:29Z","title_canon_sha256":"a6eb23f40212150dddfdb977bea734f28dcb487252adf656aed01cc8d258b545"},"schema_version":"1.0","source":{"id":"1310.3017","kind":"arxiv","version":1}},"canonical_sha256":"efd5afd1f1f5918f90e7a855435c7ddad095f7b7d64d8cb0896c7af7ac85dcfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efd5afd1f1f5918f90e7a855435c7ddad095f7b7d64d8cb0896c7af7ac85dcfa","first_computed_at":"2026-05-18T03:10:45.241848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:45.241848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8GpkRQZW1btVlOYGFCLArT1/xfetJkudrjEQw5SyHNnqZhT1pnT5TK3M4cG3Qb+0F+dEzeO16E87RIL3VVjmBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:45.242386Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b084fcf8326e9dc7f86bf7a9220861047f732c3194c4ac2d25cadcf1b9e479e4","sha256:3b7efb7c2c543e17de43f851314735466a5bc26aba7522bd43b2e3e0d7c907a8"],"state_sha256":"b2a888a62d86d242c80bc732d629c85b4b676c0ea6ce96a09929c05a6eb097e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qmV7eDpedieMuIeqP0ZIIHXOMK0r/sQBY2WszKtEyu85GWhDIscnJJAfUDpFu1dclR+NaKTkkc3HmAAfSIKkCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:53:04.293715Z","bundle_sha256":"bc4e73b3f633545d29e5f0c6c5bd8ab991252eb3853f8c75da20ef6520f787aa"}}