{"id":"W2090346727","doi":"10.1215/s0012-7094-07-13713-x","title":"Iwasawa theory and the Eisenstein ideal","year":2007,"lang":"en","type":"article","venue":"Duke Mathematical Journal","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"","keywords":"Mathematics; Iwasawa theory; Galois module; Pure mathematics; Modular form; Abelian group; Ideal (ethics); Galois cohomology; Prime (order theory); Algebra over a field; Galois group; Combinatorics","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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.01690981,0.0002290443,0.0004507684,0.000110841,0.0004252489,0.0001395545,0.000333233,0.0001282321,0.0009533496],"category_scores_gemma":[0.003899508,0.0001245588,0.000205275,0.0001893861,0.0006799915,0.0001228447,0.0001357554,0.0007154227,0.000152944],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003347639,"about_ca_system_score_gemma":0.00002906721,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":4.965185e-7,"about_ca_topic_score_gemma":8.053038e-7,"domain_scores_codex":[0.997525,0.0005325865,0.0007483223,0.0001725876,0.0005173923,0.0005040711],"domain_scores_gemma":[0.989538,0.009505753,0.0002560084,0.0003380706,0.00008685318,0.0002753846],"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":[0.0004260507,0.00008631836,0.00003044953,0.00006575564,0.00009903172,0.00008771475,0.001619262,1.469503e-7,0.00006561861,0.9925803,0.0009998183,0.003939512],"study_design_scores_gemma":[0.001693549,0.00003744681,0.0001090172,0.0000884883,0.0001098975,0.003600419,0.002248614,0.00004065328,0.0005291089,0.990543,0.0008332952,0.0001664843],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5712236,0.0005443044,0.3216287,0.001636742,0.0003083915,0.0003680323,0.000002116639,0.0001019115,0.1041862],"genre_scores_gemma":[0.9860662,0.00003113972,0.01046076,0.0006301214,0.0005317704,0.000004325992,3.44398e-7,0.000040447,0.002234863],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4148427,"threshold_uncertainty_score":0.9999599,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01892942816663608,"score_gpt":0.2936883079898664,"score_spread":0.2747588798232304,"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."}}