{"id":"W2033252115","doi":"10.1142/s0219887812500739","title":"GEOMETRIC INTERPRETATIONS OF THE SYMMETRIC PRODUCT IN AFFINE DIFFERENTIAL GEOMETRY AND APPLICATIONS","year":2012,"lang":"en","type":"article","venue":"International Journal of Geometric Methods in Modern Physics","topic":"Control and Dynamics of Mobile Robots","field":"Engineering","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Product (mathematics); Differential geometry; Affine transformation; Holonomy; Geodesic; Controllability; Manifold (fluid mechanics); Lie group; Interpretation (philosophy); Pure mathematics; Invariant (physics); Geometry; Computer science","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":[],"consensus_categories":[],"category_scores_codex":[0.001066993,0.0001674567,0.0003870087,0.003252253,0.00002083246,0.000031527,0.000593227,0.00006482346,0.00001251178],"category_scores_gemma":[0.0008428263,0.0001356279,0.0001562764,0.004630327,0.00005482761,0.0003579599,0.0001537839,0.0004626369,7.57466e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002019157,"about_ca_system_score_gemma":0.0000347897,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001649068,"about_ca_topic_score_gemma":0.000004431672,"domain_scores_codex":[0.9981799,0.0001299433,0.0008030132,0.0001297286,0.0005170943,0.0002403285],"domain_scores_gemma":[0.9981031,0.0009791926,0.0003371019,0.0002154842,0.0002892681,0.00007589875],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"observational","study_design_scores_codex":[0.00001976211,0.0003356767,0.04752586,0.00004521286,0.0001473672,9.586754e-7,0.0002070606,0.09418062,0.002866242,0.0009718723,0.00001020403,0.8536891],"study_design_scores_gemma":[0.003198375,0.00009073669,0.645126,0.0002375222,0.0001778306,0.0001152715,0.0001708966,0.3205503,0.007191769,0.02201581,0.0005617067,0.0005638279],"study_design_candidate":"design_other","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2237807,0.0045037,0.7702156,0.00004565735,0.0009341891,0.0001933256,0.00001442916,0.000009084046,0.0003033055],"genre_scores_gemma":[0.9666973,0.0005432466,0.03224497,0.00001308408,0.0004336256,0.00002262312,0.00000267817,0.00002214405,0.00002028098],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8531253,"threshold_uncertainty_score":0.5530746,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01440666761026969,"score_gpt":0.3075321182890215,"score_spread":0.2931254506787518,"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."}}