{"id":"W4205374221","doi":"10.1016/j.disc.2004.02.004","title":"Ramsey numbers in complete balanced multipartite graphs. Part I: Set numbers","year":2004,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Multipartite; Mathematics; Combinatorics; Ramsey's theorem; Discrete mathematics; Diagonal; Monochromatic color; Graph","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0006687716,0.0004901642,0.0007728035,0.0001879941,0.0002569662,0.00008347657,0.0005716562,0.0002214949,0.0002043869],"category_scores_gemma":[0.0004618257,0.0004105786,0.0003099054,0.0005051068,0.0003249079,0.0002037437,0.0002069135,0.0004444683,0.00006813709],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001132174,"about_ca_system_score_gemma":0.00004163609,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006053522,"about_ca_topic_score_gemma":0.0002060139,"domain_scores_codex":[0.9971357,0.0001036354,0.0009716433,0.0004766597,0.0005553144,0.0007570339],"domain_scores_gemma":[0.9979268,0.0004625085,0.0003613612,0.0009740582,0.00007025429,0.0002050041],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00004047056,0.0001875209,0.001789656,0.0004719372,0.0001236233,0.00005376382,0.01516827,0.0002531419,0.0002369726,0.9802916,0.001266578,0.0001164809],"study_design_scores_gemma":[0.002018363,0.0000473602,0.000391525,0.0004043656,0.00006876096,0.00004192241,0.002119458,0.0006153757,0.0004513412,0.9917195,0.001527968,0.0005940337],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9726621,0.00007847188,0.004432024,0.0003046333,0.0006161535,0.0009444266,0.0001805215,0.0003209987,0.02046065],"genre_scores_gemma":[0.9456642,0.00004692322,0.05337804,0.0002947815,0.00008846862,0.00007550847,0.00004953881,0.0001099004,0.0002926134],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04894602,"threshold_uncertainty_score":0.9998346,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0457554487334892,"score_gpt":0.3082959021620013,"score_spread":0.2625404534285121,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}