{"id":"W4285802550","doi":"10.1007/s40993-022-00344-7","title":"Euclidean ideal classes in Galois number fields of odd prime degree","year":2022,"lang":"en","type":"article","venue":"Research in Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Ideal class group; Mathematics; Euclidean domain; Algebraic number field; Principal ideal; Ring of integers; Ideal (ethics); Degree (music); Combinatorics; Unit (ring theory); Abelian group; Cyclotomic field; Rank (graph theory); Galois group; Euclidean geometry; Order (exchange); Field (mathematics); Discrete mathematics; Prime (order theory); Pure mathematics; Euclidean distance matrix; Euclidean space; 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":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.01450759,0.0002468848,0.0005560282,0.0005191792,0.000226519,0.00002978055,0.0009947729,0.0001916761,0.03521246],"category_scores_gemma":[0.002592139,0.0002525215,0.0001631945,0.002031019,0.0004130815,0.0001859977,0.001098397,0.002047754,0.0003393644],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003589553,"about_ca_system_score_gemma":0.0003087759,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003747529,"about_ca_topic_score_gemma":0.000179737,"domain_scores_codex":[0.9918979,0.00428915,0.0008361043,0.0005370617,0.001411781,0.001027981],"domain_scores_gemma":[0.9887853,0.009848245,0.000162587,0.0008980445,0.0001468913,0.0001589661],"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":[0.0009695514,0.001311921,0.06190744,0.0004034999,0.00008622736,0.0003655879,0.003976574,0.00001726158,0.0001905628,0.9071596,0.01618444,0.007427383],"study_design_scores_gemma":[0.0009822765,0.00009468895,0.0046835,0.0001343365,0.00000784195,0.00008178545,0.004926049,0.00003283088,0.001131255,0.9836528,0.004004604,0.0002679943],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8222344,0.000111728,0.0001326186,0.000288041,0.000155858,0.0005196709,0.00007246284,0.00005293293,0.1764323],"genre_scores_gemma":[0.9922398,0.00003676252,0.0008354162,0.00008402728,0.00009584893,0.0002439429,0.00002118047,0.00006407072,0.006378916],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1700534,"threshold_uncertainty_score":0.9999927,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1462633686875716,"score_gpt":0.4167773379788823,"score_spread":0.2705139692913107,"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."}}