{"id":"W1993844643","doi":"10.1090/s0025-5718-03-01559-x","title":"The arithmetic of certain cubic function fields","year":2003,"lang":"en","type":"article","venue":"Mathematics of Computation","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Ideal (ethics); Jacobian matrix and determinant; Ideal class group; Arithmetic; Arithmetic function; Algebraic number theory; Cryptography; Function field; Field (mathematics); Class (philosophy); Class field theory; Algebraic number; Function (biology); Discrete mathematics; Pure mathematics; Algebra over a field; Algorithm; Applied mathematics; Mathematical analysis; Computer science; Law","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":[0.000569488,0.00005704549,0.0001006268,0.00006671908,0.00007806336,0.00003003451,0.000218972,0.00002852924,0.000003253516],"category_scores_gemma":[0.00009636801,0.00004243068,0.00006384923,0.0002973907,0.00004492131,0.00008161087,0.00002593774,0.00004658799,0.000003004282],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000004339493,"about_ca_system_score_gemma":0.00001817297,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001210756,"about_ca_topic_score_gemma":0.000001144678,"domain_scores_codex":[0.9993429,0.00007525579,0.0002520162,0.00008007602,0.0001697054,0.00008008588],"domain_scores_gemma":[0.998946,0.0005278371,0.0001852652,0.0002251452,0.00009980088,0.00001601881],"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":[0.000002688066,0.00006016423,0.00002203808,0.00004954422,0.00001492156,1.181116e-7,0.0006907338,0.001679922,0.0002670894,0.97866,0.00005375618,0.01849895],"study_design_scores_gemma":[0.0001206069,0.0001143813,0.0001589212,0.0000267418,0.00001101583,0.000002867459,0.0001282189,0.08941771,0.003872332,0.9059314,0.0001653475,0.00005046215],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06051458,0.00007414649,0.9364806,0.00008048265,0.0001491731,0.00008122627,1.885382e-7,0.00002547569,0.002594144],"genre_scores_gemma":[0.9437572,0.000004190311,0.05618289,0.0000139739,0.000004941119,0.000003337092,3.625528e-7,0.000002925164,0.00003012792],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8832427,"threshold_uncertainty_score":0.1730273,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01313094937652154,"score_gpt":0.2334954541648223,"score_spread":0.2203645047883007,"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."}}