{"id":"W2760877405","doi":"10.46298/dmtcs.2896","title":"Primitive orthogonal idempotents for R-trivial monoids","year":2011,"lang":"fr","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Advanced Algebra and Logic","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Fields Institute for Research in Mathematical Sciences; York University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Monoid; Mathematics; Equivalence (formal languages); Semigroup; Syntactic monoid; Combinatorics; Free monoid; Pure mathematics; Algebra over a field; Discrete mathematics","routes":{"ca_aff":true,"ca_fund":true,"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","sts"],"consensus_categories":[],"category_scores_codex":[0.002520881,0.0006947786,0.0007678687,0.0002669279,0.001007346,0.0007157869,0.004093181,0.000251627,0.0002708551],"category_scores_gemma":[0.0005369348,0.0005904502,0.0004366772,0.001366549,0.008487006,0.001851092,0.002167627,0.000506738,0.0002325787],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001254476,"about_ca_system_score_gemma":0.0004381946,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003995303,"about_ca_topic_score_gemma":0.000001217801,"domain_scores_codex":[0.9939662,0.000181573,0.001024167,0.001668253,0.001273378,0.001886409],"domain_scores_gemma":[0.9957165,0.0008544176,0.0004050376,0.001423628,0.0007590388,0.0008413534],"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":[0.00003246916,0.0004458396,0.0000288309,0.0001413677,0.00003493089,0.00004167897,0.006568123,0.00004250044,0.0001940943,0.967082,0.00007704409,0.02531111],"study_design_scores_gemma":[0.0003980875,0.0005796483,0.000266885,0.0001792353,0.00004893382,0.00008153886,0.0000705093,0.4207968,0.001438019,0.5754613,0.0001779409,0.0005010811],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.01063882,0.0002964347,0.9716911,0.001177568,0.003256724,0.001090794,0.00005438717,0.0002036775,0.01159052],"genre_scores_gemma":[0.4423209,0.00001883637,0.5565532,0.0004955887,0.0003475939,0.00004928128,0.000003526881,0.00003270671,0.0001783416],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.4316821,"threshold_uncertainty_score":0.9996547,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04291743966476476,"score_gpt":0.2834317684487794,"score_spread":0.2405143287840147,"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."}}