{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7SYCLWREMPTDTBSPDOLCM6QR2H","short_pith_number":"pith:7SYCLWRE","canonical_record":{"source":{"id":"1809.05413","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-13T12:01:38Z","cross_cats_sorted":[],"title_canon_sha256":"c279d22b9047503e6b8ed22c3601bdaa3652a1b59e1057901a6b3ff1053a93d6","abstract_canon_sha256":"d532315325dc98916c099e44e61b67df58fc1cbe96028b6e62bd891b323ca823"},"schema_version":"1.0"},"canonical_sha256":"fcb025da2463e639864f1b96267a11d1e7cc38de00d725b203d8079754fba8e6","source":{"kind":"arxiv","id":"1809.05413","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05413","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05413v2","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05413","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"7SYCLWREMPTD","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7SYCLWREMPTDTBSP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7SYCLWRE","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7SYCLWREMPTDTBSPDOLCM6QR2H","target":"record","payload":{"canonical_record":{"source":{"id":"1809.05413","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-13T12:01:38Z","cross_cats_sorted":[],"title_canon_sha256":"c279d22b9047503e6b8ed22c3601bdaa3652a1b59e1057901a6b3ff1053a93d6","abstract_canon_sha256":"d532315325dc98916c099e44e61b67df58fc1cbe96028b6e62bd891b323ca823"},"schema_version":"1.0"},"canonical_sha256":"fcb025da2463e639864f1b96267a11d1e7cc38de00d725b203d8079754fba8e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:27.497252Z","signature_b64":"i5G1BcEKNv9M1XmpVTPzFOf1LFddu+rIH4OAzWoEWt8N3ynIWBavLepyett+Pnq5nEweUmuYI3qDBJVtYIz8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcb025da2463e639864f1b96267a11d1e7cc38de00d725b203d8079754fba8e6","last_reissued_at":"2026-05-18T00:05:27.496615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:27.496615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.05413","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KMw6FfrTSCyTzmziVk1wRY1OjvBmEtHIs/WfqnOUqLNORLQ/x3lvWuuydWxVDzPkrxIHAhdVEya6ivjQ0jP1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T06:20:34.601009Z"},"content_sha256":"55528c908db09b5a5192c8646d1b4c1874ebe19ffabba8b5c5d0c4f209c2f573","schema_version":"1.0","event_id":"sha256:55528c908db09b5a5192c8646d1b4c1874ebe19ffabba8b5c5d0c4f209c2f573"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7SYCLWREMPTDTBSPDOLCM6QR2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"3-colored asymmetric bipartite Ramsey number of connected matchings and cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yuejian Peng, Zhidan Luo","submitted_at":"2018-09-13T12:01:38Z","abstract_excerpt":"Let $k,l,m$ be integers and $r(k,l,m)$ be the minimum integer $N$ such that for any red-blue-green coloring of $K_{N,N}$, there is a red matching of size at least $k$ in a component, or a blue matching of at least size $l$ in a component, or a green matching of size at least $m$ in a component. In this paper, we determine the exact value of $r(k,l,m)$ completely. Applying a technique originated by {\\L}uczak that applies Szemer\\'edi's Regularity Lemma to reduce the problem of showing the existence of a monochromatic cycle to show the existence of a monochromatic matching in a component, we obta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05413","kind":"arxiv","version":2},"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":"2026-05-18T00:05:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rFF9L8C7US9slJpaifo9K/GajZWL8KS4TTS07WJx8s50Fy0p/CadiQQ7WsyDcm3frQwNMnv8gmbjStuiBApgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T06:20:34.601689Z"},"content_sha256":"ecd55a92fa787acd7a6b959c3491389ae4e27db6312ea8dffd0d3ac02ffa3027","schema_version":"1.0","event_id":"sha256:ecd55a92fa787acd7a6b959c3491389ae4e27db6312ea8dffd0d3ac02ffa3027"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SYCLWREMPTDTBSPDOLCM6QR2H/bundle.json","state_url":"https://pith.science/pith/7SYCLWREMPTDTBSPDOLCM6QR2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SYCLWREMPTDTBSPDOLCM6QR2H/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":"2026-05-19T06:20:34Z","links":{"resolver":"https://pith.science/pith/7SYCLWREMPTDTBSPDOLCM6QR2H","bundle":"https://pith.science/pith/7SYCLWREMPTDTBSPDOLCM6QR2H/bundle.json","state":"https://pith.science/pith/7SYCLWREMPTDTBSPDOLCM6QR2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SYCLWREMPTDTBSPDOLCM6QR2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7SYCLWREMPTDTBSPDOLCM6QR2H","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":"d532315325dc98916c099e44e61b67df58fc1cbe96028b6e62bd891b323ca823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-13T12:01:38Z","title_canon_sha256":"c279d22b9047503e6b8ed22c3601bdaa3652a1b59e1057901a6b3ff1053a93d6"},"schema_version":"1.0","source":{"id":"1809.05413","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05413","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05413v2","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05413","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"7SYCLWREMPTD","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7SYCLWREMPTDTBSP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7SYCLWRE","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:ecd55a92fa787acd7a6b959c3491389ae4e27db6312ea8dffd0d3ac02ffa3027","target":"graph","created_at":"2026-05-18T00:05:27Z","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 $k,l,m$ be integers and $r(k,l,m)$ be the minimum integer $N$ such that for any red-blue-green coloring of $K_{N,N}$, there is a red matching of size at least $k$ in a component, or a blue matching of at least size $l$ in a component, or a green matching of size at least $m$ in a component. In this paper, we determine the exact value of $r(k,l,m)$ completely. Applying a technique originated by {\\L}uczak that applies Szemer\\'edi's Regularity Lemma to reduce the problem of showing the existence of a monochromatic cycle to show the existence of a monochromatic matching in a component, we obta","authors_text":"Yuejian Peng, Zhidan Luo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-13T12:01:38Z","title":"3-colored asymmetric bipartite Ramsey number of connected matchings and cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05413","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":"sha256:55528c908db09b5a5192c8646d1b4c1874ebe19ffabba8b5c5d0c4f209c2f573","target":"record","created_at":"2026-05-18T00:05:27Z","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":"d532315325dc98916c099e44e61b67df58fc1cbe96028b6e62bd891b323ca823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-13T12:01:38Z","title_canon_sha256":"c279d22b9047503e6b8ed22c3601bdaa3652a1b59e1057901a6b3ff1053a93d6"},"schema_version":"1.0","source":{"id":"1809.05413","kind":"arxiv","version":2}},"canonical_sha256":"fcb025da2463e639864f1b96267a11d1e7cc38de00d725b203d8079754fba8e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcb025da2463e639864f1b96267a11d1e7cc38de00d725b203d8079754fba8e6","first_computed_at":"2026-05-18T00:05:27.496615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:27.496615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i5G1BcEKNv9M1XmpVTPzFOf1LFddu+rIH4OAzWoEWt8N3ynIWBavLepyett+Pnq5nEweUmuYI3qDBJVtYIz8DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:27.497252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.05413","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55528c908db09b5a5192c8646d1b4c1874ebe19ffabba8b5c5d0c4f209c2f573","sha256:ecd55a92fa787acd7a6b959c3491389ae4e27db6312ea8dffd0d3ac02ffa3027"],"state_sha256":"8e2c1fce937a74322def5002c13ed5d7422bf48039185c9392d3b8d00bbba849"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3GbhbcaP7v0IpMl1SFky17ZjQ2TAfJsUmoQBtibx2xroZHm7GiM3vVcnduWPcPLcz52fqNK2c4lIV+ZxHH54Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T06:20:34.604613Z","bundle_sha256":"e181310e73d07cc0f9d7686552cd04d6a6d765916b01d78f8e4af0907974d418"}}