{"id":"W4388418831","doi":"10.4153/s0008439523000863","title":"Eisenstein congruences among Euler systems","year":2023,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Division of Mathematical Sciences; Institució Catalana de Recerca i Estudis Avançats; Royal Society; National Science Foundation","keywords":"Mathematics; Congruence relation; Mathematical proof; Pure mathematics; Euler system; Conjecture; Euler's formula; Diagonal; Formalism (music); Cohomology; Algebra over a field; Mathematical analysis; Euler equations; Geometry; Literature","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0009670596,0.0003897692,0.0007062199,0.0004336053,0.0002843992,0.0002577219,0.0005481104,0.0002412402,0.009930533],"category_scores_gemma":[0.005161658,0.000347812,0.0001764952,0.0005882152,0.0004770708,0.0001173721,0.0001086867,0.0003251915,0.05385611],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002354541,"about_ca_system_score_gemma":0.0001590508,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00115601,"about_ca_topic_score_gemma":0.001571334,"domain_scores_codex":[0.9967952,0.000131441,0.0008253813,0.0004771766,0.0006146973,0.00115615],"domain_scores_gemma":[0.9953994,0.00250554,0.0001685426,0.0007415141,0.0001668369,0.001018233],"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":[0.000002506556,0.00003395468,0.00008258178,0.0007376426,0.00005431465,0.0002116837,0.0004217376,0.00002560967,0.00003153595,0.8155572,0.1827832,0.00005796094],"study_design_scores_gemma":[0.0002881195,0.00003304873,0.0001382177,0.0005433527,0.00006490847,0.00004476329,0.002043116,0.001833644,0.0001141376,0.9556496,0.03866505,0.0005820453],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6298135,0.0001762041,0.004999848,0.006627989,0.001404481,0.002417186,0.0001568478,0.002379731,0.3520242],"genre_scores_gemma":[0.8578178,0.00002311282,0.004705779,0.0002007662,0.0003340994,0.0003840932,0.00002439469,0.0002064818,0.1363035],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2280042,"threshold_uncertainty_score":0.9998974,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04441767107647664,"score_gpt":0.2865315512224068,"score_spread":0.2421138801459301,"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."}}