{"id":"W2952935212","doi":"10.48550/arxiv.0805.0775","title":"Square-free discriminants of Frobenius rings","year":2008,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"","keywords":"Mathematics; Elliptic curve; Endomorphism; Modulo; Ring of integers; Prime (order theory); Complex multiplication; Rational number; Combinatorics; Algebraic number field; Discriminant; Discrete mathematics; Pure mathematics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009598772,0.0005178099,0.000600016,0.002061875,0.001199454,0.002011542,0.0005831565,0.0004326775,0.005081814],"category_scores_gemma":[0.004186667,0.0003615952,0.0003596309,0.0008264069,0.003254169,0.003664481,0.001695723,0.001151557,0.0006221952],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001306303,"about_ca_system_score_gemma":0.0004298257,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009816563,"about_ca_topic_score_gemma":0.0006874921,"domain_scores_codex":[0.9993367,0.00008516727,0.00004084796,0.0001594304,0.0002114002,0.0001663952],"domain_scores_gemma":[0.9980898,0.0008138494,0.0003171783,0.000132137,0.0001459352,0.0005010047],"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":[0.0002875138,0.00006073074,0.007885523,0.0001455609,0.00001423958,0.0003626045,0.0008455011,0.003317562,0.0062961,0.9600614,0.001344943,0.01937837],"study_design_scores_gemma":[0.0001162997,0.0001283711,0.01267435,0.00006308917,0.00003312558,0.001128329,0.0004788302,0.01660741,0.007102325,0.9512155,0.01038563,0.00006669697],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9570333,0.0009939662,0.01282285,0.0007015633,0.00006037003,0.00001994962,0.0002148994,0.0001228193,0.02803016],"genre_scores_gemma":[0.9923316,0.0003683572,0.002152043,0.00002980531,0.0001595582,0.00001637088,0.000160782,0.00002194489,0.004759504],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005081814,"threshold_uncertainty_score":0.01700032,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08574333099040225,"score_gpt":0.3066068210107636,"score_spread":0.2208634900203614,"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."}}