{"id":"W2101456938","doi":"10.5802/aif.2264","title":"Class Invariants for Quartic CM Fields","year":2007,"lang":"en","type":"article","venue":"Annales de l’institut Fourier","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":45,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"Natural Sciences and Engineering Research Council of Canada; McGill University; Microsoft Research","keywords":"Mathematics; Quartic function; Pure mathematics; Class (philosophy); Algebraic number; Field (mathematics); Algebraic number field; Class number; Class field theory; Algebraic number theory; Algebra over a field; Discrete mathematics; Combinatorics; Mathematical analysis; Quadratic equation; Computer science; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009040241,0.0005843477,0.0004579644,0.003316756,0.001265606,0.002473805,0.0008658334,0.0006364617,0.008422283],"category_scores_gemma":[0.00173073,0.0002390759,0.000800914,0.001161958,0.002984162,0.003855078,0.001723886,0.002301391,0.001195793],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002396587,"about_ca_system_score_gemma":0.0004614248,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006858041,"about_ca_topic_score_gemma":0.0005179496,"domain_scores_codex":[0.9993097,0.00007395521,0.00003360406,0.0001444398,0.000191098,0.0002472487],"domain_scores_gemma":[0.9991426,0.0001920408,0.0002104137,0.0001329899,0.0001177553,0.0002040937],"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":[0.00002658289,0.00002700238,0.0003926822,0.00002175612,0.000002943613,0.00005141285,0.0002294165,0.000633417,0.001486429,0.9883358,0.0008181355,0.00797445],"study_design_scores_gemma":[0.00003547195,0.00007490078,0.001438405,0.00002769364,0.000009869876,0.0001727887,0.0002483665,0.008850613,0.004563896,0.9732352,0.01130149,0.00004134131],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6969006,0.0005984438,0.1642243,0.00100464,0.0005389163,0.0001339552,0.0003469898,0.001064596,0.1351876],"genre_scores_gemma":[0.9724328,0.0002018289,0.01382481,0.0001542356,0.0002747866,0.0000571208,0.000226868,0.0001818886,0.01264573],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008422283,"threshold_uncertainty_score":0.02817535,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04653695577528346,"score_gpt":0.3176830840137754,"score_spread":0.271146128238492,"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."}}