{"id":"W2993590174","doi":"10.1098/rsta.2018.0442","title":"Selmer groups in Iwasawa theory and congruences","year":2019,"lang":"en","type":"article","venue":"Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Ramanujan's sum; Congruence relation; Iwasawa theory; Mathematics; Pure mathematics; Elliptic curve; Algebra over a field; Conjecture","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":[0.001122093,0.0006635073,0.0005286839,0.001966255,0.001390809,0.003164822,0.0006238195,0.0007424208,0.006629164],"category_scores_gemma":[0.003513302,0.0002863284,0.000591208,0.001149942,0.005569627,0.005808837,0.002244221,0.001680797,0.000803943],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001088948,"about_ca_system_score_gemma":0.000402726,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005664182,"about_ca_topic_score_gemma":0.0002819986,"domain_scores_codex":[0.9992111,0.0001882028,0.00003777957,0.0001126421,0.0002280506,0.000222164],"domain_scores_gemma":[0.9989725,0.0003992495,0.0001700235,0.0001455338,0.0001025931,0.0002101106],"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":[0.00001495461,0.000007786144,0.0001505277,0.000007075815,0.000001558987,0.00005607821,0.0002996057,0.0004248296,0.0005154943,0.9968101,0.0001403227,0.001571558],"study_design_scores_gemma":[0.00001362408,0.00002491222,0.0002757049,0.000008302733,0.000002243071,0.0000975592,0.0002086957,0.002147506,0.0005744737,0.9949479,0.001689532,0.000009504688],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7940992,0.001400297,0.05660443,0.001581564,0.0002129189,0.00004377413,0.0000604762,0.0002214331,0.1457759],"genre_scores_gemma":[0.9887547,0.0002774607,0.003231358,0.0000650444,0.0001438509,0.00002104341,0.00003400446,0.00003829055,0.007434336],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006629164,"threshold_uncertainty_score":0.0221768,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01599301065121644,"score_gpt":0.248810375844816,"score_spread":0.2328173651935995,"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."}}