{"id":"W2047647860","doi":"10.1155/ijmms/2006/17641","title":"Explicit decomposition of a rational prime in a cubic field","year":2006,"lang":"en","type":"article","venue":"International Journal of Mathematics and Mathematical Sciences","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia, Okanagan Campus; University of British Columbia; Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Prime (order theory); Decomposition; Field (mathematics); Cubic form; Pure mathematics; Arithmetic; Discrete mathematics; Combinatorics; Chemistry","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":[0.0007966835,0.0001037482,0.0003249279,0.0002265265,0.00003837049,0.00005650135,0.0002799851,0.00005261368,0.00009377411],"category_scores_gemma":[0.0005846446,0.00007314846,0.0000927263,0.0001494695,0.0001005454,0.000221684,0.00005515951,0.00009133358,0.000001947027],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003411667,"about_ca_system_score_gemma":0.00004352435,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001882835,"about_ca_topic_score_gemma":0.00002059832,"domain_scores_codex":[0.9980503,0.00002915674,0.001013467,0.0001041391,0.0006795184,0.0001234141],"domain_scores_gemma":[0.9977745,0.001278486,0.0006063797,0.00006990684,0.0002259968,0.00004468314],"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":[0.00001370902,0.0006165837,0.000325793,0.00007452401,0.0000209281,0.000006324398,0.0002431271,0.00007754926,0.005601923,0.9919533,0.00004675578,0.001019486],"study_design_scores_gemma":[0.0004450526,0.0001326754,0.0002238768,0.0004069428,0.00001673747,0.00010828,0.0002659385,0.01811934,0.00290159,0.9772785,0.00001809272,0.00008300611],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6026596,0.00005504776,0.3946773,0.0004613102,0.00009416504,0.0001078895,0.000003308867,0.000005407413,0.001935943],"genre_scores_gemma":[0.8601377,0.00001151411,0.1397084,0.00001551074,0.0000787571,0.000004367265,7.627269e-7,0.000005143538,0.00003786543],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2574781,"threshold_uncertainty_score":0.2982908,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02866110772794359,"score_gpt":0.3618213347576977,"score_spread":0.3331602270297541,"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."}}