{"id":"W2093686221","doi":"10.4153/cjm-2000-036-0","title":"W-Groups under Quadratic Extensions of Fields","year":2000,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Galois group; Pythagorean theorem; Field (mathematics); Connection (principal bundle); Group (periodic table); Field extension; Algebraic number field; Extension (predicate logic); Quadratic field; Pure mathematics; Galois module; Ring (chemistry); Quadratic equation; Combinatorics; Discrete mathematics; Quadratic function; Geometry","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007576125,0.0001447383,0.0004476058,0.0002242903,0.00009620474,0.0000216698,0.0003220956,0.0001277484,0.004760997],"category_scores_gemma":[0.0006137635,0.0001202896,0.0001895954,0.0002458967,0.0001326226,0.0001124999,0.000007631971,0.0002711022,0.00005480704],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000494455,"about_ca_system_score_gemma":0.0004471095,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001109666,"about_ca_topic_score_gemma":0.001379076,"domain_scores_codex":[0.9985726,0.00006651971,0.0007792754,0.00007793542,0.0002365671,0.0002670631],"domain_scores_gemma":[0.9980119,0.0006819542,0.0003623405,0.0003399365,0.0001904134,0.0004134977],"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":[0.00003096471,0.0005266509,0.0004524283,0.0009048564,0.000526439,0.0003592816,0.0144253,0.0003533433,0.0002489103,0.9475137,0.02858604,0.006072055],"study_design_scores_gemma":[0.0003636385,0.0001326954,0.000229809,0.0003610424,0.00015019,0.0006512055,0.003043383,0.0001166498,0.0006178967,0.9932764,0.0008884083,0.0001686795],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9813633,0.0002569006,0.007077698,0.0004943689,0.0001835482,0.00009838847,0.00000842471,0.000007984951,0.01050936],"genre_scores_gemma":[0.982841,0.00001989007,0.01509093,0.0001737822,0.00009895209,8.859069e-7,5.853419e-7,0.00002493923,0.001749107],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04576267,"threshold_uncertainty_score":0.9961488,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03457677601842665,"score_gpt":0.2666650886711064,"score_spread":0.2320883126526797,"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."}}