{"paper":{"title":"Ramsey multiplicity for ordered graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bing Wei, Mengya He, Qinghong Zhao, Yaping Mao","submitted_at":"2026-08-03T14:25:23Z","abstract_excerpt":"Let \\(\\cG_1,\\ldots,\\cG_k\\) be fixed vertex-ordered graphs, each containing at least one edge. The ordered Ramsey number \\(\\oR(\\cG_1,\\ldots,\\cG_k)\\) is the least integer \\(N\\) such that every \\(k\\)-edge-coloring of the ordered complete graph \\(\\cK_N\\) contains an order-preserving copy of \\(\\cG_i\\) in color \\(i\\) for some \\(i\\in[k]\\). For positive weights \\(\\blambda=(\\lambda_1,\\ldots,\\lambda_k)\\), let \\(\\oM_{\\blambda}(n;\\cG_1,\\ldots,\\cG_k)\\) denote the minimum weighted number of correctly colored, order-preserving copies of the target graphs over all \\(k\\)-edge-colorings of \\(\\cK_n\\). When \\(\\bl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02299","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.02299/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"}