{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JGQCOCKHZVOCP2PQSRLRQAYUDV","short_pith_number":"pith:JGQCOCKH","schema_version":"1.0","canonical_sha256":"49a0270947cd5c27e9f094571803141d5bcfa5c4d46d08d19987d060f19a50d4","source":{"kind":"arxiv","id":"1602.04059","version":1},"attestation_state":"computed","paper":{"title":"Upper bounds on probability thresholds for asymmetric Ramsey properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mathias Schacht, Reto Sp\\\"ohel, Yoshiharu Kohayakawa","submitted_at":"2016-02-12T14:04:47Z","abstract_excerpt":"Given two graphs $G$ and $H$, we investigate for which functions $p=p(n)$ the random graph $G_{n,p}$ (the binomial random graph on $n$ vertices with edge probability $p$) satisfies with probability $1-o(1)$ that every red-blue-coloring of its edges contains a red copy of $G$ or a blue copy of $H$. We prove a general upper bound on the threshold for this property under the assumption that the denser of the two graphs satisfies a certain balancedness condition. Our result partially confirms a conjecture by the first author and Kreuter, and together with earlier lower bound results establishes th"},"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":"1602.04059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-12T14:04:47Z","cross_cats_sorted":[],"title_canon_sha256":"4a7f56d6420c90a4305b03082525fb1aeff89dcf3a6b2f7d82d561435ebee5d8","abstract_canon_sha256":"eaf283a4bfff78b63fa47bbbed357140bbd5b20f9937e5766659acd2dba3e4f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:54.726643Z","signature_b64":"MsJdwH9xR1m7A3nC/SZVWQECwl5i3R2J5LfOIfoyfKLfbD3s7myRW0q1QsZ4Ntqd1iXtZxt9GYhhoa2yZ7a4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49a0270947cd5c27e9f094571803141d5bcfa5c4d46d08d19987d060f19a50d4","last_reissued_at":"2026-05-18T01:20:54.726073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:54.726073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Upper bounds on probability thresholds for asymmetric Ramsey properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mathias Schacht, Reto Sp\\\"ohel, Yoshiharu Kohayakawa","submitted_at":"2016-02-12T14:04:47Z","abstract_excerpt":"Given two graphs $G$ and $H$, we investigate for which functions $p=p(n)$ the random graph $G_{n,p}$ (the binomial random graph on $n$ vertices with edge probability $p$) satisfies with probability $1-o(1)$ that every red-blue-coloring of its edges contains a red copy of $G$ or a blue copy of $H$. We prove a general upper bound on the threshold for this property under the assumption that the denser of the two graphs satisfies a certain balancedness condition. Our result partially confirms a conjecture by the first author and Kreuter, and together with earlier lower bound results establishes th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04059","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":"1602.04059","created_at":"2026-05-18T01:20:54.726155+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.04059v1","created_at":"2026-05-18T01:20:54.726155+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04059","created_at":"2026-05-18T01:20:54.726155+00:00"},{"alias_kind":"pith_short_12","alias_value":"JGQCOCKHZVOC","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JGQCOCKHZVOCP2PQ","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JGQCOCKH","created_at":"2026-05-18T12:30:25.849896+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/JGQCOCKHZVOCP2PQSRLRQAYUDV","json":"https://pith.science/pith/JGQCOCKHZVOCP2PQSRLRQAYUDV.json","graph_json":"https://pith.science/api/pith-number/JGQCOCKHZVOCP2PQSRLRQAYUDV/graph.json","events_json":"https://pith.science/api/pith-number/JGQCOCKHZVOCP2PQSRLRQAYUDV/events.json","paper":"https://pith.science/paper/JGQCOCKH"},"agent_actions":{"view_html":"https://pith.science/pith/JGQCOCKHZVOCP2PQSRLRQAYUDV","download_json":"https://pith.science/pith/JGQCOCKHZVOCP2PQSRLRQAYUDV.json","view_paper":"https://pith.science/paper/JGQCOCKH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.04059&json=true","fetch_graph":"https://pith.science/api/pith-number/JGQCOCKHZVOCP2PQSRLRQAYUDV/graph.json","fetch_events":"https://pith.science/api/pith-number/JGQCOCKHZVOCP2PQSRLRQAYUDV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JGQCOCKHZVOCP2PQSRLRQAYUDV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JGQCOCKHZVOCP2PQSRLRQAYUDV/action/storage_attestation","attest_author":"https://pith.science/pith/JGQCOCKHZVOCP2PQSRLRQAYUDV/action/author_attestation","sign_citation":"https://pith.science/pith/JGQCOCKHZVOCP2PQSRLRQAYUDV/action/citation_signature","submit_replication":"https://pith.science/pith/JGQCOCKHZVOCP2PQSRLRQAYUDV/action/replication_record"}},"created_at":"2026-05-18T01:20:54.726155+00:00","updated_at":"2026-05-18T01:20:54.726155+00:00"}