{"id":"W2157945276","doi":"10.2178/jsl/1254748693","title":"The strength of the rainbow Ramsey Theorem","year":2009,"lang":"en","type":"article","venue":"Journal of Symbolic Logic","topic":"Computability, Logic, AI Algorithms","field":"Computer Science","cited_by":37,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Ramsey's theorem; Ramsey theory; Converse; Mathematics; Rainbow; Corollary; Combinatorics; Discrete mathematics; Carlson's theorem; Randomness; Constant (computer programming); Injective function; Brouwer fixed-point theorem; Danskin's theorem; Fixed-point theorem; Physics; Computer science; Statistics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.005329707,0.0004024029,0.00124999,0.001232833,0.002224968,0.003479758,0.001774254,0.001336856,0.008621606],"category_scores_gemma":[0.02063236,0.0008108589,0.0008819742,0.0005757202,0.006356212,0.01115594,0.006380169,0.003228669,0.0007152308],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001436217,"about_ca_system_score_gemma":0.0008618375,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009102594,"about_ca_topic_score_gemma":0.0007320878,"domain_scores_codex":[0.9949754,0.001396169,0.000286028,0.001384496,0.001370793,0.0005871656],"domain_scores_gemma":[0.9764749,0.01474615,0.001439,0.003910124,0.002017037,0.001412699],"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":[0.0001292689,0.00002772961,0.001427193,0.00010389,0.00003561697,0.0001025374,0.0002461542,0.002230183,0.002725052,0.985935,0.001289119,0.005748272],"study_design_scores_gemma":[0.00003171014,0.00007047216,0.0007857825,0.00003037075,0.00003428609,0.0002722057,0.0001609917,0.0163565,0.003408505,0.975015,0.003797568,0.00003662909],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5548233,0.001259242,0.3273539,0.007713381,0.0003946566,0.00008218701,0.0004372371,0.0008136472,0.1071224],"genre_scores_gemma":[0.9875485,0.000169725,0.008617736,0.0004691167,0.0001521314,0.0000425974,0.00007191442,0.00005567067,0.002872729],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008621606,"threshold_uncertainty_score":0.02884215,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01178406988355374,"score_gpt":0.2418620093778536,"score_spread":0.2300779394942999,"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."}}