{"id":"W4398212496","doi":"10.4153/s0008439524000365","title":"Counting elements of the congruence subgroup","year":2024,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Congruence (geometry); Congruence subgroup; Pure mathematics; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001481841,0.0001525083,0.0002568496,0.0001107145,0.0001173799,0.00009011327,0.0005785467,0.00008477104,0.02294354],"category_scores_gemma":[0.00214925,0.0001045449,0.0001431336,0.000345206,0.0003018661,0.00002915713,0.00009712666,0.0003077673,0.004447763],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002076536,"about_ca_system_score_gemma":0.0003936349,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007204681,"about_ca_topic_score_gemma":0.001164024,"domain_scores_codex":[0.9981641,0.0001112954,0.0004859762,0.000237201,0.000494491,0.0005069208],"domain_scores_gemma":[0.99786,0.001165253,0.00006217139,0.000525767,0.0001009498,0.0002858355],"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":[0.000002088192,0.00002220149,0.0002544031,0.0006675877,0.00006227567,0.00003786511,0.0002966803,3.295331e-7,0.0001279545,0.9520593,0.04606898,0.0004003637],"study_design_scores_gemma":[0.0001314626,0.0000178844,0.00007271514,0.0008114862,0.00007444806,0.0000506921,0.0003576966,0.001832246,0.0006239736,0.9147424,0.08108324,0.0002017201],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.628597,0.0004488667,0.005994925,0.02226389,0.000579819,0.001774905,0.0001512889,0.000240853,0.3399484],"genre_scores_gemma":[0.9810117,0.000002748791,0.001804432,0.0002368792,0.00006507594,0.00002413723,0.000001349293,0.00004439339,0.01680924],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3524147,"threshold_uncertainty_score":0.9963274,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03315295516118162,"score_gpt":0.3096871132963898,"score_spread":0.2765341581352082,"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."}}