{"id":"W1578268323","doi":"10.48550/arxiv.1104.1208","title":"Geometric interpretations of the symmetric product in affine differential geometry","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Control and Dynamics of Mobile Robots","field":"Engineering","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Product (mathematics); Holonomy; Interpretation (philosophy); Controllability; Geodesic; Affine transformation; Symmetric space; Invariant (physics); Manifold (fluid mechanics); Pure mathematics; Lie group; Differential geometry; Geometry; Mathematical analysis; Computer science; Mathematical 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007861115,0.0007690515,0.0004862913,0.002031915,0.001066472,0.002581491,0.0007323795,0.00071486,0.006327393],"category_scores_gemma":[0.001500193,0.0002760552,0.0006612568,0.001085881,0.004469277,0.004085163,0.001640698,0.001390602,0.0007232644],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001366582,"about_ca_system_score_gemma":0.0005724718,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001005336,"about_ca_topic_score_gemma":0.0004716478,"domain_scores_codex":[0.9992792,0.0001854937,0.00003610833,0.000162427,0.0002393233,0.0000974451],"domain_scores_gemma":[0.9993767,0.0001332765,0.0001089099,0.00007515813,0.0002049485,0.0001010931],"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":[0.000003005367,0.000002840254,0.00003769253,0.000006254834,0.000001316358,0.0000254636,0.00006393995,0.0004689022,0.0002389914,0.99771,0.000266098,0.00117546],"study_design_scores_gemma":[0.000004489389,0.00001648516,0.0001345376,0.000005356441,0.000002149276,0.0000780831,0.00005902494,0.003312389,0.0002698837,0.9915314,0.004579227,0.000006998386],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2638737,0.004586485,0.5304645,0.004026353,0.0009064822,0.00009961015,0.0007637824,0.0003661712,0.194913],"genre_scores_gemma":[0.9586128,0.001624122,0.02253869,0.0003984548,0.0008423604,0.00006516653,0.0003065583,0.0001205902,0.01549124],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006327393,"threshold_uncertainty_score":0.02116722,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02669898998301026,"score_gpt":0.152799071247833,"score_spread":0.1261000812648227,"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."}}