{"id":"W1994502794","doi":"10.1016/j.jalgebra.2005.04.001","title":"Implicit function theorem over free groups","year":2005,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":71,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"","keywords":"Mathematics; Implicit function theorem; Function (biology); Quadratic equation; Algebraic number; Parametrization (atmospheric modeling); Group (periodic table); Simple (philosophy); Algebraic function; Pure mathematics; Algebra over a field; Discrete mathematics; Mathematical analysis","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":[0.001554765,0.0009060148,0.001580207,0.002971349,0.002939472,0.004719048,0.001764998,0.00167274,0.008844767],"category_scores_gemma":[0.003389455,0.0006888226,0.0008679488,0.00244522,0.004424755,0.01719909,0.00303486,0.005376134,0.001138821],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001753212,"about_ca_system_score_gemma":0.0008213345,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001020521,"about_ca_topic_score_gemma":0.000995129,"domain_scores_codex":[0.99922,0.0001400816,0.00004325914,0.0001673059,0.000300678,0.0001287409],"domain_scores_gemma":[0.998395,0.0007681399,0.0001442124,0.0001900979,0.0003085537,0.0001939335],"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":[0.0000166448,0.00001199866,0.00009874213,0.00001710457,0.000004640199,0.00002781057,0.0001778827,0.00009607598,0.0001528077,0.996813,0.000521717,0.002061582],"study_design_scores_gemma":[0.00001463464,0.000007219754,0.00009636452,0.000006284355,0.000009273133,0.00008705826,0.00004745112,0.0005330527,0.0001609285,0.9953533,0.003677727,0.000006574765],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4063696,0.004053384,0.1969488,0.01144157,0.001613597,0.00008194701,0.000749519,0.0006229594,0.3781187],"genre_scores_gemma":[0.9164949,0.001871129,0.01665441,0.0007102817,0.00134749,0.00007991659,0.0004013991,0.0001768591,0.06226357],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008844767,"threshold_uncertainty_score":0.0295887,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0177166862500824,"score_gpt":0.2740049267148079,"score_spread":0.2562882404647255,"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."}}