{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ABCVUUNFAIRFO3E7ET6KPMVN7Q","short_pith_number":"pith:ABCVUUNF","canonical_record":{"source":{"id":"1602.02501","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-08T09:25:10Z","cross_cats_sorted":[],"title_canon_sha256":"5be34a914d7fff7977ffcc2e07f0315fa9a6db733b88162aa8ca2fedc1998364","abstract_canon_sha256":"7948371eb4419729e14d0dfe7cafdaa69e972f63223a427770bd54cc6f1103bd"},"schema_version":"1.0"},"canonical_sha256":"00455a51a50222576c9f24fca7b2adfc03c6a1008cc0cc40686e73316987e8e5","source":{"kind":"arxiv","id":"1602.02501","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02501","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02501v2","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02501","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"ABCVUUNFAIRF","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"ABCVUUNFAIRFO3E7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"ABCVUUNF","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ABCVUUNFAIRFO3E7ET6KPMVN7Q","target":"record","payload":{"canonical_record":{"source":{"id":"1602.02501","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-08T09:25:10Z","cross_cats_sorted":[],"title_canon_sha256":"5be34a914d7fff7977ffcc2e07f0315fa9a6db733b88162aa8ca2fedc1998364","abstract_canon_sha256":"7948371eb4419729e14d0dfe7cafdaa69e972f63223a427770bd54cc6f1103bd"},"schema_version":"1.0"},"canonical_sha256":"00455a51a50222576c9f24fca7b2adfc03c6a1008cc0cc40686e73316987e8e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:09.578814Z","signature_b64":"TMXTnT6p1Ww9DqNfsAnAOFfP4wtRwZDEEJBG060hViuFf63IDtanRBCAbKGu802h3CpNU/7jqc/K9+LJEECeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00455a51a50222576c9f24fca7b2adfc03c6a1008cc0cc40686e73316987e8e5","last_reissued_at":"2026-05-18T00:23:09.578232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:09.578232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.02501","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":"2026-05-18T00:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tfi52cV0V0e4rrnCYJ1NpsCxuiIuVmBK8rf4WsvTAIe/jy41/4CBewDRPo/cOkTgRr4k7DgV0z2lKY3Q8LZZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:47:43.262077Z"},"content_sha256":"f08e851b4a2949db1e1dd9f148ee3cca21097c6b77b802a96368f9b2f433aa0f","schema_version":"1.0","event_id":"sha256:f08e851b4a2949db1e1dd9f148ee3cca21097c6b77b802a96368f9b2f433aa0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ABCVUUNFAIRFO3E7ET6KPMVN7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp thresholds for Ramsey properties of strictly balanced nearly bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fabian Schulenburg, Mathias Schacht","submitted_at":"2016-02-08T09:25:10Z","abstract_excerpt":"For a given graph $F$ we consider the family of (finite) graphs $G$ with the Ramsey property for $F$, that is the set of such graphs $G$ with the property that every two-colouring of the edges of $G$ yields a monochromatic copy of $F$. For $F$ being a triangle Friedgut, R\\\"odl, Ruci\\'nski, and Tetali (2004) established the sharp threshold for the Ramsey property in random graphs. We obtained a simpler proof of this result which extends to a more general class of graphs $F$ including all cycles.\n  The proof is based on Friedgut's criteria (1999) for sharp thresholds, and on the recently develop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02501","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":"2026-05-18T00:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CPig1IPvpz6kRyYnw5X5JvSZsX2a0tAuvmlWjFYz4vrRCL7hjaeNOsOaVo+NLgvmSK3854/7SruX9RgufmYDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:47:43.262523Z"},"content_sha256":"84089ad405ddec6a613b192ee68049b575ce9664fb7474faec29ef729c0aea5f","schema_version":"1.0","event_id":"sha256:84089ad405ddec6a613b192ee68049b575ce9664fb7474faec29ef729c0aea5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q/bundle.json","state_url":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q/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":"2026-05-27T04:47:43Z","links":{"resolver":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q","bundle":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q/bundle.json","state":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ABCVUUNFAIRFO3E7ET6KPMVN7Q","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":"7948371eb4419729e14d0dfe7cafdaa69e972f63223a427770bd54cc6f1103bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-08T09:25:10Z","title_canon_sha256":"5be34a914d7fff7977ffcc2e07f0315fa9a6db733b88162aa8ca2fedc1998364"},"schema_version":"1.0","source":{"id":"1602.02501","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02501","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02501v2","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02501","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"ABCVUUNFAIRF","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"ABCVUUNFAIRFO3E7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"ABCVUUNF","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:84089ad405ddec6a613b192ee68049b575ce9664fb7474faec29ef729c0aea5f","target":"graph","created_at":"2026-05-18T00:23:09Z","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":"For a given graph $F$ we consider the family of (finite) graphs $G$ with the Ramsey property for $F$, that is the set of such graphs $G$ with the property that every two-colouring of the edges of $G$ yields a monochromatic copy of $F$. For $F$ being a triangle Friedgut, R\\\"odl, Ruci\\'nski, and Tetali (2004) established the sharp threshold for the Ramsey property in random graphs. We obtained a simpler proof of this result which extends to a more general class of graphs $F$ including all cycles.\n  The proof is based on Friedgut's criteria (1999) for sharp thresholds, and on the recently develop","authors_text":"Fabian Schulenburg, Mathias Schacht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-08T09:25:10Z","title":"Sharp thresholds for Ramsey properties of strictly balanced nearly bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02501","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:f08e851b4a2949db1e1dd9f148ee3cca21097c6b77b802a96368f9b2f433aa0f","target":"record","created_at":"2026-05-18T00:23:09Z","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":"7948371eb4419729e14d0dfe7cafdaa69e972f63223a427770bd54cc6f1103bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-08T09:25:10Z","title_canon_sha256":"5be34a914d7fff7977ffcc2e07f0315fa9a6db733b88162aa8ca2fedc1998364"},"schema_version":"1.0","source":{"id":"1602.02501","kind":"arxiv","version":2}},"canonical_sha256":"00455a51a50222576c9f24fca7b2adfc03c6a1008cc0cc40686e73316987e8e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00455a51a50222576c9f24fca7b2adfc03c6a1008cc0cc40686e73316987e8e5","first_computed_at":"2026-05-18T00:23:09.578232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:09.578232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TMXTnT6p1Ww9DqNfsAnAOFfP4wtRwZDEEJBG060hViuFf63IDtanRBCAbKGu802h3CpNU/7jqc/K9+LJEECeCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:09.578814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02501","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f08e851b4a2949db1e1dd9f148ee3cca21097c6b77b802a96368f9b2f433aa0f","sha256:84089ad405ddec6a613b192ee68049b575ce9664fb7474faec29ef729c0aea5f"],"state_sha256":"dc46dbcfacafeae37ddf41b882d488fc4ae79abac2de95eaaab41839a399c047"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PuYgkGVBCkire2dQn9DWmlAjGsmsYmA65QzNZvMwq+RETFO/1Fc/83uHCXkdyJ/yaCgvoRXFkRFv3nTZv5w1Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:47:43.264909Z","bundle_sha256":"fe40798c9d755817fb1b9025a05acac4ce92a7425113e51d482d23fb1e8554ee"}}