{"id":"W2950454963","doi":"10.48550/arxiv.math/0108084","title":"Multiplicative Cellular Automata on Nilpotent Groups: Structure, Entropy, and Asymptotics","year":2001,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Cellular Automata and Applications","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Trent University","funders":"","keywords":"Multiplicative function; Mathematics; Endomorphism; Nilpotent; Discrete mathematics; Multiplicative group; Combinatorics; Group (periodic table); Pure mathematics; Physics; 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0001650766,0.0005536326,0.0004818383,0.0001768286,0.0002751785,0.0003478467,0.00192593,0.0003710355,0.00002998585],"category_scores_gemma":[0.00004491584,0.0005232879,0.0001651262,0.000307979,0.0001548665,0.0001705057,0.002646342,0.0008326095,0.0002092341],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001382297,"about_ca_system_score_gemma":0.0001021095,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006384062,"about_ca_topic_score_gemma":0.000006792309,"domain_scores_codex":[0.9969411,0.0001061001,0.0005016341,0.001488794,0.0004517804,0.0005105999],"domain_scores_gemma":[0.9964175,0.0001395152,0.0003829807,0.00267921,0.0001169981,0.0002638081],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00008847528,0.003696872,0.2135068,0.001191893,0.001604725,0.0007225125,0.008302203,0.00769164,0.1605969,0.4818494,0.009479387,0.1112692],"study_design_scores_gemma":[0.002509532,0.0003557536,0.3984376,0.0004805121,0.000284147,0.0001252555,0.0001284551,0.4343036,0.06700622,0.04910481,0.04394873,0.003315408],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.789589,0.0003835073,0.206178,0.001249251,0.0004971975,0.0008260065,0.00008969855,0.0006256026,0.0005617883],"genre_scores_gemma":[0.9862037,0.0002575863,0.01221158,0.0004007264,0.0002561625,0.00009956795,0.0002127002,0.00004766084,0.00031027],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4327446,"threshold_uncertainty_score":0.9997219,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02726465203664003,"score_gpt":0.2511042662291438,"score_spread":0.2238396141925038,"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."}}