{"id":"W2951372199","doi":"10.48550/arxiv.math/0702196","title":"Shock waves for the Burgers equation and curvatures of diffeomorphism groups","year":2007,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Diffeomorphism; Shock (circulatory); Burgers' equation; Shock wave; Mathematics; Physics; Mathematical physics; Pure mathematics; Mathematical analysis; Mechanics; Partial differential equation; Medicine","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":[0.0004059767,0.0005495627,0.0002259655,0.001683295,0.0005110669,0.001024866,0.0003452343,0.0005281664,0.001965104],"category_scores_gemma":[0.002078082,0.0001818448,0.0003967289,0.0004606291,0.001725136,0.001684829,0.001610461,0.000775888,0.0002741359],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001032535,"about_ca_system_score_gemma":0.0003292826,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008155179,"about_ca_topic_score_gemma":0.0004077843,"domain_scores_codex":[0.9998548,0.00003662368,0.000008133735,0.00002690631,0.00004863927,0.00002489713],"domain_scores_gemma":[0.9992391,0.0001564274,0.0002977815,0.00005621142,0.0001097793,0.0001406803],"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":[0.00001796533,0.00001039811,0.0009650478,0.00002178749,0.000007404886,0.0001253659,0.0004007622,0.004965196,0.003100974,0.9843034,0.0005563427,0.005525428],"study_design_scores_gemma":[0.00001254354,0.00003467334,0.001924013,0.0000141491,0.000007968459,0.0001962336,0.0001785397,0.05252974,0.001331115,0.9399664,0.003785435,0.00001920121],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7095432,0.002260945,0.2567587,0.002024341,0.0002131277,0.00006879823,0.000180324,0.0002093639,0.02874109],"genre_scores_gemma":[0.9799836,0.0008430557,0.01164739,0.00009206312,0.000118512,0.0000382144,0.00009537984,0.00003552102,0.00714626],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.001965104,"threshold_uncertainty_score":0.007491589,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.130085470156475,"score_gpt":0.327008520839877,"score_spread":0.196923050683402,"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."}}