{"id":"W2952431688","doi":"10.1007/s10455-019-09670-z","title":"Geodesic distance for right-invariant metrics on diffeomorphism groups: critical Sobolev exponents","year":2019,"lang":"en","type":"article","venue":"Annals of Global Analysis and Geometry","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","keywords":"Geodesic; Diffeomorphism; Sobolev space; Differential geometry; Manifold (fluid mechanics)","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0007673886,0.0002610018,0.0009813132,0.0002383788,0.00008803177,0.00006924084,0.0002464608,0.000153397,0.0002598808],"category_scores_gemma":[0.001142552,0.0001974003,0.0005610862,0.001676184,0.0001051455,0.0001058063,0.00008584549,0.0001048637,0.00001948713],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002169708,"about_ca_system_score_gemma":0.00001416593,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002599347,"about_ca_topic_score_gemma":0.0000181951,"domain_scores_codex":[0.9978766,0.00005444838,0.0006596975,0.0004470591,0.0005346968,0.0004275137],"domain_scores_gemma":[0.9972326,0.001517915,0.0002600123,0.0005087731,0.0002699922,0.0002107718],"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":[0.00007764481,0.0008680406,0.01659492,0.0004600731,0.001189854,0.000005871866,0.00001778151,0.0000110859,0.0000496084,0.9787328,0.0007403427,0.001252005],"study_design_scores_gemma":[0.0005920203,0.0004204172,0.04002482,0.0001276047,0.001495018,0.000002903908,0.00007045612,0.03340711,0.0002312112,0.9228003,0.0003782342,0.0004498707],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8223727,0.0004164652,0.1735576,0.0009804065,0.00009017724,0.0003062754,0.0006260045,0.00002545251,0.001624838],"genre_scores_gemma":[0.9952762,0.00009671307,0.003968199,0.000365065,0.00003850986,0.00001452023,0.00003104645,0.00001440573,0.0001954086],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1729034,"threshold_uncertainty_score":0.804975,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04836951932644877,"score_gpt":0.3505826955662876,"score_spread":0.3022131762398388,"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."}}