{"id":"W2952295140","doi":"10.48550/arxiv.math/0506625","title":"Nonabelian cohomology with coefficients in Lie groups","year":2005,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Surjective function; Mathematics; Bijection; Maximal torus; Group (periodic table); Lie group; Torus; Combinatorics; Pure mathematics; Supergroup; Physics; Lie algebra; Fundamental representation; Geometry","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":[0.0004324828,0.0005667871,0.000400467,0.001275347,0.001154387,0.001370097,0.0005409417,0.0004847745,0.004764624],"category_scores_gemma":[0.001158942,0.0002360428,0.0004033372,0.0007649857,0.002251686,0.003453725,0.001674629,0.001117541,0.000450747],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008821444,"about_ca_system_score_gemma":0.0003902544,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008770754,"about_ca_topic_score_gemma":0.0006755518,"domain_scores_codex":[0.9995703,0.00007257319,0.00001472444,0.00006921984,0.0001298188,0.0001434092],"domain_scores_gemma":[0.999408,0.00020317,0.0001159847,0.00004363933,0.00008014446,0.0001489455],"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":[0.00005183472,0.00004646882,0.001778082,0.0001026215,0.0000111501,0.0004622512,0.001475542,0.001407058,0.00642908,0.9805183,0.000554015,0.007163404],"study_design_scores_gemma":[0.0000358761,0.0000850606,0.003319144,0.00003233081,0.00001587623,0.0004880276,0.0008227442,0.008602004,0.007160741,0.9721772,0.007223742,0.0000372382],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9369153,0.0008205699,0.02159183,0.0007586498,0.0001480458,0.00002205052,0.00007576631,0.00009299548,0.03957471],"genre_scores_gemma":[0.9947916,0.0002720923,0.001548736,0.0000340257,0.0001057655,0.000009479009,0.00005850654,0.00001604304,0.003163682],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004764624,"threshold_uncertainty_score":0.01593924,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05222794534927134,"score_gpt":0.3186485396675346,"score_spread":0.2664205943182633,"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."}}