{"id":"W2078614146","doi":"10.1007/s00233-005-0506-0","title":"Levi’s Commutator Theorems for Cancellative Semigroups","year":2005,"lang":"en","type":"article","venue":"Semigroup Forum","topic":"semigroups and automata theory","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Manitoba","funders":"","keywords":"Commutator; Mathematics; Mathematical proof; Conjecture; Cancellative semigroup; Pure mathematics; Algebra over a field; Discrete mathematics; Semigroup","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":[0.0007129692,0.000384687,0.0004113451,0.0001410413,0.0004219472,0.0002339383,0.001691898,0.0001632571,0.00007088884],"category_scores_gemma":[0.00006908225,0.0003415706,0.000274184,0.0003969937,0.0001474147,0.000976983,0.0004178951,0.0002487122,0.0001691916],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001932926,"about_ca_system_score_gemma":0.00009278241,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006244648,"about_ca_topic_score_gemma":0.0001456108,"domain_scores_codex":[0.9974048,0.0000941173,0.0004669025,0.0007078857,0.0003505516,0.0009757698],"domain_scores_gemma":[0.9977696,0.0005197531,0.0002208352,0.001143705,0.0001215481,0.0002245818],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00004587075,0.0001633846,0.0005830331,0.00003811998,0.00008402709,0.000006855887,0.002933846,0.0002620994,0.005822636,0.7708812,0.06073239,0.1584466],"study_design_scores_gemma":[0.002271899,0.0004179931,0.0006706725,0.0001408177,0.00002949097,0.00009180056,0.001420843,0.1866752,0.03353619,0.1458538,0.6275625,0.001328769],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05635301,0.0027942,0.9060454,0.01342732,0.00129267,0.001337959,0.0001181466,0.001376135,0.01725513],"genre_scores_gemma":[0.9483429,0.00005393938,0.04440651,0.004482487,0.0004651245,0.0001625162,0.00003278671,0.00005596928,0.00199775],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8919899,"threshold_uncertainty_score":0.9999036,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008527195923852666,"score_gpt":0.2426187920620453,"score_spread":0.2340915961381926,"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."}}