{"id":"W2089117749","doi":"10.1142/s1005386706000319","title":"Symmetric Units in Alternative Loop Rings","year":2006,"lang":"en","type":"article","venue":"Algebra Colloquium","topic":"Mathematics and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Memorial University of Newfoundland","funders":"","keywords":"Loop (graph theory); Mathematics; Ring (chemistry); Associative property; Combinatorics; Multiplication (music); For loop; Pure mathematics; Discrete mathematics","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":[],"consensus_categories":[],"category_scores_codex":[0.0002781322,0.000154987,0.000237002,0.0002754636,0.00007125072,0.00004699716,0.0002620241,0.0000671045,0.0001143827],"category_scores_gemma":[0.0002309008,0.0001485658,0.00004391873,0.00158404,0.0000395726,0.00007998396,0.00008167565,0.0001346506,0.0001171663],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007223608,"about_ca_system_score_gemma":0.00004845729,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002520033,"about_ca_topic_score_gemma":0.00020424,"domain_scores_codex":[0.9988279,0.00003126469,0.0003888542,0.000230322,0.0002440983,0.0002775264],"domain_scores_gemma":[0.9988975,0.0004334489,0.0001517696,0.0003456092,0.0001206593,0.00005101775],"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":[0.00000316811,0.0002629532,0.0007726778,0.00005602709,0.00001353854,0.00000903764,0.0001767651,0.00001052734,0.0003445793,0.9688745,0.02922598,0.0002502704],"study_design_scores_gemma":[0.0008797917,0.00003730177,0.001635047,0.00007692149,0.00003392855,0.00001051033,0.000167651,0.002894395,0.005068409,0.9773192,0.0115145,0.0003622773],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9128922,0.00007758781,0.0025508,0.0004375509,0.00009409433,0.0005473132,0.00001691186,0.0001064513,0.08327713],"genre_scores_gemma":[0.9854215,0.00001018546,0.00648138,0.00008333905,0.0001098665,0.000141115,0.000009503206,0.00003442153,0.007708709],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07556842,"threshold_uncertainty_score":0.6058339,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03831052228915081,"score_gpt":0.2899012409193802,"score_spread":0.2515907186302294,"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."}}