{"id":"W1988612745","doi":"10.5402/2012/983403","title":"A Review on Metric Symmetries Used in Geometry and Physics","year":2012,"lang":"en","type":"review","venue":"ISRN Geometry","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Windsor","funders":"","keywords":"Homothetic transformation; Sketch; Homogeneous space; Mathematical proof; Metric (unit); Conformal map; Focus (optics); Theoretical physics; Mathematics; Pure mathematics; Characterization (materials science); Geometry; Algebra over a field; Physics; Engineering; Algorithm; Optics","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":[0.0004479166,0.0009887575,0.001157015,0.003193213,0.0003812348,0.001211141,0.0008391104,0.0007371011,0.006694566],"category_scores_gemma":[0.001058017,0.0003526423,0.0004465347,0.00493657,0.0006153593,0.002489264,0.0006956354,0.001255198,0.003822498],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006562887,"about_ca_system_score_gemma":0.001300705,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009158725,"about_ca_topic_score_gemma":0.001262888,"domain_scores_codex":[0.999768,0.0000531383,0.00002821841,0.00004941644,0.00008323536,0.00001803971],"domain_scores_gemma":[0.9995184,0.0002415645,0.00005382994,0.00002462285,0.0001365229,0.00002502239],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0000545927,0.0000707088,0.0003855478,0.01972683,0.0001074567,0.0002202855,0.0002162117,0.000699351,0.003123723,0.0584536,0.1320897,0.7848518],"study_design_scores_gemma":[0.000003007508,0.0000326965,0.0005833065,0.002332088,0.00003776146,0.0005227634,0.00006345554,0.00008533634,0.0003715922,0.009292176,0.9866608,0.00001493151],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"review","genre_gemma":"review","genre_scores_codex":[0.0003333252,0.9917253,0.001108021,0.0005732588,0.0007924073,0.0000074094,0.00007013189,0.00001949743,0.005370514],"genre_scores_gemma":[0.001710233,0.9943985,0.000805651,0.0002909237,0.0007345707,0.00001097797,0.00008286115,0.000007560782,0.00195867],"genre_candidate":"review","genre_consensus":"review","teacher_disagreement_score":0.006694566,"threshold_uncertainty_score":0.02239549,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1089990986069122,"score_gpt":0.3661834817986418,"score_spread":0.2571843831917295,"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."}}