{"id":"W2020448983","doi":"10.1007/bf03322855","title":"Finding Sum of Powers on Arithmetic Progressions with Application of Cauchy’s Equation","year":2002,"lang":"en","type":"article","venue":"Results in Mathematics","topic":"Artificial Intelligence in Games","field":"Computer Science","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Arithmetic; Mathematics; Sums of powers; Cauchy distribution; Algebra over a field; Pure mathematics; Discrete mathematics; Mathematical analysis","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":[0.001520971,0.001033097,0.001908785,0.002758598,0.001294439,0.002358492,0.001811276,0.001201951,0.006617214],"category_scores_gemma":[0.01061998,0.0007315738,0.001933268,0.001633045,0.002488764,0.006504411,0.002923967,0.003012988,0.00113294],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005767137,"about_ca_system_score_gemma":0.0008225886,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006821043,"about_ca_topic_score_gemma":0.0007328968,"domain_scores_codex":[0.9990409,0.000245803,0.00007893315,0.0002027924,0.000315913,0.0001155852],"domain_scores_gemma":[0.9973239,0.001778575,0.0001313469,0.0001947036,0.0003858023,0.0001856368],"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":[0.0003042996,0.0001087788,0.002731744,0.0004931729,0.0001047441,0.0006520427,0.0009365348,0.01311606,0.008622108,0.8618731,0.004016854,0.1070406],"study_design_scores_gemma":[0.00003013609,0.00006432503,0.0003631552,0.00003851407,0.00005942204,0.0003035993,0.0001175876,0.08714595,0.003564413,0.9055443,0.002734879,0.00003377307],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1582921,0.0008395318,0.8176154,0.0005741026,0.000351135,0.0001072834,0.0001130353,0.000247796,0.02185944],"genre_scores_gemma":[0.6684378,0.0009392902,0.3125046,0.0001839599,0.0004031458,0.0001202134,0.000380622,0.0003478647,0.01668259],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006617214,"threshold_uncertainty_score":0.02213681,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06706539319022989,"score_gpt":0.3160413100167893,"score_spread":0.2489759168265594,"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."}}