{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:R6HBWQ4LCH5RJBIC3ME6F5QXL4","short_pith_number":"pith:R6HBWQ4L","schema_version":"1.0","canonical_sha256":"8f8e1b438b11fb148502db09e2f6175f18efc67120ff505a355b747694ffc29c","source":{"kind":"arxiv","id":"1810.11386","version":2},"attestation_state":"computed","paper":{"title":"On a Diagonal Conjecture for Classical Ramsey Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Meilian Liang, Stanis{\\l}aw Radziszowski, Xiaodong Xu","submitted_at":"2018-10-26T15:32:07Z","abstract_excerpt":"Let $R(k_1, \\cdots, k_r)$ denote the classical $r$-color Ramsey number for integers $k_i \\ge 2$. The Diagonal Conjecture (DC) for classical Ramsey numbers poses that if $k_1, \\cdots, k_r$ are integers no smaller than 3 and $k_{r-1} \\leq k_r$, then $R(k_1, \\cdots, k_{r-2}, k_{r-1}-1, k_r +1) \\leq R(k_1, \\cdots, k_r)$. We obtain some implications of this conjecture, present evidence for its validity, and discuss related problems.\n  Let $R_r(k)$ stand for the $r$-color Ramsey number $R(k, \\cdots, k)$. It is known that $\\lim_{r \\rightarrow \\infty} R_r(3)^{1/r}$ exists, either finite or infinite, t"},"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":"1810.11386","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-26T15:32:07Z","cross_cats_sorted":[],"title_canon_sha256":"fef528deadfbbd6ac2b4dfeda8f1de3d84275ca902e5508f328b7d709810d958","abstract_canon_sha256":"3c1eece7c02486a4ccd83a125e8d9e1fc099990a471535a347bf0109c878e263"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:48.803172Z","signature_b64":"KJxsIjGlSpwd5/Do9o3Eg74pVoQeFJ2JuLPDin/2QIdrYl8Vb2ekiMBowzdL7pMTRvCqsp4BryfNQTAOT5TUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f8e1b438b11fb148502db09e2f6175f18efc67120ff505a355b747694ffc29c","last_reissued_at":"2026-05-17T23:42:48.802733Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:48.802733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a Diagonal Conjecture for Classical Ramsey Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Meilian Liang, Stanis{\\l}aw Radziszowski, Xiaodong Xu","submitted_at":"2018-10-26T15:32:07Z","abstract_excerpt":"Let $R(k_1, \\cdots, k_r)$ denote the classical $r$-color Ramsey number for integers $k_i \\ge 2$. The Diagonal Conjecture (DC) for classical Ramsey numbers poses that if $k_1, \\cdots, k_r$ are integers no smaller than 3 and $k_{r-1} \\leq k_r$, then $R(k_1, \\cdots, k_{r-2}, k_{r-1}-1, k_r +1) \\leq R(k_1, \\cdots, k_r)$. We obtain some implications of this conjecture, present evidence for its validity, and discuss related problems.\n  Let $R_r(k)$ stand for the $r$-color Ramsey number $R(k, \\cdots, k)$. It is known that $\\lim_{r \\rightarrow \\infty} R_r(3)^{1/r}$ exists, either finite or infinite, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11386","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.11386","created_at":"2026-05-17T23:42:48.802800+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.11386v2","created_at":"2026-05-17T23:42:48.802800+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11386","created_at":"2026-05-17T23:42:48.802800+00:00"},{"alias_kind":"pith_short_12","alias_value":"R6HBWQ4LCH5R","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"R6HBWQ4LCH5RJBIC","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"R6HBWQ4L","created_at":"2026-05-18T12:32:50.500415+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/R6HBWQ4LCH5RJBIC3ME6F5QXL4","json":"https://pith.science/pith/R6HBWQ4LCH5RJBIC3ME6F5QXL4.json","graph_json":"https://pith.science/api/pith-number/R6HBWQ4LCH5RJBIC3ME6F5QXL4/graph.json","events_json":"https://pith.science/api/pith-number/R6HBWQ4LCH5RJBIC3ME6F5QXL4/events.json","paper":"https://pith.science/paper/R6HBWQ4L"},"agent_actions":{"view_html":"https://pith.science/pith/R6HBWQ4LCH5RJBIC3ME6F5QXL4","download_json":"https://pith.science/pith/R6HBWQ4LCH5RJBIC3ME6F5QXL4.json","view_paper":"https://pith.science/paper/R6HBWQ4L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.11386&json=true","fetch_graph":"https://pith.science/api/pith-number/R6HBWQ4LCH5RJBIC3ME6F5QXL4/graph.json","fetch_events":"https://pith.science/api/pith-number/R6HBWQ4LCH5RJBIC3ME6F5QXL4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R6HBWQ4LCH5RJBIC3ME6F5QXL4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R6HBWQ4LCH5RJBIC3ME6F5QXL4/action/storage_attestation","attest_author":"https://pith.science/pith/R6HBWQ4LCH5RJBIC3ME6F5QXL4/action/author_attestation","sign_citation":"https://pith.science/pith/R6HBWQ4LCH5RJBIC3ME6F5QXL4/action/citation_signature","submit_replication":"https://pith.science/pith/R6HBWQ4LCH5RJBIC3ME6F5QXL4/action/replication_record"}},"created_at":"2026-05-17T23:42:48.802800+00:00","updated_at":"2026-05-17T23:42:48.802800+00:00"}