{"id":"W2953111785","doi":"10.48550/arxiv.0807.5028","title":"Counting Abelian Squares","year":2008,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Cellular Automata and Applications","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Abelian group; Mathematics; Permutation (music); String (physics); Square (algebra); Combinatorics; Discrete mathematics; Physics; Mathematical physics; Geometry","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0001397142,0.0002297711,0.0002302128,0.0001003011,0.000247146,0.0001642833,0.001704931,0.000177105,0.00002100688],"category_scores_gemma":[0.00002571662,0.0002350237,0.0001395142,0.0002507383,0.00006301357,0.0001597302,0.001571902,0.0004412523,0.0009174097],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004924365,"about_ca_system_score_gemma":0.0001608267,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001827879,"about_ca_topic_score_gemma":0.00001186086,"domain_scores_codex":[0.9983957,0.0000318147,0.0003015948,0.0006973758,0.0002621547,0.0003113409],"domain_scores_gemma":[0.9980284,0.00005399893,0.0001912563,0.001541935,0.00009065108,0.00009377521],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.000005588548,0.0008734434,0.7988256,0.0006605316,0.0003380383,0.0004109391,0.00668769,0.002720338,0.01638917,0.05050008,0.06022059,0.06236799],"study_design_scores_gemma":[0.0005383154,0.000046885,0.5900303,0.0003458677,0.00005724581,0.0001113862,0.00005516291,0.09831084,0.0109775,0.00752236,0.2900588,0.001945314],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8455341,0.0005720683,0.1447032,0.00157066,0.000651566,0.0002970315,0.00001152854,0.0007649747,0.005894908],"genre_scores_gemma":[0.9902919,0.0002319394,0.007989752,0.0003668393,0.0002344612,0.00008351861,0.00004582619,0.00002204099,0.0007337094],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2298382,"threshold_uncertainty_score":0.9998605,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04447420660654759,"score_gpt":0.2658426493198036,"score_spread":0.221368442713256,"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."}}