{"id":"W2115768818","doi":"10.1007/s10474-015-0529-2","title":"Exact Kronecker constants of three element sets","year":2015,"lang":"en","type":"article","venue":"Acta Mathematica Academiae Scientiarum Hungaricae","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Kronecker delta; Element (criminal law); Kronecker product; Upper and lower bounds; Binary number; Constant (computer programming)","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":[0.003563348,0.0004444679,0.0008362817,0.0003357399,0.0003004391,0.00006774654,0.001262855,0.0003957228,0.0006889006],"category_scores_gemma":[0.00231773,0.0003400189,0.0002621016,0.0007267594,0.0007440599,0.0003878377,0.0007836753,0.0006785579,0.00007045251],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001105516,"about_ca_system_score_gemma":0.0001852865,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004495615,"about_ca_topic_score_gemma":0.000006681958,"domain_scores_codex":[0.9955327,0.0001865367,0.001246799,0.0006344683,0.00156396,0.0008355263],"domain_scores_gemma":[0.9964654,0.0007653931,0.0007647112,0.001224301,0.0003059462,0.0004742634],"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":[0.0001102658,0.0006725756,0.003315628,0.0006206373,0.0004826731,0.00001788297,0.008596864,0.000004937256,0.005565139,0.8956109,0.08212595,0.002876521],"study_design_scores_gemma":[0.00107277,0.0001322244,0.0006456061,0.0001979257,0.0002389247,0.00005450394,0.0008134285,0.0009699394,0.008215222,0.9820274,0.005127726,0.0005043353],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.929736,0.0003005292,0.006584769,0.001097515,0.001136642,0.001240229,0.00009607914,0.0002212461,0.05958698],"genre_scores_gemma":[0.9573536,0.00001704895,0.04161631,0.0001455317,0.00007367248,0.00002900372,0.000006894583,0.00006152643,0.0006964128],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08641647,"threshold_uncertainty_score":0.9999052,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07703521517883734,"score_gpt":0.3332724839513295,"score_spread":0.2562372687724921,"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."}}