{"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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0006384598,0.0001361405,0.0003215054,0.000310281,0.0000642981,0.00002727413,0.0003294063,0.0001186003,0.001913225],"category_scores_gemma":[0.0006360954,0.0001003901,0.0002126246,0.0003017917,0.00005341346,0.0002570424,0.00007075176,0.0003281771,0.00006675972],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006526417,"about_ca_system_score_gemma":0.00004469025,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002628205,"about_ca_topic_score_gemma":0.000006655501,"domain_scores_codex":[0.9986853,0.00005766717,0.0005653052,0.0001069579,0.0003374019,0.0002473509],"domain_scores_gemma":[0.9985761,0.0003830949,0.0005004525,0.000289352,0.0001326406,0.0001183519],"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":[0.0001194555,0.0002406649,0.001362243,0.00002133161,0.0001928337,0.00002279847,0.0003228023,0.000007579239,0.0008857193,0.8819705,0.09272838,0.02212576],"study_design_scores_gemma":[0.001342983,0.0003958827,0.0137495,0.0000218022,0.0001212112,0.00040778,0.0001881112,0.00002450414,0.0006073471,0.9643666,0.01863255,0.000141737],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9773696,0.0004409523,0.01373419,0.002132274,0.0005835642,0.0000681011,0.000002474959,0.00002969655,0.00563915],"genre_scores_gemma":[0.991791,0.00003416853,0.005309478,0.0006396534,0.001487333,9.545865e-7,4.388927e-7,0.00002237518,0.0007145983],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08239614,"threshold_uncertainty_score":0.9989992,"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."}}