{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:FMYLFKEGONY3GEJFO2O6O5JEV4","short_pith_number":"pith:FMYLFKEG","schema_version":"1.0","canonical_sha256":"2b30b2a8867371b31125769de77524af2f116bd1d56898a0d4764f3d070840b5","source":{"kind":"arxiv","id":"2212.07234","version":3},"attestation_state":"computed","paper":{"title":"Two Ramsey-Tur\\'{a}n numbers involving triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Qizhong Lin, Xinyu Hu","submitted_at":"2022-12-14T14:16:45Z","abstract_excerpt":"Given integers $p, q\\ge2$, we say that a graph $G$ is $(K_p,K_q)$-free if there exists a red/blue edge coloring of $G$ such that it contains neither a red $K_p$ nor a blue $K_q$. Fix a function $f( n )$, the Ramsey-Tur\\'{a}n number $RT( {n,p,q,f( n ))} $ is the maximum number of edges in an $n$-vertex $(K_p,K_q)$-free graph with independence number at most $f( n )$. For any $\\delta>0$, let $\\rho (p, q,\\delta ) = \\mathop {\\lim }\\limits_{n \\to \\infty } \\frac{RT(n,p, q,\\delta n)}{n^2}$. We always call $\\rho (p, q):= \\mathop {\\lim }\\limits_{\\delta \\to 0}\\rho (p, q,\\delta )$ the Ramsey-Tur\\'{a}n de"},"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":"2212.07234","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-12-14T14:16:45Z","cross_cats_sorted":[],"title_canon_sha256":"0561305e6217412e6b823e32df8fbd83fe2953ee704a891ecb0b1bf7c105071e","abstract_canon_sha256":"9cb990cac48d24ad7e17557d2da9aa0172bf6155e4622923dc9de8d4bd7ba681"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:20:39.243583Z","signature_b64":"cRpq5JxIOQvd3BWga6xtSJPBg+2yfbnKLbXV4DAk2QCJxBpEeJMzOh7crtsp8Aap0LQQW/NZW6uxZAfraXnLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b30b2a8867371b31125769de77524af2f116bd1d56898a0d4764f3d070840b5","last_reissued_at":"2026-07-05T06:20:39.243177Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:20:39.243177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two Ramsey-Tur\\'{a}n numbers involving triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Qizhong Lin, Xinyu Hu","submitted_at":"2022-12-14T14:16:45Z","abstract_excerpt":"Given integers $p, q\\ge2$, we say that a graph $G$ is $(K_p,K_q)$-free if there exists a red/blue edge coloring of $G$ such that it contains neither a red $K_p$ nor a blue $K_q$. Fix a function $f( n )$, the Ramsey-Tur\\'{a}n number $RT( {n,p,q,f( n ))} $ is the maximum number of edges in an $n$-vertex $(K_p,K_q)$-free graph with independence number at most $f( n )$. For any $\\delta>0$, let $\\rho (p, q,\\delta ) = \\mathop {\\lim }\\limits_{n \\to \\infty } \\frac{RT(n,p, q,\\delta n)}{n^2}$. We always call $\\rho (p, q):= \\mathop {\\lim }\\limits_{\\delta \\to 0}\\rho (p, q,\\delta )$ the Ramsey-Tur\\'{a}n de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.07234","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.07234/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2212.07234","created_at":"2026-07-05T06:20:39.243235+00:00"},{"alias_kind":"arxiv_version","alias_value":"2212.07234v3","created_at":"2026-07-05T06:20:39.243235+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.07234","created_at":"2026-07-05T06:20:39.243235+00:00"},{"alias_kind":"pith_short_12","alias_value":"FMYLFKEGONY3","created_at":"2026-07-05T06:20:39.243235+00:00"},{"alias_kind":"pith_short_16","alias_value":"FMYLFKEGONY3GEJF","created_at":"2026-07-05T06:20:39.243235+00:00"},{"alias_kind":"pith_short_8","alias_value":"FMYLFKEG","created_at":"2026-07-05T06:20:39.243235+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/FMYLFKEGONY3GEJFO2O6O5JEV4","json":"https://pith.science/pith/FMYLFKEGONY3GEJFO2O6O5JEV4.json","graph_json":"https://pith.science/api/pith-number/FMYLFKEGONY3GEJFO2O6O5JEV4/graph.json","events_json":"https://pith.science/api/pith-number/FMYLFKEGONY3GEJFO2O6O5JEV4/events.json","paper":"https://pith.science/paper/FMYLFKEG"},"agent_actions":{"view_html":"https://pith.science/pith/FMYLFKEGONY3GEJFO2O6O5JEV4","download_json":"https://pith.science/pith/FMYLFKEGONY3GEJFO2O6O5JEV4.json","view_paper":"https://pith.science/paper/FMYLFKEG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2212.07234&json=true","fetch_graph":"https://pith.science/api/pith-number/FMYLFKEGONY3GEJFO2O6O5JEV4/graph.json","fetch_events":"https://pith.science/api/pith-number/FMYLFKEGONY3GEJFO2O6O5JEV4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FMYLFKEGONY3GEJFO2O6O5JEV4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FMYLFKEGONY3GEJFO2O6O5JEV4/action/storage_attestation","attest_author":"https://pith.science/pith/FMYLFKEGONY3GEJFO2O6O5JEV4/action/author_attestation","sign_citation":"https://pith.science/pith/FMYLFKEGONY3GEJFO2O6O5JEV4/action/citation_signature","submit_replication":"https://pith.science/pith/FMYLFKEGONY3GEJFO2O6O5JEV4/action/replication_record"}},"created_at":"2026-07-05T06:20:39.243235+00:00","updated_at":"2026-07-05T06:20:39.243235+00:00"}