{"id":"W1605818467","doi":"10.1023/a:1021074813291","title":"Multiplicative Cellular Automata on Nilpotent Groups: Structure, Entropy, and Asymptotics","year":2003,"lang":"en","type":"article","venue":"Journal of Statistical Physics","topic":"Cellular Automata and Applications","field":"Computer Science","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"Trent University","funders":"","keywords":"Multiplicative function; Combinatorics; Group (periodic table); Physics; Compact group; Mathematics; Haar measure; Endomorphism; Discrete mathematics; Pure mathematics; Quantum mechanics; Mathematical analysis; Lie group","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":[0.001061345,0.0004029006,0.000982232,0.002124381,0.001065307,0.002878103,0.001047995,0.001262223,0.002501114],"category_scores_gemma":[0.009756127,0.0003918512,0.0005308638,0.0007694422,0.002947509,0.003408686,0.001457883,0.001283188,0.0002260808],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00115216,"about_ca_system_score_gemma":0.0006686306,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007204823,"about_ca_topic_score_gemma":0.0008364401,"domain_scores_codex":[0.9993966,0.0001806652,0.00003641525,0.0001161999,0.0001787836,0.00009123521],"domain_scores_gemma":[0.9920459,0.005207686,0.0006861055,0.0007305266,0.0008581146,0.0004716668],"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":[0.00004028565,0.00002695175,0.001015804,0.00003344802,0.00001412606,0.00004685542,0.0001835355,0.01477177,0.001529673,0.9784715,0.0003701325,0.003495883],"study_design_scores_gemma":[0.00001122099,0.00002335454,0.0005009884,0.00001333868,0.00000956914,0.00006869396,0.00004924994,0.1392997,0.0007087165,0.8589008,0.0003953065,0.00001909519],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8256197,0.001397651,0.1573043,0.00133666,0.0001643636,0.00003910524,0.0002174417,0.0002484921,0.01367221],"genre_scores_gemma":[0.9914128,0.0003054604,0.005889831,0.00007722749,0.0001806264,0.00003768221,0.0001021259,0.00002753825,0.001966721],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002878103,"threshold_uncertainty_score":0.008367002,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0104065725661644,"score_gpt":0.2404679096402662,"score_spread":0.2300613370741018,"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."}}