{"id":"W2031397968","doi":"10.1016/j.jalgebra.2002.08.001","title":"Idempotent lattices, Renner monoids and cross section lattices of the special orthogonal algebraic monoids","year":2003,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":17,"is_retracted":false,"has_abstract":false,"ca_institutions":"Western University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Monoid; Mathematics; Idempotence; Section (typography); Lattice (music); Algebraic number; Combinatorics; Pure mathematics; Mathematical analysis; Physics","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":[],"consensus_categories":[],"category_scores_codex":[0.001019612,0.0002407305,0.000492749,0.0001888308,0.0001783995,0.00007140172,0.0002877247,0.0001762123,0.0003117627],"category_scores_gemma":[0.0009348512,0.000159795,0.0002866515,0.0004773591,0.0002128599,0.0005155175,0.00008015345,0.0005607764,0.000005387633],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005751651,"about_ca_system_score_gemma":0.0001091875,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000148861,"about_ca_topic_score_gemma":0.00002004217,"domain_scores_codex":[0.9977266,0.0001949119,0.0009772455,0.0002033229,0.0005948635,0.0003031028],"domain_scores_gemma":[0.9975726,0.0004511356,0.001203708,0.0003070008,0.0003165486,0.0001490225],"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":[0.0007209173,0.001297412,0.2989713,0.0006976829,0.001183429,0.0001376356,0.003280293,0.0006552772,0.009115638,0.6608958,0.008325648,0.01471895],"study_design_scores_gemma":[0.002076757,0.0004195301,0.08481111,0.0002278382,0.0003026396,0.0007803008,0.0006159139,0.00006069438,0.01036672,0.8926846,0.007267684,0.0003861715],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9938131,0.0008247266,0.001531812,0.0003018893,0.001343574,0.0001444633,0.00000603861,0.00001112686,0.00202327],"genre_scores_gemma":[0.9934719,0.0001911619,0.003692747,0.0001160946,0.001624656,0.000001656397,4.643243e-7,0.00003577476,0.0008655155],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2317888,"threshold_uncertainty_score":0.651625,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02285408601672684,"score_gpt":0.2970602622270484,"score_spread":0.2742061762103216,"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."}}