{"id":"W2962855835","doi":"10.1016/j.jalgebra.2014.07.039","title":"Growth of subalgebras and subideals in free Lie algebras","year":2014,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"Memorial University of Newfoundland","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Subalgebra; Finitely-generated abelian group; Lie algebra; Pure mathematics; Exponential growth; Algebra over a field; Discrete mathematics; Mathematical analysis","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":[],"consensus_categories":[],"category_scores_codex":[0.001881526,0.0001981282,0.0007930778,0.0008030083,0.00003205218,0.00002011393,0.0004551114,0.000187542,0.0002153655],"category_scores_gemma":[0.00469845,0.0001655528,0.0001578155,0.0006163368,0.0002048845,0.0002338956,0.0001349985,0.0003921242,0.00000689704],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000352506,"about_ca_system_score_gemma":0.00008118532,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004550841,"about_ca_topic_score_gemma":0.00003325146,"domain_scores_codex":[0.9977476,0.0002063618,0.001118679,0.00017282,0.0004111923,0.0003433174],"domain_scores_gemma":[0.9969352,0.001455145,0.0008619871,0.0003221905,0.0002503945,0.0001750809],"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":[0.00008891879,0.0003264989,0.04856304,0.0002696272,0.0001187252,0.00005955125,0.0006569018,7.065752e-7,0.0008952077,0.9322888,0.01174758,0.004984447],"study_design_scores_gemma":[0.001838934,0.0005019627,0.04157881,0.0001222104,0.00006675928,0.0003324207,0.0001682532,0.00001179816,0.003325156,0.9513831,0.0005030542,0.0001675547],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9926777,0.001397138,0.001891336,0.002085052,0.0003449131,0.00009836225,0.000003380788,0.00001289605,0.001489259],"genre_scores_gemma":[0.9910303,0.0002090939,0.008082421,0.0002112507,0.0002386425,0.000001385178,4.302589e-7,0.00002780913,0.0001987123],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01909428,"threshold_uncertainty_score":0.6751046,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01902909940044122,"score_gpt":0.2666728896899934,"score_spread":0.2476437902895521,"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."}}