{"id":"W3040950448","doi":"10.3842/sigma.2020.095","title":"Covariant vs Contravariant Methods in Differential Geometry","year":2020,"lang":"en","type":"article","venue":"Symmetry Integrability and Geometry Methods and Applications","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"","keywords":"Covariance and contravariance of vectors; Covariant transformation; Differential geometry; Curvature; Scalar (mathematics); Mathematics; Differential (mechanical device); Formalism (music); Scalar curvature; Geometry; Pure mathematics; Algebra over a field; Mathematical physics; Physics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.004682908,0.0004668013,0.001254274,0.000685938,0.0002776707,0.0002036199,0.0003902528,0.0003982462,0.0005257558],"category_scores_gemma":[0.005135155,0.00037734,0.0002528627,0.004646545,0.0003400268,0.0001927594,0.0002857219,0.0009789639,0.000009404337],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005388217,"about_ca_system_score_gemma":0.00005589635,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001598491,"about_ca_topic_score_gemma":0.00002137875,"domain_scores_codex":[0.9956439,0.001224439,0.001121166,0.001152291,0.000315143,0.0005430671],"domain_scores_gemma":[0.9937724,0.004501423,0.0003010595,0.0007103509,0.0001894949,0.000525273],"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":[0.0001095157,0.0006483771,0.007045711,0.0005099004,0.0002770735,0.000003580295,0.0005150898,0.000003038393,0.004123179,0.5242522,0.0002827336,0.4622295],"study_design_scores_gemma":[0.003560567,0.0006139483,0.05589633,0.0001155337,0.001141829,0.00006569761,0.00476621,0.01556625,0.005026573,0.8222486,0.08903135,0.001967038],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.03590396,0.001363134,0.9578546,0.002690543,0.0000871936,0.0008480544,0.00007307387,0.0001008214,0.001078579],"genre_scores_gemma":[0.3306341,0.0002891384,0.667873,0.000582883,0.0002060188,0.000233866,0.00002607031,0.00003358316,0.0001213599],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.4602625,"threshold_uncertainty_score":0.9998679,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05243670231634332,"score_gpt":0.3962536926391312,"score_spread":0.3438169903227879,"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."}}